zotero/storage/UDNRN72X/.zotero-ft-cache

CONTENTS XI
Tomonaga's covariant formulation of quantum field theory 267
Feynman's theory of positrons, and the space-time approach to quantum electrodynamics 274
Dyson and the equivalence of the radiation theories of Schwinger, Tomonaga, and Feynman 287
Feynman and Schwinger-cross-fertilization 294
9 Green's functions and the dynamical action principle 298 The Greening of quantum field theory 298 The first trip to Europe 304 Gauge invariance and vacuum polarization 307 The quantum action principle 315 Electrodynamic displacements of energy levels 328 Quantum field theory and condensed matter physics 329
10 The world according to Stem and Gerlach 337 The quantum theory of measurement 340 Angular momentum 355 Potential problems and quantum oscillators 360 'Is spin coherence like Humpty Dumpty?' 366
11 Custodian of quantum field theory 371 Phenomenological field theory 373 An excursion into dispersion relations 380 Spin, statistics, and the TCP theorem 381 Euclidean field theory 385 Schwinger terms 389 Gauge invariance and mass 394 Quantum gravity 399 Magnetic charge 403
12 Electroweak unification and foreshadowing of the standard model 411 A brief history of weak interactions 411 'The dynamical theory of K mesons' 415 'A theory of fundamental interactions' 418 Glashow's thesis (V - A and all that) 428 Non-Abelian gauge theory 433 Glashow, Weinberg, Salam, and 't Hooft 435 The standard model and its successes 438 Conclusions 442

XII CONTENTS
13 The Nobel Prize and the last years at Harvard 445 The Nobel Prize and its aftermath 445 The Nobel lecture and the new perspectives 449 Source theory 451 Weinberg and effective Lagrangians 473
14 Move to UCLA and continuing concerns 481 Reception of source theory at Harvard and UCLA 481 Strong~field electrodynamics revisited 489
The November revolution: the discovery of J/,jl 493
Renormalization group without renormalization group 496
Deep inelastic scattering and Schwinger's reaction to partons and quarks 500
Source theory and general relativity 507 Magnetic charge and dyons 514 Supersymmetry; the master and his disciples 519
15 Taking the road less traveled 528 Introduction 528 The Casimir effect 528 The Thomas-Fermi atom 538 Cold fusion 548 The Casimir effect and sonoluminescence 554 Conclusions 561
16 The diversions of a gentle genius 567 Confessions of a nature worshipper 567 'I will be a compc;,ser by the time I'm 30!' 571 Tennis, skiing, and swimming 573 A reader, a listener, and a cat lover 574 Traveling in style 576 A gourmet and his vineyard 583 The teacher and his disciples 590 Tributes to Tomonaga and Feynman 605 Celebration of his life 615
Appendices 627 A Julian Schwinger-list of publications 627 B Ph.D. Students of Julian Schwinger 639
Index of names 645
Index of subjects 655

1
A New York City childhood
Growing up
Julian Seymour Schwinger was born on 12 February 1918 ('just five score and nine years after the birthday of Abraham Lincoln'') in New York City into a middle class family. His father, Benjamin Schwinger, was born in the town of Nowy Saez in the foothills of the Carpathian Mountains in the part of Poland which throughout the nineteenth century remained under the rule of Austro- Hungarian Empire. Nowy Saez, then called Neusandez by the Austrians, became home for a small Jewish community brought there by Emperor Leopold II of Austria in an attempt to install them on land as farmers. The settlers eventually returned to their traditional professions and trades and moved into the town, which became recognized among members of the orthodox Jewry for its rabbinical dynasty established by Chaim Halberstam, also called by his numerous disciples Reb Chaim Sandzer.
Benjamin chose to emigrate and came to the United States of America by himself around 1880 as a very young man. Having to support himself prevented him from obtaining more than the most basic education. He attended schools only to learn English, but did not go to college. In New York City he became a very successful designer of women's apparel. Benjamin eventually acquired his own couturier business, which prospered as Julian was growing up. However, he lost it in the stock market crash of 1929, and his life became difficult; he began to work for various firms as a designer. Since he was a gifted designer of women's clothes, with an eye for lines and design, he became well known in the Seventh Avenue clothing trade. Although the family was no longer as affluent as before, still they were quite well off and lived a quiet and comfortable life.
Julian's mother Bella (called 'Belle' by everyone), was born in the Polish industrial city of Lodz; she came to New York City as an infant with her family. In the nineteenth century Lodz flourished as a commercial and financial center with a large concentration of textile manufacturers, where German, Polish, Jewish, and Russian cultures mixed and coexisted; it became one ofthe foremost intellectual and cultural centers of East European Jewry. Belle's family owned a prosperous clothing manufacturing business in Lodz. Her father, Solomon
,

2 CLIMBING THE MOUNTAIN
Rosenfeld, had been raised as an orthodox Jew, and he maintained this tradition in his household. He continued his career as a clothing manufacturer after he emigrated to the United States; he was also involved in the import business, and Julian recalled that he used to import toys from Nuremberg.2
At the time of his birth, Julian Schwinger's parents lived on the West Side, 141st Street on Riverside Drive, but some years after he was born they moved to a larger and newer apartment on 103rd Street, still on Riverside Drive. Their first child, a son named Harold, had been born in 1911 when they lived in a well-to-do Jewish neighborhood in Harlem, preceding Julian by seven years. Belle's parents rented an apartment next to their daughter's; following the old tradition the two families lived side by side and Belle was quite dependent on her mother.2
Benjamin's work and family were his life. He worked very hard and spent less time with his children than did his wife. Belle became the disciplinarian of the family; she nurtured Harold and Julian's artistic talents and got them to partake of the great cultural riches of New York City. On the other hand, having been raised as a princess, she was not very maternal toward her son.' Julian always remembered running over to his maternal grandparents' house and cherished 'distinct olfactory memories of foods prepared in the old Polish style:2 There were marvellous breads, soups, and other things, and Julian was left with an abiding taste for Middle European cuisine. The maternal grandparents showered a lot of affection on Harold and Julian, and the two boys were quite 'spoilt' with the attention they received.
Belle had a younger sister and a brother. Her sister had children of her own, and Julian had interactions with them. The brother, Al Rosenfeld, was a successful businessman; he dealt tn perfumes and took many trips to Europe, and made a great impression on Julian with his stories about travels to the faraway world. None of the family had any interest in science or other intellectual pursuits, and when Julian became seriously interested in physics 'they tolerated me, but had no understanding of what it was about:2
Julian did not remember any time in his life, even in his earliest memories, when he could not read or write. His parents employed a German nursemaid, Hedwig, as well as a Hungarian maidservant. Hedwig would take Julian to a movie house every Saturday, and at the age of three the boy amazed her by reading the marquee from a long distance and telling her what it said.
There occurred a couple of episodes in Julian's early life that attracted his attention towards scientific and technical things. One was a total eclipse of the Sun (which took place on 24 January 1925). 'I have a distinct memory ofputting my head out of the window and staring with awe at this phenomenon. Then I equally well remember-as we know, the United States received reparations from Germany after World War I-and one of them was a dirigible called

A NEW YORK CITY CHILDHOOD 3
Shenandoah that flew over New York. It must have come from Dresden airport, one of the early transatlantic flights, and again I remember looking out of the window at this incredible thing flying over. The Shenandoah arrived in 1923which would have made me five years old, practically an adult!'2
As a little boy, Julian attended a kindergarten. He recalled one incident when he played hooky. The whole class was taken on an outing and they all went to wherever it was, a few blocks from his house. At one point he decided that he had had enough of that, so he 'gradually faded away' and went home. 'It's the only memory l have of kindergarten.'2
As they grew up, Harold and Julian shared a large room at home, and attended a public school, P.S. 186 on 145th Street between Broadway and Amsterdam Avenue, five blocks away from their home. At school Julian was interested in everything, and was a quick learner. Even though he was advanced to a higher grade several times, he was not considered nearly as bright as his older brother. At the elementary school, Harold won all the recognition and all the prizes came his way, but still his teachers complained that he was not living up to his potential. Julian followed in his brilliant brother's footsteps. In their mother's eyes, Harold was always the successful one. 'She always thought Julian was a kind of a failure.* His brother became a lawyer and Jewish mothers always want their sons to be lawyers, and Julian didn't. Someone said to her, after the Nobel Prize, "You must be very proud ofJulian!" "Well, ...." '5
From the elementary school Julian remembered an incident when the teacher was trying to explain why the Moon always presents the same face to us. 'As she was describing all this I remember sitting at my desk and looking up at her and following what she was saying by moving my fingers. That was the Earth and that was the Moon and she saw what I was doing and nodded, "yes, yes, that's it!"2 This happened when Julian was perhaps in the second grade. 'It was very early and I was obviously very eager to learn.'2
It was very helpful to have a brother who was several years older. Harold of course went to high school and college, but his textbooks were always lying around, and Julian began to read them. Two things became very important: 'One was that college level books were available to me at an early age; second, the family had somehow acquired a set of Encyclopaedia Britannica, in which I read the scientific articles from cover to cover. My family had acquired it for Harold; it was very valuable to have an older brother! Of course, for a boy of ten he wouldn't have had much of an interest in a three-year old, but my memories of interacting with him come from much later when I was sent to a summer
• Sidney Borowitz recalled an encounter between his wife and Julian's mother at a restaurant years later. Belle was disparaging ofJulian's accomplishments compared with those of Harold, who also had provided her with a grandchild.4

4 CLIMBING THE MOUNTAIN
camp where he was counselor. [In the camp, Julian spent most ofhis time sitting on his bunk and devouring books. Harold had literally to drag him away from the books to the lake where he managed to teach him how to swim.*] The camp was in the Adirondacks, and that must have been when I was ten or eleven, that's a later stage:2
Julian was not without interest or ability in athletics. He recalled the visit of a famous tennis pro to summer camp. 'Bill Tilden came through [this summer camp] on some lake in northern New Hampshire. He gave a demonstration and of course all the campers were there. It was a big tennis court and they were all distributed around. Tilden was playing with somebody and then a ball went astray and I reached up and caught it and threw it to Tilden. He looked at me and said, "You have a great future ahead of you." I've always interpreted that to mean in tennis.... I was also pretty good in baseball.'2
Julian was certainly precocious. 'That's an objective fact, because I ran very rapidly through the elementary school, skipping classes and all sorts of things. I don't think anybody directed my attention to scientific and technical things; it was somehow in the genes. There was no doubt that I was bright, and particularly overspecialized even then. I would pick up my brother's mathematics books, perhaps the calculus. I certainly remember the calculus book; I remember once when I was lying in bed reading his book and he was doing something else, and I turned to him and asked, "What does osculating mean?" I did not know what osculating meant. Osculating, as one knows well, means kissing. Funny thing to remember! I was reading a fairly innocuous book on mathematics, not a lurid novel, and I asked my brother about this word when it occurred in the book.'2
After elementary school, Julian attended a junior high school in Upper Manhattan, near Broadway and 180th Street, some 40 blocks from home, and he had to use the s~bway. Then, very soon, he enrolled in Townsend Harris High School, from where he would graduate in 1933.
In 1848 New York's Board of Education had decided to establish the city's first municipal institution of free higher education, the New York Free Academy, which, in due course, became the City College ofNew York. It had a preparatory component known as the 'introductory' year which later separated and grew into Townsend Harris High School. It was named after Townsend Harris, the president ofthe Board of Education at the time ofinception ofthe Free Academy, and was located on the campus of the City College on Amsterdam Avenue at 136th Street. It flourished until 1942 when it was closed as being 'inessential' by New York Mayor Fiorello La Guardia.
• In fact, on one occasion his father visited the camp and found Julian reading in his bunk, so Benjamin grabbed him and threw him in the lake.3

A NEW YORK CITY CHILDHOOD 5
Julian did not recall having been inspired by any of his teachers until he went to Townsend Harris. 'Before that I was simply enduring it. My education came from myself rather than from my teachers. Townsend Harris High School was exceptional. In 1929, there occurred the crash of the stock market and the Depression began. My family suddenly became poor. Of course, they wanted to send me to college. Why my father's business should have been wiped out by the Depression, that I never understood. However, they no longer felt that they could send me to Columbia University. That was the logic for my attending Townsend Harris: there was no tuition to be paid there; it was one of the regular high schools, but it was specifically oriented towards City College.'2 Besides, Harold had also attended Townsend Harris.
During the Depression, the City College was an outstanding institution. Admission was highly selective, yet for most of these bright students, attendance at one of the tuition-free colleges of the City of New York was their only opportunity of obtaining a college education. Moreover, with the economic crisis, talented people who, for example, were working for their doctorates at places like Columbia or New York University, simply had to earn money by taking teaching jobs in schools, and this was typical of teachers at Townsend Harris High School. They were a very unusual set of teachers, people who were active researchers at the same time, and that was just wonderful for the young Julian Schwinger. 'I did not have much interaction with my fellow students, but I was interested in the teachers. I was fascinated by courses in physics, much less so in chemistry. I imposed myself outrageously on one of my teachers, Irving Lowen, who was doing research for his doctorate at New York University. [He later taught at NYU.] Already then I was at a level when Lowen said, "Look, instead of talking to me, why don't you go to see my professor at the University?" In a sense I had begun to do research, though not so much at Townsend Harris as at the City College, but the connection had been made at Townsend Harris. Some of these teachers of mine, who were graduate students at various universities, and not my fellow students, became my friends.' 2
Bernard Feld recalled a legend told at City College, of how Lowen discovered Julian. 'Irving came across this kid sitting in the library reading the Physical Review and he looked.over his shoulder and there was this kid reading Dirac and so Irv thought, well, here's another of these smart aleck kids that, you know, we get them every once in a while, so he quiz7ed him about what he was reading and Julian allegedly was not only capable of telling him what he was reading but also told him what needed to be done to complete what Dirac hadn't completed in this particular paper.'6
Lowen was a good teacher of physics. He explained to his pupils all about the Bohr theory of the atom and Julian would go to him afterwards and ask about quantum mechanics. 'That was an exciting period. I found books in

6 CLIMBING THE MOUNTAIN
the public library. Beginning with the local libraries, which I exhausted very quickly, I went to the New York Public Library at 42nd Street, where everything was available, including periodicals. The announcement of the Nobel Prize in Physics in 1933 to Heisenberg [for 1932] and Dirac and Schrodinger caught my fancy. There were articles in the newspapers referring to this mysterious quantum mechanics. I went through the popular books, which, of course, I left in disgust, but there was a book by [James] Jeans,7 in which I found murky references to strange things going on inside atoms as compared to macroscopic physics. But Jeans' attempt at popularization left me completely frustrated, so I kept going. That's when I began hunting for books on quantum mechanics:2
Julian used to receive a small allowance from his parents, which he would use for subway fares and buying books. Sometimes he wouldn't have enough money left to get back home. 'Subway fare must have been five cents. And I remember I once had four pennies, not five.' 2 Being almost a child he began to cry and someone stopped to inquire what the matter was, and said, 'Here's a nickel; which brought Julian home.2
As he recalled, 'there was something else I was preoccupied with: electrical engineering. Gadgets. I would read all about radios and some of the underlying theories about inductances, capacitances, and so forth, until I gradually realized that I didn't really care about that very much. Somewhere I encountered a mysterious set of equations .invented by Maxwell, and that's where I had to go.'2
With the help of sharp razors and glue Julian put together very beautiful toy airplanes. 'I wasn't impractical, but I did not build radios. Actually I did build things, but they were not radios; they were model airplanes. I had models of all the fighter planes of World War I, in particular those of the famous Red Baron [Baron von Richthofen], who flew a triplane. I did play with electrical things, but I don't know why I didn't play with radios. I do remember that I used to do things like putting wi'res into sockets and making sparks; I'm surprised I'm still alive!' 2
Julian encountered P.A. M. Dirac's classic book on The principles ofquantum mechanics in 1931, a year after its first publication.~ He was 13 years old. He also read George Birtwistle's Tl1e quantum theory of the atom, which had been published in 1926, and of which Julian bought a second-hand copy at Barnes and Noble, the used book shop on lower Fifth Avenue.9 Birtwistle's book summarized all the recent papers on quantum mechanics, and it gave a sequential development of all the recent work on the subject; Julian found it exciting and provocative. Julian became a prolific reader and books became his world. He was not much interested in activities typical of boys of his own age. This is not to say that he was uninterested, for example, in sports. As David Saxon recounted many years later, referring to the war years at the MIT Radiation Lab, 'I discovered to my astonishment that he was interested in sports. We'd have

A NEW YORK CITY CHILDHOOD 7
a picnic and he'd throw a left-handed football very well. That was part of the reason he came [to UCLA in 1971]; he wanted to play tennis, ski, and swim. He had the kind of normal athletic interests that any young kid would have. He had a quiet background interest that would not be revealed except under the right circumstances.'5
When Irving Lowen told Julian about going to meet his professor at New York University, he did indeed do so. The physics professor was Otto Halpern. A year and a half later, Halpern and Schwinger published a paper together in the Physical Review, but that happened only after Julian had enrolled in the City College after graduating from Townsend Harris High School. He did perfectly well in his grades, and his family had nothing to worry about. His brother Harold (who had received a bachelor's degree in business from City College in 1931, and a master's degree from Columbia a year later) got a law degree from Fordham University in 1936. After taking his degree, Harold held two jobs simultaneously-he worked as a law clerk during the day for $10 a week, so he had to make ends meet by working at night in a bank.3
Going to college
In the fall of 1933 Julian Schwinger became a student at the City College of New York (CCNY). He started as a sophomore and first took the normal run of general core courses. Quite soon at the City College Julian came into contact with Hyman Goldsmith, who later became one of the founders of the Bulletin ofAtomic Scientists. At that time, Goldsmith was 'in the category of permanent graduate students, somewhat dilettantish, with a great interest in music, which was a very important sideline for me. Goldsmith did wonderful things for me by bringing me into a musical environment. He did one terrible thing for me because he was interested in tennis. I had been interested in tennis when I was quite young and then I stopped being athletic. He said, "Oh, I want to play tennis. Want to come along?" I said okay. They were hitting the ball and I said, "Can I try that?" So I picked up a racket and he hit a ball to me and I was totally awkward because I hadn't touched a tennis racket in five or six years. So I just put the racket out and the ball went straight up in the air. He walked over, took the tennis racket away from me, and said, "That's all." And I was just mad as hell because with a little bit of practice I could have shown my inherent tennis ability, which does exist. I do think I'm quite good at tennis. Sometime in the 1950s he died in a foolish accident by drowning. He loomed very large as an influence on me.'2 Goldsmith and Schwinger published four joint papers after Julian went to Columbia University.
Townsend Harris provided automatic entry into the City College. Thus far Julian had been a solitary type of person, but 'at City College I began to meet

8 CLIMBING THE MOUNTAIN
people, especially the students, who were at my level, and that was a novelty. I met Joseph Weinberg and Morton Hamermesh. There was an incredible number of good people. There was Robert Hofstadter; he went to Stanford and won the Nobel Prize for scattering electrons off nuclei and determining the form factor of the proton. For the first time I ran into people, not exactly my contemporaries, because I was still the youngest one around, but people who were teaching themselves and were aware of the developments. Not so much in physics as in mathematics, but that was much easier to come by. Certainly Hamermesh, with his interest in mathematics and chess, was one. They were a little closer to my own age but not at the same level. Joseph Weinberg was the person I talked to the most:2
Weinberg vividly recalled their first meeting. Because of his outstanding laboratory reports, he had been granted the privilege of entering the closed library stacks at City College. One day he was seeking a mathematics book (Townsend's book on real variables 10 ) which had been mentioned at the Math Club the day before, and while he reached for it, another youngster was trying to get it. They had both heard the talk, on functions which are continuous but nowhere differentiable, so they shared the book between them, balancing the heavy volume on one knee each. The other fellow kept finishing reading the page before Weinberg, who was a very fast reader. Of course, his impatient co-reader was Julian Schwinger. Both were I5. Weinberg mentioned that he usually spent his time, not in the mathematics section of the library, but in the physics section, which turned out to be Julian's base as well. Weinberg recalled that Dirac's book on quantum mechanics' was very interesting and exciting, but difficult to follow. Julian concurred, and said it was because it was polished too highly; he said that Dirac's original papers were much more accessible. Weinberg had never conceived of consulting the original literature, so this opened a door for him. 11
Later on in 1937 Schwinger and Weinberg attended the Summer School together at the University ofMichigan in Ann Arbor. 'When I went to Columbia, Weinberg and I lost contact, but somehow got together again to go to Michigan. Later on, when I arrived in Berkeley to work with Robert Oppenheimer, he (Weinberg) was already there as a student. He got his degree from Oppenheimer in 1942. His thesis is still occasionally referred to as an early attempt [to formulate] certain aspects offield theory.'2 Weinberg ended up with an endowed professorial chair at Syracuse University.
At the City College, Julian took the normal run of courses on general education subjects. At Townsend Harris he had studied French and German. He dropped the German when he went to City College and concentrated rather heavily on French. He later found it useful in France, but not otherwise. 'It is the one foreign language that I can speak fairly fluently. I learned American

A NEW YORK CITY CHILDHOOD 9
history a great deal. I had the standard liberal arts education. I joined the City College as a sophomore, and there were requirements which, of course, I went through.* But I was beginning to become more and more reluctant to spend time on things other than physics. And so I took physics courses; I had to take elementary physics and felt very uncomfortable. I was bored. I'm afraid I occasionally got uppity. I remember there was one lecturer who did not belong to the special class of people I knew. He was telling us about heat and asked, "Does anybody know about what happens to the spectrum when you change the temperature?" So I raised my hand and said, "The Planck distribution is such and such," and he stared at me and said, "Sit down. I don't want to hear about that!" I think I was occasionally brash. The teacher was put off by my remark. At least he did not think there was anyone in the class to bring up such topics. He may not have known it himself; it was not common knowledge at that time. I look back at these things with horror!'2
Edward Gerjuoy was one of Julian's classmates at City College. 'My main claim to fame is that Julian and I took the same course in mechanics together, taught by a man named Shea, and I got an A and Julian a B,' because Julian did not do the work. 'It took about a week before the people in the class realized we were dealing with somebody of a different order of magnitude.' At a time when knowledge of a bit ofvector algebra was considered commendable, 'Julian could make integrals vanish-he was very, very impressive. The only person in the classroom who didn't understand this about Julian was the instructor himself 'He was flunking out of City College in everything except math and physics. He was a phenomenon. He didn't lead the conventional life ofa high school student before he came to City College'-unlike Gerjuoy and Sidney Borowitz he was not on the math team in high school so they had not known him earlier-'when he appeared he was just a phenomenon.' 12
Morton Hamermesh recalled another disastrous course. 'We were in a class called Modern Geometry. It was taught by an old dodderer named Fredrick B. Reynolds. He was head of the math department. He really knew absolutely nothing. It was amazing. But he taught this course on Modern Geometry. It was a course in projective geometry from a miserable book by a man named Graustein from Prince~on, and Julian was in the class, but it was very strange
• City College had an enormous number of required courses. Among them were two years of gvmnasium. One had to pass exams in hurdling, chinning, parallel bars, and swimming. Because Weinberg and Julian had nearby lockers, they often fell into physics conversations half dressed, and failed the class for lack of attendance. Weinberg remembered seeing Julian's hurdling exam. Julian ran up to the bar, but came to a standstill when he was supposed to jump over sideways. The instructor reprimanded him, at which point Julian said, sotto voce, 'there's not enough time to solve the equations of motion.' 11

10 CLIMBING THE MOUNTMN
because he obviously never could get to class, at least not very often, and he didn't own the book. That was clear. And every once in a while, he'd grab me before class and ask me to show him my copy of this book and he would skim through it fast and see what was going on. And this fellow Reynolds, although he was a dodderer, was a very mean character.* He used to send people up to the board to do a problem and he was always sending Julian to the board to do problems because he knew he'd never seen the course and Julian would get up at the board, and-of course, projective geometry is a very strange subject. The problems are trivial if you think about them pictorially, but Julian never would do them this way. He would insist on doing them algebraically and so he'd get up at the board at the beginning of the hour and he'd work through the whole hour and he'd finish the thing and by that time the course was over and anyway, Reynolds didn't understand the proof, and that would end it for the day.'l 4 Sidney Borowitz, another classmate of Julian's, recalled that 'we had the pleasure of seeing Julian attack a problem de nova, and this used to drive Reynolds crazy:4
Julian also took advanced courses in mathematics. There was one course in group theory. 'However, I have no memory of City College. I can't quite separate what was at City College and what was at Columbia University. But, of course, I was interested in mathematics.' Julian was at the City College for only about one year or so, and then he transferred to Columbia in I935. By the time Julian went through the City College, he knew quantum mechanics quite well at the advanced level. He particularly cherished Dirac's classic book. 'No doubt it was my bible. I have distinct memories of Joe Weinberg and me talking about the book of Dirac, which we both recognized as the only thing to be considered. Of course, I had access to Birtwistle's book, which I studied at the same time as Dirac's book. I also knew the book of Pauling and \Vilson.15 I also read Hermann Weyl's bodk on Group theory and quantum mechanics,16 the English translation of which came later; it had a tremendous effect on me. I think I took group theory at Columbia. But by then I was so much imbued with Dirac's book that I did not need group theory. I thought that the mathematical niceties of group theory were quite unnecessary. Quantum mechanics had the idea of symmetry built in it and if I needed symmetry ideas in quantum mechanics I would use quantum-mechanical language, not this entirely separate knowledge of group theory, which, of course, is a very old-fashioned idea. I've felt that way all through my life. If you want a branch of mathematics, you develop it in the physical context, not as something separate, which you then try to apply, rather than integrating it from the beginning. That's part of my philosophy.'2
• In addition, he was also apparently a notorious anti-Semite. He used to discourage Jewish students from studying mathematics, which worked to the advantage of physics. 13

A NEW YORK CITY CHILDHOOD 11
Eventually Joe Weinberg persuaded Julian to join the Math Club. His inaugural talk was on the quantum-mechanical harmonic oscillator in Dirac's operator representation, showing that you only needed to compute the ground state, and everything else could be constructed by use of raising and lowering operators. The mathematicians in the audience did not receive this presentation very well, because they were not concerned about getting 'pregnant formalisms.' We see that Julian was already anticipating his insightful work on angular momentum as an adolescent. Later, Weinberg was studying the anomalous Zeeman effect, which was treated in the first edition of Dirac's book,8 and suspected that what underlay Dirac's treatment was the presence of a Lie group. Weinberg discussed this with Julian, and neither recognized the group-it turned out to be SP(2, R). They discussed the nature of the group and realized that it could be represented by two harmonic oscillators-which was the basis of Julian's monumental paper on angular momentum many years later [69] .11 •*
The Julian Schwinger archive at the University of California, Los Angeles, contains a small notebook dating from the City College days, probably 1935.17 About half the pages are filled with notes from mathematics courses that Julian was taking there on group theory and complex variables. But interspersed with that are citations to important contemporary papers, along with a detailed, remarkably mature, working out of those papers in his own hand. This document, and other similar notebooks, is extremely revealing regarding the process by which Julian taught himself what was going on in current research. The papers he worked out included Pauli and Weisskopf's 1934 paper on the quantization of the scalar relativistic wave equation [spin and statistics],18 the 1929 paper of Heisenberg and Pauli on quantum electrodynamics,19 Heisenberg's 1934 paper on fluctuations in electric charge,20 Bethe's paper on neutron phase shifts,21 two papers by Dirac from 1929 and 1933,22 and several others.
At the City College Julian met and became friends with Lloyd Motz, who was a part-time instructor there. This encounter had a strong impact on Schwinger's future career, since it was Motz who introduced him to Columbia University. Motz was about ten years older than Schwinger. Beginning in 1926 he attended City College and excelled in his studies so consistently that on the basis of his grades he was judged the top sophomore. Each year the sophomore with the highest grades was awarded the Naunberg fellowship to spend a year in any foreign university, which was uncommon and something ofa high honor at that time. Motz studied physics but was also seriously interested in mathematics; therefore he chose to go to Gottingen, where he spent the entire academic year 1928-1929 and had a very exciting time taking courses from Max Born, Walter Heider, and Robert Wichard Pohl, among others. Upon his graduation from
• Square brackets [ ] signify the references to Schwinger's papers in Appendix A.

12 CLIMBING THE MOUNTAIN
City College in 1930, Motz was accepted as a graduate student at Columbia University. At first he did not work directly under Isidor Isaac Rabi, but took a course in statistical mechanics from him; he earned a good reputation, received Rabi's attention and eventually a $1,500 Columbia fellowship.
Motz heard about Julian from his older brother. 'I became very friendly with Harold Schwinger at that time. [Harold and Lloyd Motz were classmates at the City College.] He came to me one day (in 1930 or 1931) and said, "Lloyd, I have a brother who I think is a genius, but we don't know." And later Hyman Goldsmith, whom I knew very well, was talking about a young kid at Townsend Harris and said, "This kid is mcredible; he knows so much!" So he introduced me to him and that's when I first met Julian. It must have been around 1933. At first, I didn't do much with him, but Julian was the sort of youngster who wanted to have intimate relationships with professors. He wanted to be invited to things but he would never ask. You had to invite him, then he would respond. His response was always very warm; he was a very warm, loving young man.'n
Schwinger never took a course taught by Motz, but he did meet him at the City College. 'I suppose I had become a sort oflocal celebrity. There's a strange mixture in my makeup. I'm by nature very shy, and yet in these matters I'll press forward. If I have something to say I'll say it, and so it became known that this kid knew a lot. Rather than a "celebrity;' more like a "peculiar chap." I did go to classes where many of these people came, and just as I mentioned the Planck distribution, which was totally gratuitous, but I couldn't help myself, I knew it so why shouldn't I say it? [he made himself known]. Now Lloyd Motz and I got to know each other at the City College, and just the same thing happened with Hyman Goldsmith and Irving Lowen. These were people with contacts at Columbia and New York University, and I followed both avenues.'2
Schwinger began working with Motz in 1934, when the latter was already a University Fellow. He became a frequent visitor to Motz's eighth-floor office at Columbia. Motz was surprised by the 16-year-old Schwinger's scientific skills. 'We would come into my office and he would start working and before I knew it he was so far ahead of me, so quick, that I could not always follow what he was doing. Absolutely right though all the time!'23
This was Schwinger's first real research calculation in physics; it was related to a just published article by Bethe and Heitler24 on the stopping of fast charged particles by the emission of radiation under the influence of the electric field of a nucleus, and it had obvious implications for cosmic-ray physics. Bethe and Heider had calculated the energy loss of a charged particle by the emission of radiation caused by the braking of the particle's acceleration by the electromagnetic field, the famous Bremsstrahlung effect; they had also used the Born approximation to compute the consequences of a similar effect due to electron-antielectron pair creation. After reading this article, Julian suggested to Motz that they consider an additional effect: the interaction of electrons

A NEW YORK CITY CHILDHOOD 13
back on the field. They worked on it and thought that they had a beautiful theory until Motz submitted the calculation to Hans Bethe, who dismissed it by pointing out that the interaction operator which Motz and Schwinger had used was non-Hermitian and thus unphysical.23 Schwinger, the perfectionist, was extremely upset and crestfallen because it was he who had talked Motz into using that operator, despite his older colleague's earlier objections which had been basically in line with Bethe's later criticism.
Paper Number Zero
By the end ofhis short stay at the City College, Julian had learned and well understood most of the current attempts to expand the scope of quantum mechanics to field theory. He had started by reading and following papers in the Physical Review, such as the article by Wendell Furry and J. Robert Oppenheimer25 in which they had eliminated the infinite Dirac sea of electrons in which the emptiness rather than the fullness ofa state of negative kinetic energy is regarded as being equivalent to the presence of a particle. Soon Schwinger's reading of original papers expanded to include everything that was available in English, German, or French. In particular, he read N. F. Mott's articles on electron scattering, including his 1930 paper entitled 'The Collision Behveen Two Electrons''" on the Coulomb interactions behveen two similar, thus indistinguishable, particles. Contrary to the scattering of different particles, this problem required using symmetrized or antisymmetrized wavefunctions, depending on whether the particles obeyed Bose or Fermi statistics. In 1930 one could not be sure of the implications of such a procedure, even whether the so-called leading-order differential cross-sections would reproduce the classical Rutherford formula as is the case for different particles. At the same time, Julian studied a paper by Christian M0ller,27 in which he had calculated the hvo-particle scattering crosssection by using a retarded interaction potential. Of course, Schwinger read all of Dirac's papers on quantum field theory, and was particularly impressed by the one on 'Relativistic Quantum Mechanics,'28 'in which Dirac went through his attempt to recreate an electrodynamics in which the particles and light were treated differently. [It was] a paper in 1932, in which the electromagnetic field was not described by an energy but was simply an operator function of time.'2 In a paper of Dirac, V. A. Fock, and B. Podolsky, 29 'it was recognized that this was simply a unitary transformation of the Heisenberg-Pauli theory19 in which the unitary transformation was applied to the electromagnetic field. And I said to myself, "\Vhy don't we apply a similar unitary transformation to the secondquantized electron field?" I did that and worked out the lowest approximation to the scattering amplitudes in unrelativistic notation. It was a relativistic theory but it;.vas not covariant. That was in 1934, and I would use it later; [the notion,

14 CLIMBING THE MOUNTAIN

called the 'interaction representation'] is always ascribed to Tomonaga, but I had done it much earlier.'2
Thus before he left the City College, Schwinger did write his paper 'On the Interaction of Several Electrons' [O], in which he introduced a procedure which he would later call the interaction representation to describe the scattering of spin-½ Dirac particles, electron-electron scattering, or M0ller scattering.* 'Furry and Oppenheimer had written their paper on multiparticle interactions using a local potential and second quantization.25 And I thought to myself that relativistic interactions are not local; they are functions of momenta and so on as in the M0ller interaction. So I asked myself whether I could develop a second quantized theory which would allow for non-local interactions, which is an essential aspect of a relativistic theory.'2
The original typescript ofthis unpublished paper is in the Schwinger archive at UCLA. 17 The flavor of this short six-page note is caught in its second paragraph: 'It is the fundamental assumption of all field theories that two particles do not interact directly but, rather, the interaction is explained as being caused by one of the particles influencing the field in its vicinity, which influence spreads until it reaches the second particle. Hence we may express the Hamiltonian of our system of particles in terms of the Hamiltonians of the several particles in interaction with the field. The well-known expression for the Hamiltonian is then
L af(plH + Ulq)aq,
pq

where

H =ca• p + f3mc2

(1.2)

and

U = -e(</> - a• A).'

(1.3)

Here aq and a; are annihilation and creation operators for electrons in the
states q and p, respectively. The scalar and vector electromagnetic potentials are
given by</> and A, respectively, while f3 and a are the usual Dirac matrices, for a spin-½ charged particle of mass m and charge e, c being the speed of light.

* Sometime earlier, perhaps, Julian had helped Weinberg calculate the Klein-Nishina formula for Compton scattering, for which there was no clue in Heitler's book. Weinberg's calculation had 'fallen apart,' and he asked Julian to have a look at it. Julian calculated it correctly, in which 'he ran through spin sum after spin sum, and got them all right; and detected the simple error in Weinberg's calculation. 11

A NEW YORK CITY CHILDHOOD 15

The key point occurred on the second page, when Schwinger transformed the

unperturbed Hamiltonian away, by the unitary transformation

IV= e-(i//1)//oti/J,

L Ho= af(PIHlq)aq,
pq

thereby leaving the theory in the 'interaction representation: Then, by 'successive approximations,' i.e. a perturbative expansion, Schwinger obtained, quite straightforwardly, the Schrodinger equation (back in the Schrodinger picture)

(1.5)

where the second term in the braces involves 'M0ller's expression for the matrix element of the interaction between two electrons,'

(1.6)
The notation is standard: the us are the momentum-space wavefunctions for the electrons, and p and E stand for the electron's momentum and energy in the various states. Vis the infinite volume of space, a normalizing factor.
In deriving this result, Schwinger had to omit a term which 'represents the infinite self-energy of the charges and must be discarded.' This he eventually came to see as a mistake: 'The last injunction merely parrots the wisdom of my elders, to be later rejected, that the theory was fatally flawed, as witnessed by such infinite terms, which at best, had to be discarded, or subtracted. Thus, the "subtraction physics" of the 1930s.' [197]
This particular paper, which Schwinger did not publish, was important for his later work because this was the starting point of his work on covariant perturbation theory. 'Although it took me a while to recognize it, it was part of my makeup already. This was worked out at the City College. I wrote it as a paper, but why I did not send it for publication I don't know. At that time I had no idea what a publishable paper was; I was still pretty young [Julian was then 16 years old].'2 He did rtot even ask Lloyd Motz what to do with his paper on the interaction representation. 'I was rather secretive about it,' he recalled. 'It was written for myself, a little practice in writmg.'2
First publications
While working on his secret paper, Julian was also engaged upon other research that led to two publications in Letters to the Editor of the Physical Review. Both articles were co-authored with experienced physicists who had suggested the

16 CLIMBING THE MOUNTAIN
topic of research and offered advice, but the actual calculations were done by Julian alone.
The first ofthese letters, 'On the polarization of electrons by double scattering' [I], was co-authored with Otto Halpern and dated 6 June 1935. Schwinger was then 17, but the paper contained results of earlier work, and was finished as early as 1934, while he was still a student at the City College.
Julian's first collaboration with Halpern was not successful. 'Bethe had written a paper on the stopping power ofa neutrino if it had a small magnetic moment. I don't think Halpern was aware of that paper. I was. But he brought up the same question. "If the neutrino had a small magnetic moment, how would you calculate something, like the scattering properties?" So I did [the calculation]. And he said, "Oh, that's nice, we must write a paper." And then I think I said, "Oh, but you know Bethe has already written a paper on this subject." I took for granted that Halpern would have known about the paper. I was learning that not everybody reads all the literature.'2
The fact that young Julian had a joint paper with Halpern was in itself remarkable. Otto Halpern, an emigre physicist ofJewish descent was offered a professorship of theoretical physics at New York University (as successor to Gregory Breit who had left for Wisconsin) after he was forced out of Nazi Germany. His stimulating but patently contrarian attitude in scientific discourse was legendary. He was a man of imposing physique who dominated a room by his presence; he engaged in heated arguments with any recognized authority, even of the stature of Enrico Fermi. He was especially intimidating to doctoral students, whom he ignored until he deemed them worthy of the privilege of discussing physics with him. Together with I. I. Rabi, Halpern conducted a weekly seminar which attracted large audiences to University Heights on Wednesday nights. Morton Hamermesh described these events as 'a sort of battlefield, just violent fights.' 14 Despite that, Julian Schwinger, who was unbashful in scientific matters, had agreed to give a talk in Halpern's seminar on two recently published papers by Max Born and Leopold Infeld in the Proceedings of the Royal Society ofLondon on the quantization of the electrodynamic field equations.30
Schwinger gave a lucid, well-organized presentation which impressed everybody. Halpern treated the young man with respect and soon the two were exchanging ideas on a problem of electron scattering theory. They discussed Mott's study of electron scattering31 in which he had made use of Dirac's theory to compute the cross-section for the elastic scattering of electrons from the Coulomb field of nuclei. Julian's familiarity with this work dated from days before he wrote his 'Paper Number Zero' [O]. Halpern suggested that Julian investigate the discrepancy between the measured distributions of polarizations of electrons scattered by nuclei and Mott's theoretical values. Mott's calculations were relativistic and had been carried to one order beyond the lowest

A NEW YORK CITY CHILDHOOD 17

Born approximation. This was necessary because the experimental tests of theoretically derived cross-sections for one-on-one collisions were intrinsically difficult. Even if very thin metal foils were used as targets, a substantial portion of electrons interacted with more than one nucleus. Another significant higher-order process that affected the results was the quantum shielding effect from atomic electrons. Mott had not considered the shielding effects, which are relevant only for small values of the scattering angles, but included double scattering on two separate nuclei in the target. He noticed that since Coulomb scattering processes were spin dependent, the electrons that took part in two consecutive interactions should have partially polarized spins. The experimental data showed no evidence of polarization and the reason for this discrepancy remained obscure.
In fact, Mott's final expression for the cross-section was incorrect, but the error went unrecognized for a long time until the calculation was redone in 1948 by Feshbach and McKinley.32 However, in 1934 so little was known about the nature of forces at nuclear distances that ascribing the discrepancies to a still unknown additional interaction betvveen the electron and the nucleus was a question worthy of investigation. On Halpern's advice, Schwinger repeated Mott's calculations for the case of a Coulomb potential slightly weakened by the admixture of a short-range repulsive potential of the type

b V(r) = 5r ,

( 1.7)

truncated at short distances from the center to avoid the effects ofthe singularity at the origin. Julian found that the magnitudes of the free parameter b and the required short distance cutoff could be appropriately fitted to make the polarization effects disappear from the second-order perturbation.
The assumption worked because the correcting potential was significant only near the surface of the nucleus where the Coulomb interaction is strong, and the electrons scatter at large angles. Incidentally, this was the area where the effects of Mott's error were most significant. Also the supplementary potential weakened the Coulomb field of the nucleus, thus simulating some effects of shielding. Therefore it is not surprising that with a proper choice of the inverse power of the distance and of the parameter b Schwinger found a fit for a single physical quantity calculated in low orders of the perturbation expansion. Still, for Julian it was real research work and he remembered it as a fascinating and illuminating experience. It was indeed the first time that he, entirely by himself, had successfully carried out a complete, fully relativistic, perturbation calculation by a proper accounting of spin effects.
In August 1935, shortly after publishing the paper with Halpern, Schwinger (with Motz) submitted another letter to the Physical Review, entitled 'On

18 CLIMBING THE MOUNTAIN
the f3-Radioactivity of Neutrons' [2]. Like the preceding paper, it contained the results of research completed by Julian as a student at the City College. Schwinger had no special regard for this article, which contained the results of a not very original calculation applied to an unsuccessful model of weak interactions. However, one must remember that it was produced by a 17-year-old trying to resolve valid theoretical questions related to beta decay, and not even a full three years after the discovery of the neutron! Therefore it is worthwhile to compare the events of young Schwinger's life with the scientific revelations that began with the discovery of the neutron.
\\'hen in 1932 James Chadwick announced the surprising discovery33 of a chargeless constituent component of the atomic nucleus, the neutron, Schwinger was 14. One year later, in October 1933, the seventh Solvay Conference was convened.34 For nuclear physics it was an important event, marked by the general acceptance ofthe Heisenberg and Majorana two-body theories of nuclear forces based on the exchange principle, which reasonably explained, to within an order of magnitude, the nuclear binding energies and disintegration rates through alpha particle emissions. As for beta decay, it was not even clear whether free neutrons are stable or can decay spontaneously. Wolfgang Pauli's intriguing proposal of the neutrino made at that conference began slowly to prevail, although even great physicists like Bohr and Heisenberg still remained unconvinced, and thought that energy and angular momentum might not be conserved in the neutron's disintegration.
Pauli's hypothesis of the new particle, and the discussions in Brussels, inspired Fermi to propose a Hamiltonian interaction for weak interactions which, with some modifications, reigned under the rubric of'the four-fermion theory' until the advent of modern gauge theories. Fermi's article was rejected by the editor of Nature as being 'too speculative; but he published it in a shortened version in La Ricerca Scientifica, and later in full detail in Italian and German in II Nuovo
Cimento and Zeitschrift fur Physik, respectively.35 \\'hen the latter two articles
appeared in 1934, Schwinger was 16. Fermi wrote his Hamiltonian as

where 'Vi and <I>; represent components of electron and antineutrino spinor wavefunctions, respectively, Q is the operator that transmutes a proton into a neutron, and g is the strength of the weak coupling responsible for beta decay. This Hamiltonian was soon replaced by a more general four-fermion interaction

H = g[ (\JI cC\ \J'i,) (\J'[, 011 \Jl 11 ) + complex conjugate],

( 1.9)

where the operators(\ and Ott act on what are now called the leptonic (elec-
tron and neutrino) and hadronic (proton and neutron) field components,

A NEW YORK CITY CHILDHOOD 19
respectively, and are constructed from the Dirac matrices as Lorentz scalars, pseudoscalars, polar or axial vectors, or tensors.
In 1935 Konopinski and Uhlenbeck36 found significant discrepancies, mainly in the low-momentum part of the electron spectrum, between weak decay spectra and the predictions of the Fermi theory. They tried to improve the agreement by replacing the polar vector coupling with a space-time gradient of the neutrino wavefunction,
(1.10)
The life of the Konopinski-Uhlenbeck model, because of the derivative coupling being even more singular than the four-fermion theory, was short. It was unsuccessful and quickly abandoned: however, in 1935, only a year after the introduction of the four-fermion theory, there was no reason to reject it out of hand. It appeared attractive to Lloyd Motz, and his 16-year-old collaborator was already perfectly able to apply the Konopinski-Uhlenbeck Hamiltonian in practical calculations of the neutron's lifetime and the cross- section for nuclear reabsorption ofan antineutrino from a decaying neutron. Julian found no difficulty in carrying out a standard quantum -mechanical calculation which, in the first order of approximation, followed from the expression given by Konopinski and Uhlenbeck,
(1.11)
for the probability P(E) of the process n--+ p + e- + v, as a function of energy
E of the electron (in units of the electron's rest mass). Here, f-0 is the total
energy released in the process. The calculation produced an inaccurate estimate of about 3.5 days for the neutron's half-life (the correct lifetime is 15 minutes), and a (then) negligibly small probability of a neutrino capture in the extremely
rare process p + i7--+ n + e+.
Conclusion
By 1935, at the age of 17, after Julian Schwinger had spent two years at City College, it was already clear that he would make a major mark in physics. He had mastered the literature of the most fundamental branch of science at the time, nuclear physics, and was beginning to make original contributions to research. All those who were in contact with him then were aware of his prodigious powers. All that was needed for his genius to flower was a transplantation to a research environment. The career of one of the greatest American physicists of the twentieth century had begun.

20 CLIMBING THE MOUNTAIN
References
1. J. S. Schwinger, in his autobiographical sketch appended to Les Prix Nobel 1965 (Norstedt, Stockholm, 1966), p. 113.
2. Julian Schwinger, conversations and interviews with Jagdish Mehra in Bel Air, California, March 1988.
3. Barbara Grizzell (Harold Schwinger's daughter), interview with K. A. Milton, in Reading, Massachusetts, IO June 1999.
4. Sidney Borowitz. telephone interview with K. A. Milton, 25 June 1999. 5. David Saxon, interview with K. A. Milton, in Los Angeles, California, July 1997. 6. Bernard T. Feld, talk given at J. Schwinger's 60th Birthday Celebration, UCLA,
March 1978 (AIP Archive). 7. James Jeans, Atomicity and quanta [Rouse Ball Lecture delivered on 11 May 1925],
Cambridge University Press, Cambridge, 1926. 8. P. A. M. Dirac, The principles of quantum mechanics, 1st edn. Clarendon Press,
Oxford, 1930. 9. G. Birtwistle, The quantum theory of the atom. Cambridge University Press,
Cambridge, 1926. 10. E. J. Townsend, Functions of real variables. Holt, New York, 1928. 11. Joseph Weinberg, telephone interview with K. A. Milton, 12 July 1999. 12. Edward Gerjuoy, telephone interview with K. A. Milton, 25 June 1999. 13. Edward Gerjuoy, talk given at the University of Pittsburgh and at Georgia Tech,
1994, private communication. 14. M. Hamerrnesh, 'Recollections' at Julian Schwinger's 60th birthday celebration,
UCLA, 1978 (AIP Archive). 15. L. Pauling and E. B. Wilson, Introduction to quantum mechanics. McGraw-Hill, New
York, 1935. 16. H. Wey!, Gruppentheorie und Quantemnechanik. Hirzel, Leipzig, 1928. [English
translation: Group theory and quantum mechanics. Methuen, London, 1931 (translated by H.P. Robertson).] 17. Julian Schwinger Papers (Collection 371), Department of Special Collections, University Research Library, University of California, Los Angeles. 18. W. Pauli and V. Weisskopf, Helv. Phys. Acta 7, 709 (1934). 19. W. Heisenberg and W. Pauli, Zeit. fur Phys. 56, I (1929); ibid, 59, 168 (1930). 20. W. Heisenberg, Ber. Siich. Akad. Wiss. (Leipzig) 86,317 (1934). 21. H. A. Bethe, Phys. Rev. 47,747 (1935). 22. P.A. M. Dirac, Proc. Camb. Phil. Soc. 25, 62 (1929); Solvay Congress, 1933 [see Jagdish Mehra, The Solvay conferences on physics, Reidel, Dordrecht, Holland, 1975, p. 218]. 23. l.loyd Motz, conversations and interview with Jagdish Mehra, in Los Angeles, California, 25 November 1988.

A NEW YORK CITY CHILDHOOD 21
24. H. A. Bethe and W. Heider, Proc. Roy. Soc. London Al 46, 83 (1934).
25. W. Furry and J. R. Oppenheimer, Phys. Rev. 45,245 (1934).
26. N. F. Mott, Proc. Roy. Soc. London Al 26, 259 (1930). 27. C. M0ller, Zeit. fur Phys. 70, 786 (1931). 28. P.A. M. Dirac, Proc. Roy. Soc. London Al 36,453 (1932). 29. P.A. M. Dirac, V. A. Fock, and B. Podolsky, Phys. Zcit. Sowjetunion 2,468 (1932). 30. M. Born and L. Infeld, Proc. Roy. Soc. London Al44, 425 (1934); ibid, Al47, 522
(1934). 31. N. F. Mott, Proc. Camb. Phil. Soc. 27,255 (1931). 32. W. A. McKinley and H. Feshbach, Phys. Rev. 74, 1759 (1948).
33. J. Chadwick, Proc. Roy. Soc. London Al 36,692 (1932).
34. Rapports du '1' Conseil Solvay de Physique. Structure et Proprietes des Noyaux A.tomiques. Gauthier-Villars, Paris, 1934.
35. E. Fermi, Ric. Scicntifica 4,491 (1933); II Nuovo Cimento 11, 1 (1934); Zeit. fur Phys. 88, 161 (1934).
36. E. J. Konopinski and G. E. Uhlenbeck, Phys. Rev. 48, 7 (1935).

2
Julian Schwinger at Columbia University
Transfer to Columbia
Although Benjamin Schwinger was not able to fulfill his dream of sending his sons to Columbia University, Julian did not think much about it; in any case, he became a frequent visitor to the excellent Columbia University Library. The Schwingers lived quite close to the University, and Julian often walked there, casually entering the library, picking up a book and finding a quiet place somewhere to read. This normally unallowed procedure continued for several months until one day a librarian, puzzled by his young age, asked Julian whether he had library privileges. He lied to her that that he did, and she asked for his name, then looked up the list of library card-holders to verify. To the amazement ofthe young boy, who was already resigned to hear a reprimand, a strange thing happened: She indeed found a Schwinger on the list of registered users! From then on, mistaken for this unknown relative, Julian continued to use the library at will until he became a regular student at Columbia.'
In early 1935 Schwinger also began frequenting seminars and colloquia at Columbia in the company of Lloyd Motz. He found them exciting and became a regular visitor there. After he had been attending these events for several months, Isidor Rabi noticed him and, intrigued by his youth, asked Motz: 'Who is that sleepy-eyed kid you bring along with you?' Motz explained that 'he is a very brilliant, incredibly bright sophomore from the City College' and promised to bring him over one day and introduce him to Rabi.2 The occasion presented itself soon, when one day Julian and Motz were talking in front of the library. The library and Rabi's office opened on to the same hallway on the eleventh floor of the Pupin Physics Laboratory. Suddenly the door opened and Rabi appeared; he invited Motz into his office to discuss 'a certain paper by Einstein in the Physical Review.' Motz introduced Julian and asked if he could bring his young friend along; Rabi did not object, and so it began.'
The Einstein article turned out to be the famous paper of Einstein, Podolsky, and Rosen,3 with which young Julian was already familiar. He had studied

SCHWINGER AT COLUMBIA UNIVERSITY 23
quantum mechanics with Professor Wills at the City College, and discussed with him the problem of the reduction ofa wave packet after additional information about a quantum system is gained from a measurement. 'Then they [Rabi and Motz] began talking and I sat down in the corner. They talked about the details of Einstein's paper, and somehow the conversation hinged on some mathematical point which had to do with whether something was bigger or smaller, and they couldn't make any progress. Then I spoke up and said, "Oh, but that is easy. All you have to do is to use the completeness theorem." Rabi turned and stared at me. Then it followed from there. Motz had to explain that I knew these things. I recall only Rabi's mouth gaping, and he said, "Oh, I see. Well, come over and tell us about it." I told them about how the completeness theorem would settle the matter. From that moment I became Rabi's protege. He asked, "Where are you studying?" "Oh, at City College." "Do you like it there?" I said, "No, I'm very bored:' '1
Watching young Julian demonstrate such 'deep understanding of things that were at the time at the frontier and not clearly understood;2 Rabi decided on the spot to talk to George Pegram, then chairman of the physics department and dean of the graduate faculty, to arrange Julian's immediate transfer to Columbia. He and Motz left Julian waiting and went to see Pegram who also had an office in the same building. Motz stayed behind and waited outside Pegram's office. Rabi emerged a few minutes later with the word that there might be a scholarship available and Pegram would help in carrying the transfer through. Motz hurried to bring the good news to Julian, but he was astonished to find the independently minded Schwinger hesitate. The unique intellectual atmosphere of the City College where he had made many friends and felt at home had worked very well for him so far; therefore he decided not to rush and first to seek a transfer to the honors program at the College, and only if this didn't work would he accept Rabi's offer.2
The honors program at the City College was generally available, with the approval of the physics department's chairman Charles Corcoran, to the best physics majors after they had completed the core curriculum physics courses, but Schwinger had finished only the basic first-year requirements and was at odds with Corcoran for not returning his laboratory reports. Therefore Motz felt that he had better chances with Corcoran than did Julian, and offered to bring up the subject with the boss himself. The chairman had already heard about Julian, but the City College at that time was a unique place, full of excellent students, brought up with the attitude of studying and passionate about learning, more brilliant than the faculty, who had come from backgrounds that did not emphasize intellectualism much.' The place abounded with talent and Corcoran did not see anything extraordinary in Schwinger, whose grades outside mathematics and physics were quite abominable because he always

24 CLIMBING THE MOUNTAIN
performed poorly if the nature of the course did not agree with his individualistic patterns of study. After Motz made an impolitic remark that Julian knew more about physics than did most people on the faculty, Corcoran bristled with anger and ruled that the proposition was out of the question. According to Bernard Feld, 'Corcoran is alleged to have said, "Over my dead body. As long as I'm chairman of this department, no smart-ass kid is going to be allowed to skip taking my course in elementary physics." '4 Several days later he even criticized Motz in a department meeting for trying to ruin the fine-tuned process of educating the young man in the only natural way, that is gradually.2 ' *
Rather upset, Schwinger returned to Rabi and asked him to set the process of transfer to Columbia in motion. To Rabi's astonishment it turned out to be more difficult than he had expected. The obstacle was Julian's terrible grades. An official who examined his transcripts from the City College declared that on their basis Julian could not even be admitted to Columbia University. Rabi felt a little insulted and asked: 'Suppose he were a football player?' and decided to override the administration with Pegram's assistance and the help of Hans Bethe. Bethe provided an enthusiastic letter of support after he read Julian's notes on electrodynamics.6 Bethe's letter, dated 10 July 1935, reads as follows:
'Dear Rabi, Thank you very much for giving me the opportunity to talk to Mr. Schwinger. When discussing his problem with him, I entirely forgot that he was a sopho-
more 17 years of age. I spoke to him just as to any of the leading theoretical physicists. His knowledge of quantum electrodynamics is certainly equal to my own, and I can hardly understand how he could acquire that knowledge in less than two years and almost all by himself.
He is not the frequent type of man who just "knows" without being able to make his knowledge useful. On the contrary, his main interest consists in doing research, and in doing it exactly at the point where it is most needed at present. That is shown by his choice of his problem: When studying quantum electrodynamics, he found that an important point had been left out in a paper of mine concerning the radiation emitted by fast electrons. That radiation is at present one of the most crucial points of quantum theory. It has been found to disagree with experiment. It is quite conceivable that the error which Mr. Schwinger found in my paper might bring about agreement between theory and experiment which would be of fundamental importance for the further development of quantum electrodynamics. I may add that the mistake has not
* 'The rigidity of Corcoran's concerning the physics department's requirements was typical of the whole CCNY curriculum. There was an astoundingly large numher of required courses outside the major, which just couldn't be avoided:5

SCHWINGER AT COLUMBIA UNIVERSITY 25
only escaped my own detection but also that of all the other theoretical physicists although the problem has been in the centre of discussion last year.
The way in which Schwinger treated his problem is that of an accomplished theoretical physicist. He has the ability to arrange lengthy and complicated calculations in such a way that they appear simple and can be carried out without any great danger of errors. This gift is, I believe, the most essential requirement for a first-class theoretical physicist besides a thorough understanding of physics.
His handling of quantum theory is so perfect that I am sure he knows practically everything in physics. If there are points he does not know, he will certainly be able to acquire all the necessary knowledge in a very short time by reading. It would be just a waste of time ifhe continued listening to the ordinary physics course, 90% of whose subject he knows already while he could learn the remaining 10% in a few days. I feel that nobody could assume the responsibility of forcing him to hear any more undergraduate (and even the ordinary graduate) physics courses.
He needs, of course, some more courses in minor subjects, principally mathematics and chemistry and a small amount of physical laboratory work. In physics the only thing he has to learn is teaching physics, i.e., to explain himself very simply-an art which can be learnt only by experience. He will learn that art automatically ifhe works at a great institution with other students of similar caliber.
I do not need to emphasize that Schwinger's personality is very attractive. I feel quite convinced that Schwinger will develop into one of the world's foremost theoretical physicists if properly guided, i.e., ifhis curriculum is largely left to his own free choice.'* Eventually, Schwinger was admitted to Columbia as a junior, with a full tuition scholarship starting in September 1935, but in the preceding summer semester he had to take some required courses that he had missed out at the City College.1 Rabi laid down a contract to Julian. 'You're coming here and you are going to take all undergraduate courses and I want you to get As in all those dasses.'2 Julian obliged for a while, but soon returned to his own individualistic ways. He disliked writing themes .or laboratory reports and treated them as a nuisance that distracted him from his real vocation, which was learning physics. He admitted unabashedly: 'I did not learn anything in my physics courses [other] than what I already knew from my own private studies.' 1 Therefore, to avoid any pressure to attend lectures he began to develop work patterns which gradually drifted into later and later working hours, extending deep into the night. He
* We are grateful to Karl von Mevenn for bringing to our notice a complek photocopy of Bethe's letter to Rabi.

26 CLIMBING THE MOUNTAIN
would sleep through the day and show up at Columbia around 6 o'clock in the evening. He spent most of his time reading advanced texts in physics and mathematics and journal articles in the library, and writing papers. It was a relatively simple matter for him to pass oral examinations by stunning his professors who watched him inventing on the spot his own proofo or nonstandard methods of approaching standard problems. Sometimes this did not work, and he flunked the chemistry course ofVictor LaMer, who had the custom of introducing his own peculiar notation and demanding that his students make full use of it, and which was obscure to anybody who did not attend his class regularly.7• *
Rabi recalled, 'LaMer was, for a chemist, awfully good. A great part of his lifework was testing the Debye-Hlickel theory9 rather brilliantly. But he was this rigid, reactionary type. He had this mean way about him. He said, "You have this Schwinger? He didn't pass my final exam." I said, "He didn't? I'll look into it:' So I spoke to a number of people who'd taken the same course. And they had been greatly assisted in that subject by Julian. So I said, I'll fix that guy. We'll see what character he has. "Now Vicky, what sort of guy are you anyway, what are your principles? What're you going to do about this?" Well, he did flunk Julian, and I think it's quite a badge of distinction for him, and I for one am not sorry at this point, they have this black mark on Julian's rather elevated record. But he did get Phi Beta Kappat as an undergraduate, something I never managed to do:6
Norman Ramsey added an amusing footnote to this story. In 1948 Schwinger had to repeat his brilliant lecture on quantum electrodynamics three times at the American Physical Society meeting at Columbia, in successively larger rooms.+ 'It was a superb lecture. We were impressed. And as we walked back together-Rabi and I were sitting together during the lecture-Rabi invited me to the Columbia Faculty Club for lunch. We got in the elevator [in the Faculty Club] when who should happen to walk in the elevator with us but LaMer. And as soon as Rabi saw that, a mischievous gleam came into his eye and he began by saying that was the most sensational thing that's ever happened in the American
* It was a dull course with a dull exam. A question on the final exam was 'Prove that
= dE d~ + dry; where none of the variables E, ~, or 17 were defined. 8
1 Phi Beta Kappa is the most honored academic fraternity of young American students, to which they are elected by their peers and seniors entirely on the basis of academic excellence. + K. K. Darrow, secretary of the Physical Society, who apparently had little appreciation of theory, always scheduled the theoretical sessions in the smallest room. Schwinger's second lecture was given in the largest lecture hall in Pupin Lah, and the third in the largest theatre on campus.;

SCHWINGER AT COLUMBIA UNIVERSITY 27
Physical Society. The first time there's been this three repeats-it's a marvelous revolution that's been done~LaMer got more and more interested and finally said, "Who did this marvelous thing?" And Rabi said, "Oh, you know him, you gave him an F, Julian Schwinger." '7
Somewhat later George Uhlenbeck came from Holland as a visiting professor to Columbia and taught a course in statistical mechanics in which he was a great expert. A large 11umber of students signed up to take his class and many faculty members also attended. Schwinger registered, but never went to class, and did not bother to take the final exam. Uhlenbeck complained to Rabi that he was not even given a chance to see the invisible student. Rabi became infuriated. He knew that Schwinger had just begun dating and felt concerned that he might be getting distracted away from physics. He decided to see Julian in person and ordered him to take the oral examination (as was the Dutch custom) immediately. Schwinger bargained that he would do so but only at 10 o'clock in the evening. This request was beyond Uhlenbeck's limit of tolerance, yet a special examination date was arranged for 10 o'clock in the morning. With Schwinger's answers in the examination, Uhlenbeck was overwhelmed: 'I can say nothing. Not only did he hand in a perfect paper, but he did it in the way I did everything, as though he had sat through every lecture. This is amazing. So I have nothing to say; he declared to Rabi. 2' 6' 10
Schwinger's lack of attendance at lectures and completion of coursework caused other problems as well. Jvlany years later Norman Ramsey recalled that when he proposed him for membership in Phi Beta Kappa, many people objected and cited his uncompleted courses and bad grades. Julian was eventually elected to Phi Beta Kappa, but only after a big argument in which Ramsey pointedly remarked that Schwinger had published more papers that year than anybody on the faculty. 7·'
At Columbia, Julian had somewhat severed his relations with most of his peers in class. To a greater extent than at City College, when because of his young age he could develop by emulating his fellow students, at Columbia he benefited more from the faculty. He had good working relations with graduate students and professors and generally enjoyed interacting with people. He participated in seminars and was a good listener, since from his early articles it is evident that he had a detailed knowledge of the most recent experimental data and formal developments. He also offered himself as a lecturer in seminars and discussion groups and discussed matters in a mature manner.
I.loyd Motz vividly described one such seminar talk, given at a weekly tea meeting of the Astronomy Journal Club run by Jan Schilt and attended by astronomers from colleges and universities in the New York metropolitan area. Neutron stars were then the hot topic in their discussions, some two years before the definitive paper of Oppenheimer and Volkov appeared. 11 Schilt looked for

28 CLIMBING THE MOUNTAIN
someone able to present at the Journal Club the rules of the new quantum statistics, the questions related to quantum degeneracy, properties of the degenerate electron gas, and similar topics. Motz suggested Schwinger as the most suitable person for the task. Julian quickly agreed: 'Sure, no problem. As soon as you want me!'2 The lecture was a revelation. 'Everything was perfect. He would begin writing at one end of the blackboard, and then finish at the other. He would do things with his left band. He was ambidextrous so he would write on the board with both hands. It was all so beautiful. It came out of him the way music came out of Mozart, as though he had been born with it. He never made a mistake. It didn't matter what question you would ask him; he always had a ready answer.' 2
Julian sought isolation for his work. Of course, the habit of shifting to work late in the evening and sleeping through the day had to be in conflict with the basic responsibilities of the undergraduate's life. Julian ceased attending classes; he felt he did not need them. Very likely he shifted his life into the night pattern just to avoid being pressured to go to classes and waste his time listening to other people explaining what he already knew. He was indeed a very strange kind of undergraduate, whom Rabi often asked to be his substitute for teaching a graduate quantum mechanics class for him when he was away or had other engagements. According to Rabi, '\Vhenever I had to go away, I'd ask Julian, who was an undergraduate, to take the class. I can assure you it was a great improvement. He's a much better teacher than I ever was.'6
Rabi praised Julian enormously for his willingness to offer help in any calculation; he would not stop at the final formula, but work with the phenomenological data until he could produce a final number as an answer. Similarly, he was very friendly and helpful in his interactions with fellow students. Morton Hamermesh recalled Schwinger teaching him U) group theory, and the intricacies ofusing Bessel fun!=tions in theoretical calculations: he coached Hamermesh for days, several hours at a time. 12
Rabi had great confidence in his protege, but it was not limitless. He was afraid that one day his genius would turn out to be a flash in the pan and he had to reassure himself periodically by introducing Schwinger to any physicist of consequence who visited Columbia. They all left impressed by his age and by the sheer volume of knowledge he had acquired. Wolfgang Pauli wrote a letter to Rabi saying how impressed he was and closed with the words, 'And give my love to this physicist in knee pants.' Recall that in the summer of 1935 while Rabi was trying to get Julian into Columbia, Hans Bethe arrived and Rabi asked him to assess Julian's progress and send a written evaluation. Bethe sent a letter full of superlatives including a strong endorsement. After receiving this remarkable assessment, a happy and beaming Rabi showed Bethe's letter to Motz with the words, 'Now, I am satisfied.'2

SCHWINGER AT COLUMBIA UNIVERSITY 29
Spin resonance
At Columbia University Schwinger, for a while, continued his research contacts with Halpern and l\lotz, but soon he gained so much confidence in himself that he did not need their support and encouragement. Besides, they were no match for him in the speed of doing calculations. By September 1936, at the age of 18, only one academic year and two summer sessions after his matriculation at Columbia, Julian received his undergraduate degree and, in passing, produced a quantity of research ordinarily considered sufficient for a doctoral dissertation. Rabi recalled that it was not altogether trivial to get Julian's undergraduate degree in such short time. Columbia required more than just completing a sufficient number ofhours. You had to have 'a certain weight of ordinary credits and a certain weight of maturity credits. One Sunday morning I was called up by the dean, Dean Hawkes, and he said, what shall I do about Schwinger? I said, what's the problem. He said he has enough credits to graduate but he hasn't enough maturity credits. It seemed too absurd. How can you talk about things that way? So I said, well, you have your rules. I don't know what you can do about it. I wasn't going to make a great plea. See how the thing'd work. Well, he was a real man, and on Sunday, he was a religious person, he said, I'll be damned if I won't let Schwinger graduate because he doesn't have enough maturity credits. Of course, this gave me great faith.'" It seems that Edward Teller was the first person to deem Schwinger's work on neutron scattering as worthy of a PhD,2' 13 but the requirements of the graduate school at Columbia set a minimum twoyear residence period for doctoral candidates. Considering Julian's young age, there seemed to be no compelling reason to depart from this rule. Schwinger himselfdid not see any point to the rule:'\Vhy they didn't let me out ofColumbia two years earlier, I will never know.' 1 In the meantime he registered for more courses, and ever faithful to his custom, he seldom if ever attended classes and kept on working on problems of scattering theory and spin. He soon became a sought-after expert in this subject, a real catalyst (Motz [illed him a 'spark plug')
for Rabi's spin resonance team and also J. R. Dunning's cyclotron experimental
group, where he helped to interpret the influx of data produced with the use of this emerging (just five-year-old) technology.
Julian carried around ever thicker-growing notebooks, but never felt compelled to write articles, even though Motz and Rabi insisted that he finally write up at least a part of his results. Finally, during the year 1937, Schwinger published five papers in the Physical Review. They became his doctoral dissertation; he never sat down to write a doctoral thesis as such, but submitted a bound-up set of these papers as his dissertation.
The common trait of these articles was that they were all devoted to spin and magnetic moment-dependent aspects of neutron scattering. In 1936 and

30 CLIMBING THE MOUNTAIN
1937 so little was known about the neutron that in his comprehensive review of nuclear physics, published then in the Reviews ofModem Physics, 11 Hans Bethe still had to invoke the argument of simplicity to justify a value of one-half for neutron's spin over an equally plausible magnitude of three-halves. Due to the fact that the neutron has no charge, nuclear physicists had to rely on indirect information from nuclear spins and from the data gathered in proton-neutron and proton-deuteron scauering experiments.
Rabi remained the strongest influence upon Julian at that time and it was therefore no accident that the first two articles Schwinger wrote at Columbia, begun while still an undergraduate, were related to his interests. In these articles, Schwinger improved upon or corrected the works of Rabi and Felix Bloch. The first of his Columbia papers was a full-length article 'On the Magnetic Scattering of Neutrons' [3], which included the work he had completed by himself, albeit with Rabi's blessing, in 1936. Earlier that year, Felix Bloch had proposed a technique for measuring the neutron's magnetic moment from the spatial distribution of neutrons scattered twice on targets magnetized in different directions. 15 Bloch argued that since the range of nuclear interactions is short and the neutrons carry no charge, the scattering of thermal neutrons from atomic targets is dominated by the magnetic interaction between the neutron's spin and the atomic electrons. Therefore an unpolarized stream of neutrons scattered by a magnetized target (ideally by saturated magnetized iron plates) becomes partially polarized. If it is then scattered for the second time, the angular distributions of emerging neutrons depend on the relative orientations of magnetization vectors of the targets and on the magnitude of the neutron's magnetic moment, which can therefore be determined from such data. Soon after the publication of Bloch's paper, a preliminary experimental trial of the double scattering method was performed by Bethe, Hoffman, and Livingston. 10 Their experiment had indeed registered an asymmetry in the scattered beam caused by rotating the magnetization vector of the analyzer, but the effect was too small to produce any reliable estimate for the magnitude of the magnetic moment.
Schwinger did not trust Bloch's calculations, which were based on the classical form of interaction between two magnetic dipoles. Julian had done somewhat similar work on Coulomb double scattering for his paper with Halpern [l], and now he decided also to recalculate the magnetic effect. He employed the techniques he had learned from Mott and Massey's Theory ofatomic collisions,'~ and used an interaction Hamiltonian in which in addition to the term corresponding to the magnetic interaction between neutron's magnetic moment and electron spin, he also included the nudeonic potential at the position of the neutron. According to the current practice (which soon thereafter, also thanks to Schwinger's work, was found to be incorrect [13 J), Julian considered it to be

SCHWINGER AT COLUMBIA UNIVERSITY 31
a potential of a central (spin-dependent) force of still unknown nature. Such a form of interaction was then known as Wigner's force, although Schwinger attributed it to Van Vleck. 18 The situation was difficult, because this unknown interaction was strong and had to be included exactly, while the better-known magnetic force was to be treated as a perturbation. However, Schwinger was still able to carry out the calculation because only the slowest thermal neutrons spend a long enough time in the proximity of the target atoms to experience any significant magnetic effects. He knew that thermal neutrons do not create metastable states with iron nuclei and, having zero orbital momentum, scatter on the nuclear potential in a spherically symmetric manner almost independently of the actual form of the Hamiltonian. For the cross-section for long-range magnetic scattering only the asymptotic forms of the wavefunctions corresponding to the scattering by nuclear forces are important and, for the zero orbital momentum neutrons, the single most relevant parameter that characterizes that asymptotic behavior is the phase shift of the scattered S-wave with respect to the incident wave. It is linked to the overall strength of the nuclear force, and Schwinger was able to infer its magnitude from other neutron-scattering experiments.
This allowed Schwinger to proceed to the next step of the approximation, using the magnetic moment~spin interaction as a perturbation. This fully quantum-mechanical calculation produced an angular distribution and spin density of the elastically scattered neutron different from Bloch's. In addition to the classical term, which Bloch had correctly derived, it included a pure quantum term in the part dependent on the spin density of the incident radiation. Julian continued with a discussion of how to configure the experimental trials optimally. He applied his results to the scattering of polarized and unpolarized beams from ferromagnets. Then he analyzed the practical limitations of measuring the spatial distributions of neutrons double-scattered from two separate magnetized targets. The thoroughness of this analysis substantiated Rabi's opinion that Julian represented the ideal of a theorist from an experimentalist's viewpoint, one who was always willing and able to come up not only with a general analysis but also with 'a final number as an answer.'2
Schwinger found that 'the intensity of double scattering with parallel orien-
tation of magnetizations lcould be] 15 times that with antiparallel orientation.
However, despite the large magnitude of the asymmetry, this effect will be difficult to detect with present methods because of the small intensity of the double-scattering neutrons.' Thus he proposed studying the induced polarization of the undeflected beam. If the transmitted beam was subsequently scattered, the experimenter could measure a polarization asymmetry defined as the 'difference in intensity between antiparallel and parallel orientations of magnetization divided by the average intensity.' The asymmetry, in certain

32 CLIMBING THE MOUNTAIN
configurations, could reach a value of more than 90%. He also proposed a double transmission experiment in which there was a compromise between having sufficient intensity transmitted and yet having a substantial polarization. Polarization asymmetries of about 40% were nevertheless achievable.
Although they were more feasible in yielding information than was double scattering, double transmission and transmission scattering were never successfully applied for the purpose of measuring the neutron's magnetic moment. Instead, subsequent experiments were based on resonance depolarization in neutron beams and were similar to the method used in Rabi's original molecular beam spin resonance apparatus, except that the neutrons passed not through Rabi's constant magnetic fields with opposite gradients but through ferromagnetic plates. 19 By then the more elaborate theory of magnetic interactions of neutrons had already come to exist, but Schwinger's calculation represented the first correct quantum-mechanical quantitative description of Bloch scattering.2u
Hans Bethe was the referee of the paper, and, while praising it, suggested it be rewritten to emphasize the difference between the classical interaction between the dipoles, used by Bloch, and the correct Dirac treatment. He suggested that Schwinger was being too modest. The editors of the Physical Review, however, disregarded this advice, and the paper was published unchanged. u
Schwinger's next article in 1937 [4] appeared side-by-side with a related paper of Rabi on magnetically induced spin transitions in atomic beams. 21 Like the previous article on Bloch scattering, it contained a detailed and expanded calculation of an effect that had been previously analyzed semi-classically, this time by Rabi, who had studied the behavior of spin one-half atoms in a precessing magnetic field. 22 A few attempts on the theory of this effect already existed, but they were very limited in scope, and Motz, who looked at Rabi's results, found a troublesome discrepancy between them and those obtained somewhat earlier by Giittinger23 for the case of a rotating magnetic field. The discrepancy demanded immediate reconsideration with the help of rigorous quantum-mechanical procedures, and Rabi presented Julian with the task of performing it.
The underlying physics involved the classic problem of the evolution of a state coupled to a variable external field. If the transition between any two states of the field was rapid (as in the case of a sudden reversal of an external magnetic field), the dynamical state of the system would be unchanged. On the other hand, in the case of an adiabatic transition (such as the infinitesimally slow rotation of the same field by 180°), Ehrenfest's adiabatic theorem applies and the system follows the external changes continuously and gradually evolves from one energy eigenstate into another.
Being interested in the most general case of a time-dependent interaction, Schwinger considered the Schrodinger equation for a system with a

SCHWINGER AT COLUMBIA UNIVERSITY 33
Hamiltonian which involved no time-dependent variables except those associated with the external field. In such perturbative calculations one expands the wavefunction in a complete set of orthogonal energy eigenfunctions, treating the coefficients of expansion as time-dependent functions depending on the external field. Knowledge of these functions suffices for finding the transition amplitudes; however, the coefficients must be determined from the equations that expressly involve the energy eigenfunctions themselves. Therefore, in general, it is necessary first to solve the full dynamical problem and find the eigenfunctions, and only then proceed with the calculation of the lifetimes of individual energy levels.
In the simpler case of a magnetic field rotating with constant angular velocity, Glittinger had derived a set of equations for the coefficients that had the advantage of not involving the eigenfunctions, but only the energy eigenvalues, which in some cases could be inferred without the complete knowledge of the individual eigenfunctions. Starting from scratch in the general case, Schwinger recovered the Giittinger equation, but with an additional term which included the eigenfunction. Julian found a way of solving for this function in a general case and expressing this term by means of the angular momentum, magnetic quantum numbers, and the spherical components of the external magnetic field. This additional term happens to vanish for the transitions induced by a steadily rotating magnetic field; therefore Giittinger's results were correct for the case he considered, but not for the case of Rabi's precessing field. That is, only in the case when the magnetic field was perpendicular to the precession axis was Glittinger's result correct. This explained the discrepancy found by Motz, who had used the unmodified Glittinger equations outside the bounds of their applicability.
This paper was a precursor to Schwinger's later definitive work on the theory of angular momentum. As Schwinger noted, 'In fact, this was the origin of the work I did later about the general theory of angular momentum and so on [69]. But the whole interest in angular momentum goes back to these Rabi, molecular, atomic beam problems. And I'm sure this was done while I was still an undergraduate, or very soon thereafter.' 1 Norman Ramsey, then Rabi's graduate student, characterized the significance of the Rabi-Schwinger papers: 'They are the fundamental papers for nuclear magnetic resonance.''
'Because I, not my distinguished colleague, wrote it'
In the mid- l 930s convincing evidence had emerged that nuclear forces were spin dependent. For example, neutron-proton binding forces were found to be much stronger than the forces between the neutrons or the protons themselves. Also, the exclusion principle ruled out any binding between pairs of neutrons or

34 CLIMBING THE MOUNTAIN

protons unless they had antiparallel spins so they could form only singlet bound states. No such restriction applied to neutron-proton pairs, yet no singlet states had been observed. In I 935, Gregory Breit and Eugene Wigner pointed out24 that if one includes a singlet state in neutron-proton scattering processes then, in order to provide even crude agreement with experimental data, the singlet and triplet bound states must yield drastically different contributions to the total cross section. This could not be explained on the basis of existing models or small modifications of them.
As we have noted earlier, global effects of scattering of slow neutrons are well described by the phase shift of the scattered wave with respect to the incoming S-wave. The phase shift is a dynamical quantity dependent on the interaction potential. Since it is readily calculable and directly connected to the total cross section for S-wave scattering of neutrons it was used as a convenient tool in model testing, together with the Fermi scattering length, which is the radius of a sphere of surface area equal to the total cross section taken with a sign depending on that of the phase shift. At low energies, the relation between the phase shift 8, the energy E, and the scattering length a is

kcot8 = --l,
a

k- -v~ 12hm-E ,

(2.1)

m being the mass of the neutron. The scattering length depends on the volume of the potential well, but is
relatively insensitive to its shape. Therefort' all initial attempts to adjust the form of the nuclear potential to achieve satisfactory accord with experimental data failed hopelessly. For example, Wigner's calculation25 with the use of rectangular well potentials produced low momentum neutron-proton cross sections of about two and a halfbarns,* while the experimental value was then thought to be about 13 barns.26 Wign~r suggested that there must also exist a singlet neutronproton bound state, different from the triplet ground state of a deuteron.27 It ought to have a very small binding energy but a very large scattering cross section at low energy. The total cross section would then be a sum of the cross sections due to the singlet state and those due to triplet states with statistical weights of one and three-quarters, respectively. However, the singlet binding energy revealed little about the nature of the binding potential. As a first step, the sign of the scattering length was needed because the sign of the ratio of the triplet to the singlet scattering lengths determined whether the singlet state was real or virtual, that is, whether the binding energy was positive or negative. No such information could be found from S-wave neutron scattering cross sections by protons in bulk matter.

' A barn, an originally facetious term referring to its unexpected largeness, is 1024 cm'.

SCHWINGER AT COLUMBIA UNIVERSITY 35
In 1936, Edward Teller remarked that, if nuclear forces are spin dependent, one should expect differences between the scattering cross sections in orthoand parahydrogen,28 which have parallel and antiparallel spins, respectively. He also noticed that since the waves scattered on two hydrogen nuclei in a molecule interfere, such scattering should provide information about things like the sign
of the scattering length and the range of the n-p force.
Schwinger learned about Teller's suggestion from Bethe's review articles in the Reviews of Modern Physics. 14 He saw it as another opportunity to deploy his skill in calculations involving spins and started to compute the cross sections without hesitation. He progressed rapidly and soon he had some results to show to Rabi. Rabi suggested that he should go to Washington and discuss them directly with Teller, who was then at George Washington University. Teller was very interested in solving the problem of neutron scattering by molecular hydrogen, but apparently was not able to do the calculations by himself. He greatly welcomed help and invited Schwinger to come to Washington, and offered him a room to stay in his house.
Julian stayed with the Tellers for about two weeks, during which time he became timidly but intensely infatuated with the grace and enchanting accent of Teller's Hungarian wife, Mitzi.1 This unexpected relapse into adolescence did not take his mind away from the project, which he continued and completed, doing all the calculations by himself. Apparently Teller offered advice and critique, but did not contribute to the progress of the work. The preliminary results of this somewhat uneven cooperation soon appeared in a
letter to the Physical Review l5], and a regular article on 'The scattering of
neutrons by ortho- and parahydrogen' [8] followed shortly thereafter.* The Schwinger-Teller paper quickly inspired experiments and thus this was the first Schwinger article which became a standard textbook reference. Schwinger made no bones about whom the credit for this work should belong to. In 1979, a collection of his major articles was published29 and in it he provided pithy, often one-line comments on these selected papers. The punch line included on the paper with Teller read: 'Because I, not my distinguished colleague, wrote it.'
The article was written in the characteristic style of Schwinger's early papers, in which the details of complex calculations were mixed with phenomenological approximations based on generally scarce data, and which ended with the interpretation of possible results for future experiments. In the absence of an accepted theory of underlying forces, the calculation had to be essentially model-independent; thus, as in the case of Bloch scattering, it required neutrons
' It is interesting to note that the abstract of the article was quite long, a habit Schwinger often cultivated, and is nearly identical to the entire letter submitted two months previously.

36 CLIMBING THE MOUNTAIN

of de Broglie wavelength large enough to be insensitive to the details of the spatial form of the nuclear potential. This restriction had an additional simplifying effect: Schwinger could calculate the coherent scattering cross-sections by simply summing up the scattering amplitudes from the two participating nuclei. Not having to worry about the radial dependence of the force, Schwinger treated the interaction potential as a contact interaction, vanishing unless the position of the proton and neutron, rp and rn coincide, and proportional to

Uat(l + Q) + ~as(l - Q)] 8(rn - rp),

(2.2)

where Q is a spin operator constructed from the Pauli spin matrices of the proton and neutron and having the eigenvalue plus one in the triplet and minus one in the singlet state of proton-neutron system, and at and as are the scattering lengths for triplet and singlet spin states, respectively. The potential for coherent scattering was a sum of two terms of the type (2.2), one for each of the different hydrogen nuclei in a molecule. The final form of this sum turned out to contain two types of terms, one symmetric, the other antisymmetric in the proton spin. The antisymmetric part could induce transitions between the states of orbital quantum number differing by one unit, thus inducing conversions previously thought to be forbidden between the ortho- and parahydrogen. It was propor-
tional to at - as and even the very existence of such transitions, no matter how
rare, would demonstrate a spin asymmetry of the nuclear interaction. By treating the molecule as a quantum rigid rotator, and neutrons as plane
waves normalized in a finite volume, Schwinger calculated the transition probabilities between the lowest energy levels of orbital angular momentum equal to zero or one, which were the only states that could significantly contribute to the total cross section at low temperatures. Experiments had to be performed at cryogenic temperatures so that neutrons had energies small compared with molecular rotational energy levels, which are different in ortho- and parahydrogen. With the rotational excitations eliminated, any difference in cross sections would have to be caused by the spin dependence of the interaction. The results confirmed Teller's expectations: the cross sections for ortho- and parahydrogen were different for very slow neutrons; moreover, the difference between the two
depended very strongly on the relative sign of at and as. The conclusion of the
letter and the article was straight to the point. '(a) The orthoscattering cross section for liquid-air neutrons should be abo~t 300 times the corresponding parascattering cross section. (b) The parascattering cross section for ordinary thermal neutrons should be roughly 100 times the parascattering cross section for liquid air neutrons. For a real singlet state, however, these ratios are of the order of one: Although not stated explicitly in the original article, but as may be easily inferred from the cross sections given there, in the limit of zero initial

SCHWINGER AT COLUMBIA UNIVERSITY 37

energy for the neutron there exists a simple relation between the cross sections (which are purely elastic in this limit)

aortho -

apara = -323r-r (at -

2
as)

(2.3)

The approximate value of as, had already been found by Wigner, but now it became possible to determine its sign, since for a1 and a,, having opposite signs, the difference aortho - apara would be much larger than in the case of identical signs. Naturally, the former alternative appeared to be more likely, as it implied that the as-yet unobserved singlet energy level of a deuteron was virtual.
The chances for successful experimental applications were excellent. Indeed, many experimenters rushed to do so, and the results of the first experiment by Otto Stern and his collaborators were even published before the appearance of the article of Schwinger and Teller.'0 They confirmed the suspected virtual nature of the singlet state.

Exploring the properties of neutrons
In 1937, having made the transition from being an undergraduate to a graduate student (a matter of pure technicality, since he had completed the entire graduate curriculum as an undergraduate), Julian Schwinger remained focused on the physics of neutrons, which was pursued aggressively by the research community at Columbia University. By then, Rabi began to realize that he had taught his protege all he could. Therefore, he encouraged Julian to broaden his contacts and learn from new experiences by interacting with other physicists. Large numbers ofinteresting physicists came through Columbia, and Schwinger literally met all of them. With no more lectures to attend, he just did research; this was the goal he was aiming at and working for all along. He kept on lending his help to experimentalists and in the course of the next two years these collaborations proved to be fruitful; however, only a portion of all this work was ever published, often after a delay of several years. Some of it was presented as short communications at meetings of the American Physical Society, such as the one with Rabi on 'Depolarization by neutron-proton scattering' [6]. A conceptual descendant of the work with Teller, this paper discussed a method for determining the relative signs and magnitudes of singlet and triplet neutron-proton scattering lengths and described an alternative, viable, but not very practical, design of a suitable experiment in which the changes of the polarization vector of a neutron beam due to collisions with protons in a hydrogen-rich target would be used to determine the ratio of scattering lengths. The idea of such an experiment was Rabi's, while Schwinger derived the polarization formula which was the heart of this brief report: 'I just worked out the theory of it, which was two lines!>!

38 CLIMBING THE MOUNTAIN

At the same Spring 1937 Washington meeting of the American Physical Society, Hyman Goldsmith and John Manley, both from Columbia, spoke about their joint experiments on neutron absorption [7]. Manley was about to move to the University of Illinois, but at the same time he was still working with Rabi's group. He was a talented experimentalist with considerable experience in molecular beams, but his interests were just then turning to neutron physics. Manley teamed with Goldsmith, who had a good knowledge of virtually all the literature on this subject, and they enlisted Schwinger's help to carry out the computation and interpretation of the data. This work eventually grew into a longer article [10], which addressed the puzzling problem of selective energy absorption of slow neutrons which had been described about two years earlier in England and the United States.31 The absorption of neutrons had all the characteristics of a resonance process. The absorption rates changed if the beam had been previously filtered through a thickness of the same material as the absorber; they seemed to be greater in a given element if the same element was also used as a detector of radiation. The discovery of these properties had led to the concept of neutron 'groups,' actually neutrons of separate bands of different kinetic energies, labelled by letters and characterized by the element which was their best absorber. However, the absorption process itselfwas poorly understood and the existing models involved large numbers of free parameters.
Manley, Goldsmith, and Schwinger explained the energy-selective absorption as a resonance capture in which a neutron and a nucleus create a virtual bound state. Quantum mechanics predicts that the cross section for such a capture by an individual nucleus is a bell-shaped (Lorentzian or Breit-Wigner) function
of energy with width and height depending on the total width r of the bound
state, the resonance energy Bo, and the energy E,

1

a(E) ex - - - - - - •

(2.4)

'

(E-Eo)2+r2/4'

r, the full width of the cross section curve, is inversely related to the lifetime
of the resonant state. The theory was to be tested on the known transmission curves for various thicknesses of rhodium, indium, and iridium, but the interpretation of these data was made complex by several factors such as the absorption taking place in bulk matter, the position of the resonance being affected by a Doppler shift due to recoil (which turned out to be negligible), and also because the angular distribution of resonance neutrons was unknown and had to be assumed.
A particular consequence of the resonance character of neutron absorption is the so-called 'self-reversal' of resonance lines. The energy-selective absorption process removes from the beam those neutrons whose energy is close to the resonance value, and most of them disappear from the beam within a

SCHWINGER AT COLUMBIA UNIVERSITY 39
small thickness of the absorber. A larger thickness is thus less effective in further reduction of the beam's intensity and the apparent absorption coefficient paradoxically appears as a rapidly decreasing function of the thickness of the absorber. The main achievement of Manley, Goldsmith, and Schwinger was the determination of the cross section for the capture at resonance and the width of the characteristic resonance (ofrhodium) from such 'self-reversal' curves. A single resonance was sufficient to account for the activation of the 44 s half-life rhodium state, 104Rh. In doing so, they arrived at the value of the scattering cross section (to be precise, at the effective absorption coefficient, which is proportional to the cross section at the resonance) that was 20 times larger than that obtained in 1936 by Fermi and Arnaldi,32 who had not yet recognized the importance of the self-reversal effects. However, since they defied the great authority of Fermi's school, the recognition of these correct results came only slowly.
On his own: a winter in Wisconsin
One day in 1937, Rabi had a conversation with Julian in which he said something like, 'Well, I have taught you everything I know. Why don't you go and study with other people?' 1 He suggested that Julian might go first to Madison, and work through the winter with Gregory Breit and Eugene Wigner at the University of Wisconsin. He arranged a traveling fellowship for Schwinger for one year: first to go to Wisconsin, and, maybe sometime in spring, he might go and work with J. Robert Oppenheimer's group at Berkeley. This was the Tyndall Fellowship, which Schwinger retained when he returned home to Columbia in the Fall of 1938. Before that trip, Schwinger, in the company of his college friend Joe Weinberg,* also went to Ann Arbor to attend the 1937 Summer School, which was then organized and run by Samuel Goudsmit and George Uhlenbeck at the University of Michigan. The activities at the school did not fully occupy Julian and left him enough time to learn to drive a car, courtesy of a friendly acquaintance.' Julian was fascinated by cars and eventually over the years even developed a strong affinity first for Cadillacs and then exotic sports cars, but for
* \Vcinberg recalled that Julian received graduate credit at Columbia for attending the Summer Symposium at Ann Arbor, Michigan. So Weinberg, who was not yet a graduate student, approached Chlenbeck to request graduate credit as well. To support his petition, he showed him a manuscript he had written on weak interactions. Uhlenbeck glanced at it, said it was 'impossible' because it violated parity-after all, Michigan was the home of Laporte, ofLaporte's Rule fame-and unceremoniously discarded the paper in the wastebasket. Julian stayed in the 6 Y house with the lecturers, for example, Fermi and Uhlenbeck, 33 while Weinberg, feeling a less exalted status, stayed in the graduate dormitory.

40 CLIMBING THE MOUNTAIN
a while he had no opportunity to put this new interest into practice. Until he reached Berkeley he could not afford an automobile; before that, living in New York, he could comfortably get by without one.
Schwinger went to Madison for the fall semester and then stayed on there through the entire severe Wisconsin winter. As Van Vleck telegraphically noted later, 'Columbia is to be felicitated in giving Schwinger a traveling fellowship to Wisconsin in 1937 so that he could get a good education right after his doctorate [sic]. This was the golden year in theoretical physics in Madison with Schwinger, Wigner, and Breit all on campus at the same time.''" He had never before lived alone nor had to fend for himself for that long a period of time; he had always lived at home with only occasional excursions. In Madison, he settled in a small room in a boarding house which Gregory Breit found for him. He had arrived in Madison equipped with a trunk full of clothes and basic necessities which his concerned mother had chosen and packed for him. He still depended on his family for all his daily needs so completely that when the frigid winter weather set in he was freezing in his autumn clothes and suffered unnecessarily, totally unaware that there was a nice, warm winter coat waiting for him at the bottom of his only partially unpacked trunk. 1
For Julian, the encounter with his new energetic hosts did not turn out to be as fertile as his interactions with Rabi. He had arrived in Madison with a specific research project in mind. 'During the fall of 1937 and all through 1938, I was thinking about tensor forces. I was certainly working on a field theory because the inspiration for the consideration of tensor forces came from field theory. I recall a paper written in 1937 by a fairly well known, but not famous, person who worked out a theory of spin-one particles. It could have been Nicholas Kemmer [certainly Schwinger had in mind Kemmer's articles on the "Nature of the nuclear field" and "Charge dependence of nuclear forces"3']; he wrote a paper in which he worked out his spin-one theory. So I read that paper and noticed the spin-orbit tensor forces, which I thought was very interesting. Why don't I incorporate them into the theory? I was a nuclear physicist fundamentally at that time, so I said to myself. "Why don't I see what effect the tensor forces have on nuclear physics'" '1 . Thus Schwinger decided to try to incorporate non-central tensor and spinorbit forces and see what their effect might be on the nuclear bound states and nucleon scattering. He found the atmosphere at the University of Wisconsin very pleasant, largely because he needed a temporary respite from analyzing data for experimental groups. Few people knew him at Madison and nobody expected anything in particular from him. Of course, it was anticipated that he would join his hosts in their research in some way. At that time, Breit and vVigner were completely absorbed in their work on the resonances in cross sections for the absorption of neutrons by nuclei. It was only a year since they had explained

SCHWINGER AT COLUMBIA UNIVERSITY 41
the shape of these resonances in cross sections by the famous Breit-Wigner formula (2.4). 16 Even though not particularly fascinated with the problems they were working on, after his experience with Manley and Goldsmith, Schwinger felt very confident in this area and was willing to join in. Unfortunately, to his horror, he found that the style of collaboration between Breit and Wigner relied on constant interaction, discussions, and excited conversations; in his shyness he perceived all this as 'constant giggling,' 1 which did not sit well with his own more private and concentrated method of working. He decided that he could not commit himself to their rules of engagement and, for fear of being controlled and pressured, he began to avoid encountering them. This was not at all difficult since both Breit and Wigner were day persons, while Julian worked best at night. He had already developed his favorite technique of avoiding unwanted interruptions by working late at night. Now Schwinger was free, with no obligations of student life, courses, examinations, and what at Columbia had merely been a preference in Wisconsin became a norm-he became a completely nocturnal person. He studied and worked in his room until dawn, then slept long, and did not interact with anybody until late afternoon. He still met some interesting people and learned from them a few things which broadened his horizons. The main influences upon him at that time were not Breit and Wigner but Julian Knipp, a theorist who later turned up at Purdue, and Robert Sachs, a young man just one year senior to him, and with whom Schwinger developed a lasting friendship. The two also collaborated in writing a joint paper on the magnetic moments oflight nuclei immediately before the entry of the United States in World War II [32, 36].
Rabi later amusingly summarized Schwinger's year in Wisconsin. 'I thought that he had about had everything in Columbia that we could offer-by we, as theoretical physics is concerned, [I mean] me. So I got him this fellowship to go to Wisconsin, with the general idea that there were Breit and Wigner and they could carry on. It was a disastrous idea in one respect, because, before then, Julian was a regular guy. Present in the daytime. So I'd ask Julian (I'd see him from time to time) "How are you doing?" "Oh, fine, fine!' "Getting anything out of Breit and Wigner?" "Oh yes, they're very good, very good." I asked them. They said, "We never see him." And this is my own theory-I've never checked it with Julian-that-there's one thing about Julian you all know-I think he's an even more quiet man than Dirac. He is not a fighter in any way. And I imagine his ideas and Wigner's and Breit's or their personalities did not agree. I don't fault him for this, but he's such a gentle soul, he avoided the battle by working at night. He got this idea of working nights-it's pure theory, it has nothing to do with the truth.'" But the theory seems validated. 1 37
Breit and Wigner let Rabi know that their contacts with Schwinger were minimal, although they could see that he was doing fine on his own. Schwinger was

42 CLIMBING THE MOUNTAIN
virtually invisible most of the time, but he gave up his plans to go to California, studied eagerly, showed up regularly at weekly seminars and himself gave four talks. 13 His first seminar, in October, was on neutron scattering in ortho- and parahydrogen; then in winter, he spoke twice on the magnetic scattering of electrons. Before returning home in May 1938, he gave one more talk, this time on deuteron reactions. Schwinger did not publish anything major during his stay at Madison. He studied field! theory and made progress on several projects in nuclear physics, which he completed later on (sometimes with the help of others if extensive numerical computations were required).
Joseph Weinberg, it turned out, was also at Wisconsin that year, now as a graduate student. He was very unhappy working with Breit. Weinberg seldom saw Julian, although they occasionally double-dated, and recalled that Julian favored short girls, his own height. He noted that Julian was beginning to get interested in music, a passion of Weinberg, but exclusively in Mozart. Julian's interests were narrow, with no interest in history, or literature, or even biology.* He thought the work that Julian was doing in Madison on the deuteron was uninspiring. In any case, Julian was very reluctant to discuss what he was doing. 33
Schwinger later recalled his work at Wisconsin leading to the prediction of a quadrupole moment for the deuteron, an outgrowth of his study of tensor forces. 'Well, I wasn't exactly inactive then. I was reading the literature. And there was a paper written by Kemmer which was on the then very primitive theory of the mesotron, explaining, looking into the kind of nuclear forces that would come out of that theory. This was in 1937. And among those forces was one that's quite familiar electrically, such as the force between two magnets, which depends on angles, and so I looked at this and I said, that's kind of interesting, nobody's thought about this in nuclear physics. What would it do' So I began in '37, kept on in '38, applied it to neutron-proton scattering, gradually got around to saying what would it do to the ground state of the deuteron and of course what it would do was produce a quadrupole moment. Now I came back to Columbia working on this, totally unaware that meanwhile at the same time they were busy discovering the quadrupole moment. So here in Columbia, independently, the theory, ready to receive the experiment, and experimental facts, and it all fitted together. In other words, things were just exploding.'r He presented his prediction of the quadrupole moment of the deuteron in a talk at the November 1938 meeting of the American Physical Society meeting in Chicago [13]. Rabi and Ramsey had already experimentally discovered that quadrupole moment, but let Schwinger present his result first. In an historic roundtable at which both Rabi and Ramsey were participants, Schwinger later
* In Berkeley he later asked Weinberg 'why Oppy was interested in so many things.'

SCHWINGER AT COLUMBIA UNIVERSITY 43
stated, 'I went to give a paper at the November 1938 meeting in Chicago-the Physical Society-which was generally about the so-called tensor forces and I remember you came to me and said, are you going to talk about the quadrupole moment? I looked at you surprised. I didn't think you knew-and I said, yes, and then you didn't say anything, you walked away, and I didn't until later appreciate that in a way you were letting me scoop you-I didn't-because nobody paid any attention to it.'17 • *
The only paper bearing his Wisconsin address, and one in which he duly acknowledged his 'deep gratitude to Professors Breit and Wigner for the benefit of stimulating conversations on this and other subjects,' was a letter to the Physical Review 'On the spin of the neutron' [9]. This short paper contained the first quantitative analysis of the scattering data to support the hypothesis of neutrons being spin one-half particles. Previously this proposition could be supported only by arguments of simplicity because all data appeared to be equally consistent with the value of spin being one- or three-halves. This letter was an extension of Schwinger's earlier work on ortho- and parahydrogen [8] and followed it closely in all technical aspects. He recalculated the cross section for a transition between ortho- and para- states of molecular hydrogen assuming spin-~ neutrons. Such high-spin neutrons would produce quintet rather than singlet excited states with protons; the algebra of spin states would be different and would result in a different value for the ratio of cross sections, aortho/apara, than in the case of spin-½ neutrons. The calculated value, of order unity, was in such discord with reality that it removed any doubts one might still have about the spin of the neutron.
The final year in graduate school
Julian Schwinger left Wisconsin and gladly returned home in the spring of 1938. The trip to Berkeley was postponed until after graduation and he could look forward to another year of complete freedom from outside pressure or obligations. Undistracted, he studied intensively and pursued a variety of fields and topics. He considered himself first and foremost a 'quantum mechanician' who completely devoured the works of Heisenberg, Pauli, and Dirac, all of whom he revered as gods and with whose creations he intellectually identified himself. He also developed a working interest in thermodynamics; the kinetic
* lf Schwinger had remained at C:olumbia during the winter of 1937-38, he might have known of the discovery of the quadrupole moment of the deuteron earlier. But since Schwinger was back in C:olumbia during the fall and winter of 1938, it is surprising he did not receive a hint of the experimental result.8 However, in the abstract for the November 1938 meeting Rabi's group only claimed an anomaly. The existence of a quadrupole moment was only asserted in print in early 1939.38

44 CLIMBING THE MOUNTAIN
theory drew him into the study of relaxation phenomena of molecules and eventually to the propagation of sound and acoustic dispersion in gases. 1
Schwinger pursued such interests only as sidelines of his main projects in nuclear physics. He always maintained a keen interest in experimental work and enjoyed the diversity of work on several concurrent projects. Rabi was stunned by Schwinger's surge of energy and was glad to see that after a year in seclusion at Madison, spent on purely theoretical studies, he again engaged himself in experimental collaboration. First of all, the article with Manley and Goldsmith on the width of nuclear energy levels had to be written up [10]. The situation was somewhat complicated since the attempts to apply the method to another isotope, 115 In, were frustrated by inconclusive data [12], and Manley in the meantime had gone to the University of Illinois in Urbana. Goldsmith teamed up with Victor Cohen, another denizen of Columbia laboratories, who also worked on nuclear magnetic moments.
At the end of the decade of the 1930s, one of the most interesting experimental challenges was to devise techniques for measuring the magnitudes of neutron~proton scattering cross sections. The first attempts were undertaken as early as 1936 by Enrico Fermi. Fermi was the inventor of many practical methods which made it possible to analyze complex nuclear scattering data. The difficulty in measuring the scattering of neutrons off protons was that the latter were bound in a material such as paraffin. Fermi pointed out that in typical experiments with slow neutrons on paraffin targets, hydrogen nuclei in paraffin in general could not be treated as free protons unless neutrons have energies above the ground state vibrational level of the paraffin molecule. 19 This energy level is about 0.3 eV, which is roughly ten times the energy of thermal neutrons. Although it was possible to estimate the effects of binding, the results involved a high degree of uncertainty due to subtle factors, such as the effects of imperfect geometry of the beam and counters, the thickness of the scatterer, and the scattering of neutrons by carbon nuclei in paraffin. With still quite rudimentary experimental methods, which further added to the uncertainty, it was easier to use higher neutron energies, of the order of at least a few electronvolts. Although in this range of energies it was difficult to generate neutrons sufficiently homogeneous in energy and design selective detectors, the total cross section could be easily determined from the exponential drop of intensity of the beam as a function of the thickness of the scatterer.
Cohen, Goldsmith, and Schwinger achieved the equivalent of a monoenergetic source by utilizing the resonance levels for neutron absorption in the energy range of between one and ten electronvolts. Rhodium plates surrounded by cadmium that removed background thermal neutrons served both as absorbing filters and energy-selective detectors. Irradiated with neutrons, the detectors emitted secondary ionizing radiation which was subsequently

SCHWINGER AT COLUMBIA UNIVERSITY 45
measured with proportional Geiger-Millier counters. In this particular experiment, Schwinger's role was more than just providing theoretical support: he was truly dominant in all aspects of the work. The original suggestion to do the experiment came from him, and he designed it and fully participated in taking the data. 13 The experimental procedure was not very sophisticated; it consisted of essentially irradiating samples with neutrons from a radon-beryllium source and measuring secondary radiation, but it required much leg work since the experimenters did not have a laboratory and equipment of their own. The Geiger counters were located on the other side of the building from the neutron sources and rapidly decaying samples had to be rushed back and forth across the Pupin Laboratory building. (The separation was presumably necessary to avoid background radiation.) Most of this running took place from late evening until the middle of the night. Later, Schwinger's co-workers would retire but he, after taking a hearty meal, would return to his desk for several hours of quiet work and study. Hamermesh recalled that at the time 'I would work up at NYU or City College, come to Columbia around three o'clock, start doing calculations. Julian would appear sometime between four and six and we would have a meal which was my dinner and his breakfast, and then we would begin the evening's work, which was a strange combination of theoretical and experimental work. We were experimenters, if you can call us thal fhat is, we were
capable of putting foils in front of a radon beryllium sr y.ce and measuring
transmissions through them and activations, like grabbing the foils, running down the hall of Pupin-it was on the top floor-running like crazy, putting the foil on a counter, and taking a reading. And then we would run back, put them up again, and start doing theoretical work. And we would work rather strange hours. It seemed to me that we would work usually to something like midnight or one a.m., and then go out and have a bite to eat. This would mean two or three hours during which I would get educated on some new subject. I learned group theory from Julian, and I must admit I forgot it all immediately, but as I recall, I had all of Wigner's book given to me, plus a lot more at the time and this was a regular process we went through and I think this must have gone on for a year or so and we started doing calculations of ortho-paradeuterium ahd on ortho-parahydrogen, scattering of neutrons, and this involved just an unbelievable amount of computation.'12
Feld was also involved in this experimental work. 'Probably when Morty and the other people working with him at Columbia had gotten pretty tired of running up and down the hall with the foils, I was recruited, as a sophomore then, to do the running. I guess Morty doesn't remember but I spent six months at Columbia doing the sprinting. I was a pretty good sprinter. I didn't know anything else but they were studying resonances in rhodium-I've forgotten what the mean life is now, but it's really very short [44 s]. You had to take

46 CLIMBING THE MOUNTAIN
these foils and sprint the 40 yards from the irradiation to the Geiger counter and I was the fastest sprinter they could find. I was a real good sprinter then, so I made out real well. As a result of that I not only got to hang around at Columbia at night but even when they went up to see Julian to consult on the theory or when something had gone wrong with the experiment or they got bored and just went up to talk with Julian, I was allowed to go with them, and so I got to listen.'4 When all the measurements were done, Schwinger computed the proton-neutron cross section and obtained a magnitude of 20 barns, substantially larger than the then accepted value of 13 barns calculated earlier by Fermi and given in the Bethe 'bible.'14 This result 'remained valid over the years'29 and was cited as a benchmark value well into the 1950s [11]. The increase in the cross section affected the singlet neutron-proton interaction Schwinger had calculated with Teller [8]. The experiment was a diversion for Schwinger from several other undertakings, directed mostly towards a better understanding of the character of nuclear forces.
The contemporary theories of the neutron-proton interactions were based on the Schrodinger equation for a two-particle wavefunction depending on the coordinates and spins of participating nucleons. The potential energy was a function of the distance between the nucleons; in addition, there was an exchange operator, the action of which interchanged the variables within the wavefunction. There were four types of such operators, including the case of no exchange at all, known as the Wigner force. Another possibility was an operator that exchanged only the spins of the interacting nucleons, known as the Bartlett force. The Heisenberg force exchanged both spin and coordinate variables, and the fourth type of interaction, known as the Majorana force, took place by the exchange of coordinates alone. No single such exchange process was able to describe all the properties of the neutron-proton interaction. For example, under the com;dinate-switching Majorana operator all eigenstates of odd angular momentum quantum number changed their signs, making the interaction angular-momentum dependent. On the other hand, the sign of the Bartlett potential alternates with increasing values of the total spin. These changes of sign make the force oscillate between being repulsive and attractive, which was against experimental evidence. Therefore it was believed that tlfe interaction involved a mixture of all kinds of exchanges with the Heisenberg or Bartlett forces contributing to about one-quarter and the Wigner or Majorana forces to three-quarters of the total interaction potential.40
In order to find more about these forces, Schwinger decided to turn to more advanced applications of the interaction of neutrons on light nuclei. He still continued his friendship and collaboration with Lloyd Motz, and together they started to work on the interaction of thermal neutrons on deuterons. A letter and a Physical Review article [16, 17] appeared sometime later, in 1940, and was

SCHWINGER AT COLUMBIA UNIVERSITY 47
completed by an exchange of correspondence, for by then Schwinger had left Columbia for Berkeley. This work was interesting in certain respects: it again demonstrated that Schwinger had achieved maturity in handling extensive, complex calculations. It was mostly a computational piece of work, conceptually straightforward but very complex in execution. The point of departure was the interaction potential of the most general form which involved both position and spin exchange operators, assuming equal forces between both kinds of nucleons. The inclusion of polarizations would have been exceedingly difficult and cumbersome, so Schwinger and Motz decided to neglect them; they also replaced the deuteron's exact ground state wavefunction by a superposition of two Gaussian functions whose height and width were determined from graphical fitting. Despite these simplifications, the calculation was still a complex quantum three-body problem, the handling of which required considerable technical virtuosity. The challenge lay mostly in the ingenious mixing of approximations based on physical intuition with the mathematical methods of solving integral equations, so that the problem could be simplified enough to be reduced to a system of 20 linear algebraic equations solvable with the help of mechanical crank calculators. (They thank a Jerome Rothenstein for help on the numerical work.) Schwinger and Motz had access to the recent, still unpublished, accurate results of Dunning and his Columbia student Carroll. After comparing them with their own calculations they had no doubt that they agreed best with the mixture of the coordinate-exchanging Heisenberg and Majorana forces, without any admixture of Bartlett or Wigner interactions.
Schwinger also worked on similar subjects with Morton Hamermesh, his good friend with whom he had studied together and occasionally played chess in the past. As we have noted, they had also interspersed experimental work with their theoretical calculations. Together they generalized the Schwinger~ Teller theory of scattering by ortho- and parahydrogen to the more complex case of deuterium and to a wider range of neutron energies. It was good phenomenological work, aimed at finding the cross sections for transitions from the ground state to other low-level states of ortho- and paradeuterium, which in conjunction with experiment could be useful for determination of the spin dependence of the nuclear force. This research was completed in 1939, and presented at the APS meeting at Columbia in February [14], but Schwinger's work on new projects delayed the publication of the detailed article. Hamermesh describes the agony of writing this paper vividly. 'Well, this work went on for a while and we got all these computations done, except that this was a period, as I recall it was around 1938, beginning of 1939, and I think Juliar, -~ •. 5etting ready to go off to Berkeley, and the paper was done and we were going to write it up and I looked upon this as my magnum opus. You know, I was going to be doing a thesis with Halpern, but who cared about that. This was really great

48 CLIMBING THE MOUNTAIN
stuff. Then we started to write the paper.* The only trouble is that at this time Julian was already very much interested in the tensor forces and I remember very well helping him with some calculation involving the coupled differential equations that you get; [moreover,] I was a great reader of the literature and I was always telling him about interesting problems and unfortunately one day I mentioned the absorption of sound in gases and that started him off on an enormous amount ofwork which I don't think he ever published, as far as I can tell. But he did all sorts of calculations on this and there I was, trying to get him to write a paper and he's a rather finicky writer-maybe he isn't so finicky any more-but I can recall that there were only a few weeks before he was to leave and there was the paper and we were still in the first paragraph and every night we would start, we would write six or seven lines, and we wouldn't get it done, and here I could see the time slipping and I would go home and I would cuss hell out of him-to myself. And at one point I contemplated murdering him, but I didn't. He went off to Berkeley, paper not done. 12
'The next time I saw Julian was at Cambridge. I came to the Harvard Radio Research Lab in '43 and Julian arrived there about the same time, at the radiation lab, and we saw each other and he said to me, well, you know, we really ought to write that paper. That's a great idea. It turned out, of course, he really had a point. He had found a very neat trick for reducing all this unbelievable amount of calculation that we had to do to what then amounted to four days of work, and so we did it all over again very, very quickly and the paper was finished in about two weeks, I think, of writing. He had improved his style by then and it was published I think in '46 [33 j and another one in '47 [38 j. Well, essentially what I'm trying to say is that I think I should claim that I'm Julian's first student. I believe I learned more from him than I learned from anybody else. In fact, I think he's the only one from whom I ever learned anything.' 12 Julian's incredible productivity always made it difficult for him to find time for polishing up the details and writing papers. On this occasion, the delay was extremely long because of the war; the paper, under the title 'The scattering of slow neutrons by ortho- and paradeuterium' [33 j, did not appear until the end of 1945, more than six years after the original calculations had been completed. Schwinger's attitude towards writing papers, to say it mildly, was rather hesitant. He was so full of ideas that he assigned low priority to putting finishing touches to essentially completed work. He also often felt he could improve the paper if he waited a bit to come up with a better idea for doing the calculation more elegantly, which was certainly true in this case. Nothing illustrates Julian's
* Elsewhere Hamermesh recalled, 'I remember that at one point when we were trying to write up our result for publication we worked steadily for several davs with little sleep. We went to a seminar of fermi's and both fell asleep during the whole seminar.'·11

SCHWINGER AT COLUMBIA UNIVERSITY 49

attitude in these matters better than his work on the theory of nuclear tensor forces.
Recall that Schwinger developed the concept of tensor forces during his stay in Wisconsin. He was frustrated by the fact that the existing theory, while capable of providing reasonable agreement with the experimental data 011 nuclear binding energies or total cross sections, could do it only with persistent discrepancies. He hoped that the gap between the experiment and theory could be narrowed or eliminated with an admixture of yet another type of force. If, like all other fundamental forces, it were invariant under rotation and space inversion it could, in principle, be proportional to any even power of the product (<r; • r) of spin and position operators. Here ½<1; is the spin of the ith nucleon, and r is the relative position of the two nucleons. However, for spin one-half particles, all higher powers of this product reduce to the lowest order ones, leaving only two candidates [13, 22, 23, 24],

(2.5)

where

(2.6)

and where½ Tis the isospin of the nucleon, with Tz = ±I for the proton or neu-
tron, respectively. Interactions not involving S12 were a linear combination of the conventional Majorana, Heisenberg, Wigner, and Bartlett forces described above.
Schwinger chose this particular linear combination in order to have zero spatial average over all directions in space. Despite its resemblance to the classical expression for the magnetic coupling between two magnetic dipoles of magnetic moment <T, he expected that the strength of this new interaction must be characteristic of the other nuclear forces, submerging any corrections due to the electromagnetic spin coupling.
The introduction ofthe tensor force was Schwinger's first significant and truly original contribution to nuclear physics. It did not merely add yet another phenomenological term to obtain somewhat better agreement with experimental data; the tensor term had a profound effect on the symmetry properties of the distribution of nuclear matter inside neutron-proton bound states, and even changed the quantum number structure of nuclear energy levels.
Firstly, the ground state wavefunctions oftwo-particle bound states created by central forces are always spherically symmetric. This would preclude deuterons from having electric quadrupole moments. On the other hand, by their very nature tensor forces endow the deuteron with a non-zero quadrupole moment. In 1938, Schwinger had not yet heard about any experimental indication in

50 CLIMBING THE MOUNTAIN
support of such a claim, in spite of the ongoing experiment in Rabi's group.38 His prediction was made without any basis of quantitative information, and he could not yet even say whether the quadrupole moment was negative or positive. No wonder he was cautious and somewhat apprehensive about announcing the new idea publicly. When he went to the Chicago meeting in November 1938, he learned, to his astonishment, that Rabi's group was just at the same time discovering the quadrupole moment by using his molecular beam techniques, as described above. Soon afterwards Rabi's group indeed measured the quadrupole moment, consistent with the distribution of charge in the shape of a spheroid prolate 14% along the direction of the deuteron's spin axis.42
The second major departure from established theory was that while all central forces were invariant under rotations of space and spin coordinates separately, the Hamiltonian of the tensor force was not; it required a coupled rotation of space and spin reference frames. In other words, the Hamiltonian operator was invariant only under those rotations in which the observer's point of view turned simultaneously with the space coordinates.
Therefore, with central forces alone, the operators of orbital angular momentum and spin commute with the Hamiltonian and the quantum numbers of two nuclei comprise of the values Land S of the angular momentum and spin, and their respective projections mr and ms. Incidentally, these were the same quantum numbers as used in atomic spectroscopy, and the lives of early nuclear theorists were made easier because the language and many useful techniques of special functions developed for atomic physics were readily adaptable for new applications in nuclear physics.
Just as in atomic physics, the situation changes when spin-orbit forces are considered. With even the smallest admixture ofa tensor interaction, the energy eigenstates of nuclei must be described by a different set of quantum numbers
= because the total angular momentum J L + S, rather than L or S separately,
commutes with the Hamiltonian. Although the eigenvalues J of the total angular momentum and its projection m, still remain good quantum numbers, the total spin and its projection no longer do. In the case of deuterons, the Hamiltonian is symmetric in spin variables and the corresponding wavefunction is either symmetric or antisymmetric. This makes it possible to distinguish between the singlet and triplet states from the criterion of symmetry alone, which permits the use of total spin as a quantum number in this case. However, ms is not available; in its place, the fourth variable necessary to provide a complete set of quantum numbers of a neutron-proton bound state proposed by Schwinger was parity, the eigenvalue of the space reflection operator. In consequence, the energy eigenstates were mixtures of wavefunctions corresponding to either even or odd values of L, since these transformed differently under reflections. One important consequence of that was that even the stable ground state of the

SCHWINGER AT COLUMBIA UNIVERSITY 51
deuteron was different; in the spectroscopic notation, it was a combination of the states 3 S1 and 3 D1, while in the absence of the tensor force it was a pure 3 S1 state.
In order to investigate the amount of the admixture of the tensor potential, Schwinger wanted to compute the ground state wavefunction of the deuteron, the cross sections for radiative capture ofthermal neutrons, scattering of neutrons by protons, and an especially interesting process-the photodisintegration of deuterons-which would provide accurate information about the deuteron's binding energy. For this he needed precise solutions of the Schrodinger equation with the tensor potential method. Unfortunately, despite using the simple square well potential, he could not find analytical solutions even for the lowest energy states. He realized that the equations must be solved numerically by power series expansion. Schwinger had done numerical calculations before, but this time the task was overwhelming and it would take him away from fundamental research. Therefore he decided to wait and look around for someone more adept in this art than himself. He abandoned the largely finished work, made a preliminary announcement ofit at the APS meeting in Chicago in November 1938 [13], as noted above, but eventually published the entire work only in 1941, sharing the credit with William Rarita, who had done the numerical calculations, while on leave (from Brooklyn College) at Berkeley. The articles became known as the famous Rarita-Schwinger papers [23, 24 [, which had considerable impact on the development of theoretical nuclear physics. (It is interesting to note that in [23] Schwinger again thanks Breit and Wigner for the benefit of stimulating discussions at Wisconsin, where he began the investigation. Of course, the presentation improved with the pas-
sage of time, and he thanks J. R. Oppenheimer and R. Serber as well.)
References
1. Julian Schwinger, conversations and interviews with Jagdish Mehra in Bel Air, California, March 1988.
2. Lloyd Motz, interviews and conversations with Jagdish Mehra in Los Angeles, California, 25 November 1988.
3. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 ( 1935 ). 4. Bernard T. Feld, talk at J. Schwinger's 60th Birthday Celebration, February 1978
(AIP Archive). 5. Edward Gerjuoy, talk at the University of Pittsburgh and Georgia Tech, 1994, private
communication. 6. I. I. Rabi, talk at J. Schwinger's 60th Birthdav Celebration, Februarv 1978 (ATP
Archive).

52 CLIMBING THE MOUNTAIN
7. Norman Ramsey, Reminiscences ofthe thirties, videotaped at Brandeis University, 29 March 1984 [in Julian Schwinger Papers (Collection 371), Department of Special Collections, University Research Library, University of California, Los Angeles].
8. Norman Ramsey, interview with K. A. Milton, in Cambridge, Massachusetts, 8 June 1999.
9. P. Debye, Phys. Zeit. 31, 142 (1930); E. Hiickel, Zeit. fur Physik 60,423 (1930). 10. I. I. Rabi, Reminiscences of the thirties, videotaped at Brandeis University, 29 March
1984 [in Julian Schwinger Papers (Collection 371), Department of Special Collections, University Research Library, University of California, Los Angeles].
11. J. R. Oppenheimer and G. Volkov, Phys. Rev. 55, 374 (1939). Precursors were given
by L. D. Landau, Phys. Zeit. Sowjetunion 1,285 (1932); S. Chandrasekhar, M. N. 95,
207 (1935); J. R. Oppenheimer and R. Serber, Phys. Rev. 54, 530 (1938). 12. M. Hamermesh, talk at J. Schwinger's 60th Birthday Celebration, February 1978
(AIP Archive). 13. S. S. Schweber, QED and the men who made it: Dyson, Feynman, Schwinger, and
Tomonaga. Princeton University Press, Princeton, 1994, p. 283. 14. H. A. Bethe and R. F. Bacher, Rev. Mod. Phys. 8, 82 (1936); H. A. Bethe, ibid, 9, 69
(1937); M. S. Livingston and H. A. Bethe, ibid. 245 (1937). 15. F. Bloch, Phys. Rev. 50,259 (1936). 16. J. G. Hoffman, M. S. Livingston, and H. A. Bethe, Phys. Rev. 51, 214 (1937). 17. N. F. Mott and H. S. W. Massey, Theory ofatomic collisions. Oxford University Press,
London, 1933. 18. J. H. Van Vleck, Phys. Rev. 48,367 (1935). 19. L. W. Alvarez and F. Bloch, Phys. Rev. 59, Ill (1940). 20. 0. Halpern and T. Holstein, Phys. Rev. 59,560 (1941). 21. I. I. Rabi, Phys. Rev. 51,652 (1937). 22. I. I. Rabi, Phys. Rev. 49, 324 ( I 936). 23. P. Gilttinger, Z. Phys. 7.3, 169 (1931). 24. G. Breit and E. P. Wigner, Phys. Rev. 49,918 (1935). 25. E. P. Wigner, Z. Phys. 83,253 (1933). 26. E. Amaldi and E. Fermi, Phys. Rev. 50,899 (1936).
27. Quoted by E. Fccnbcrg and J. K. Knipp, Phys. Rev. 48, 906 (1935). 28. E. Teller, Phys. Rev. 49, 421 (1936). 29. M. Flato, C. Fronsdal, and K. A. Milton, (Eds.) Selected Papers (1937-1976) ofJulian
Schwinger (Reidel, Dordrecht, Holland, 1979). 30. J. Halpern, I. Estermann, 0. C. Simpson, and 0. Stern, Phys. Rev. 52, 142 (I 937). 31. T. Bierge and C.H. Westcott, Proc. Roy. Soc. London Al 50, 709 (1935); D. P. Mitchell,
J. R. Dunning, E. Segre, and G. P. Pegram, Phys. Rev. 48, 175 (1935); J. R. Tillman and P. B. Moon, Nature 136, 66 (1935). 32. E. Amaldi and E. Fermi, Ric. Scientifica 7,454 (1936); English translation in Phys. Rev. 50, 899 (1936).

SCHWINGER AT COLUMBIA UNIVERSITY 53
33. Joseph Weinberg, telephone interview with K. A. Milton, 12 July 1999. 34. J. H. Van Vleck, telegram to K. A. Milton, quoted by Victor F. Weisskopf at
J. Schwinger's 60th Birthday Celebration, February 1978 (AIP Archives). 35. N. Kemmer,Nature 140, 192 (1938); Proc. Camb. Phil, Soc. 34,354 (1938). 36. G. Breit and E. P. Wigner, Phys. Rev. 49, 519 (1936). 37. J. Schwinger in Reminiscences of the Thirties, videotaped at Brandeis University, 29
March 1984 [in Julian Schwinger Papers (Collection 371), Department of Special Collections, University Research Library, University of California, Los Angeles].
38. J. M. B. Kellogg, I. I. Rabi, N. F. Ramsey, and J. R. Zacharias, Bull. Am. Phys. Soc., 13, No. 7, Abs. 24 and 25; Phys. Rev. 55, 318 (1939).
39. E. Fermi, Ric. Srientifica 7, 13 (1936). 40. D.R. Inglis, Phys. Rev. 51,531 (1937). 41. Morton Hamermcsh, ktter to Clarice Schwinger, private papers. 42. J. M. B. Kellogg, I. I. Rabi, N. F. Ramsey, and J. R. Zacharias, Phys. Rev. 57, 677
(1940).

3
Schwinger goes to Berkeley
Arrival in Berkeley
In the spring of 1939 Julian Schwinger was 21 years old, a fresh PhD with a sizable number ofarticles already published in the Physical Review to his credit, several of which were quoted and considered significant. The time had come to find a postdoctoral appointment, and this meant leaving home and New York City. Julian was still greatly attached to his family, and had become accus tomed to taking advantage of the special privileges he had earned at Columbia; therefore he was not at all eager to leave this environment. Indeed, this was relatively the freest period of his life, virtually devoid of all responsibilities, and he devoted every minute of it to physics.
After the disappointing experience of the winter trip to Wisconsin, where his contacts with his highly energetic hosts Gregory Breit and Eugene Wigner had been almost non-existent, Julian felt that it would be better to forgo any travel opportunities for a while. With Rabi's blessing he indefinitely postponed his visit to J. Robert Oppenheimer in Berkeley. Considering Oppenheimer's strong personality and domineering attitude towards his co-workers, it was probably a wise decision to stay close to Rabi, who had already shown his superior qualities as a mentor. Rabi was also a powerful personality, but in Julian's case he exercised a different type of influence; their talents complemented each other, and in such a relationship there was no room for domination. Rabi understood Schwinger's difficulty in making a premature transition to adulthood; he did not press any advice on Julian who, outside physics, was just a normal young man with the normal torments of his age and in need of more time to develop and mature.
Before World War II, job prospects for doctoral graduates in physics were generally bleak. Postdoctoral positions were rare and many young PhDs, while waiting for an opening, taught in high school or, if they could afford it, did unpaid work in research. Many young physicists engaged in scientific projects at Columbia were working gratis as guests through personal association with somebody from one or another research team. Unlike them, Julian had won an almost certain right to choose any research institution of his liking; he even received very prestigious unsolicited invitations. Hendrik Kramers invited him

SCHWINGER GOES TO BERKELEY 55
to spend a year in Leyden, and John H. Van Vleck offered him a coveted threeyear fellowship at Harvard's Society ofFellows. 1 Schwinger was not interested in either of these offers. Scientifically they would not provide him with\nything better than he had already been enjoying at Columbia, and the prospect of starting an independent life was still of no interest to him. 'My father's financial situation had begun to improve. Of course, after losing his company during the Depression, he never again acquired that level of affluence, but he was a very much sought after designer of women's apparel on Seventh Avenue-which meant a certain [amount of] mass production, but he was very skilled and I'm sure he got paid very well. There was a difficult period during which everybody was broke and he had to moonlight, I think. That was difficult. He worked for one company and then another one. I can't say affluence, but at least ease had returned. My brother got his degree in business from [Columbia] University and he worked for a bank. Somewhere along the line he decided to become a lawyer. He must have gone to law school. Could it have been Fordham law school? [It was.2 ] He was not yet married,* but probably still living at home, but surely gainfully employed. But I was very happy to leave home.''
By 1939 there was no point in waiting any further and the time had come to part company with Rabi. Julian decided to make a move to Berkeley. Why did he choose to go to Oppenheimer? 'Oppenheimer was the name in American theoretical physics. Where else could I have gone? I had already tried Breit and Wigner and found them wanting. So, who else was there? The only real school of theoretical physics, outside Princeton, was Oppenheimer. So it was inevitable, and I still don't know why I didn't go to Berkeley in 1937. Very strange.... Maybe I was afraid that the second half [of the year] would be just as bad as the first half. I had this example of not being particularly attracted to the gurus of the trade.''
Julian took it for granted that all major transitions of his life happened by themselves, with a kind of invisible intervention from friends or superiors, without having to worry about the mechanism. This time was no exception. Still not convinced that Oppenheimer was the best match for Schwinger, Rabi at the last minute suggested that he go to Pauli instead, but to no avail.t Julian was firm in his decision, .so Rabi just advised him what he must do and how to apply for a stipend, and offered to pull some strings for him if necessary. He vigorously recommended him for a National Research Council fellowship, and from then on everything worked perfectly smoothly. Schwinger was awarded
* Harold got married during the war, while in the Navy.~ t As Rabi recalled: 'I thought he should go to Pauli but [Schwinger] thought Oppenheimer was a more interesting physicist, and he went there.'4

56 CLIMBING THE MOUNTAIN
an adequate $1500 stipend for one year, the value of which was comparable to postdoctoral fellowships of today, and he left for California.
Schwinger arrived in Berkeley on 1 September 1939, the fateful day ofthe German invasion of Poland. 'I remember stopping at a fleabag hotel on Telegraph Avenue and remember getting out in the morning, looking around and seeing a mountain. I had never seen a mountain next to a town before. Oppenheimer had heard of me, and my going to him had been cleared through Rabi. In any event, I had several years of published papers already. However, the only paper that would have interested him was the paper I had not published [0j. I was in nuclear physics by and large; he was not. He was in cosmic rays and aspects of electrodynamics. I don't remember in detail how we got together. [Oppenheimer] certainly said, "Well, you have to have a good place to stay," and I believe he took me around to International House on Bancroft Way. Anyway, he got me established and then said, "I have to find a comfortable chair here because I assume we're going to do a lot of talking." '3 This, however, was not immediately possible in the limited comforts of Julian's new quarters, so they had to continue their conversation in Oppenheimer's office.
In 1939 Schwinger could be characterized as a nuclear physicist. He had a broad background in physics, but all his accomplishments were in the field of neutron and proton interactions. Therefore he surprised Oppenheimer with the choice of his latest interest, the anomalous sonic dispersion of gases, which became the subject ofhis first seminar. This work emerged from a rather obscure aspect of the kinetic theory of gases-molecular relaxation phenomenawhich, as we recall from Chapter 2, was inspired by an article brought to Schwinger's attention by Morton Hamermesh, who was a promiscuous reader of all scientific literature. Julian devoted some time to this subject and produced a considerable amount of calculations on it, which later shared the fate of volumes of his never published research. Oppenheimer complimented Julian on his work, but remarked: 'You are interested in very strange things!'' It was a compliment, but it did not mean acceptance. Oppenheimer exerted a very stimulating influence on his younger co-workers, but he often enjoyed intellectually subduing his entourage, from which he expected respect and enthusiastic affirmation of his ideas. At first it seemed that Oppenheimer and Schwinger would not be able to communicate and interact with each other productively. In Julian's eyes, 'He was overwhelming. And you may appreciate the dilemma that put me in, as was already indicated by the way I behaved in Wisconsin, in which I did not want to be overwhelmed. Oppenheimer was not only impressive, he liked to impress. He was a showman. I was impressed, no question about it. But I also resisted him. Not at the beginning perhaps, but more and more.' 1
Schwinger would accept no idea without prior gestation, remolding and rephrasing it in his own way, and Oppenheimer initially misinterpreted this

SCHWINGER GOES TO BERKELEY 57
reserved attitude as an ostensible manifestation oflack of interest. He allegedly reached the point of seriously thinking about getting rid of the strange newcomer altogether and requesting the National Research Council to transfer him elsewhere. 'I have heard rumors and I do not know the basis of it, that Oppenheimer in my first month was enough disappointed with me . . . that he was thinking of having me sent back to Columbia. Someone mentioned this just in passing to me. It might have been Rabi.'' Schwinger had a frank explanation for Oppenheimer's feelings. 'At the early stage perhaps I didn't measure up in the sense of ritual, in which everybody would come into Oppenheimer's office at some early hour of the morning and they would sit around and talk. I presume I was still a late riser and so never came to these get-togethers. Maybe he didn't like my dissident ways at first. I never heard a direct statement, but it's very plausible that I was a strange fish to begin with until he appreciated that I could produce nevertheless. So perhaps in the first month he didn't quite like the "cut of my jib." '3 Rabi corroborated this rocky beginning. 'I spoke to Oppenheimer later and he was terribly disappointed. He came to the point of writing a letter to the National Research Council suggesting that Julian go somewhere else, because it took a man like Oppenheimer quite a bit to get used to Julian. Pauli once referred to Oppenheimer's students as being Zunicker. Somebody who knows enough German knows what this means-people who nod heads-and Julian was not that way-that, and his hours. However, he thought better of it and soon learned not only to accept him but to love him.'"
The differences were quickly mended after Oppenheimer realized that despite appearances Schwinger was learning intensely from him and that he would become a productive research partner. 'After all, I was there to learn from him, which I did do because he introduced me to areas of physics I had not actively worked on, like aspects of cosmic rays. I did not know anything about cosmic rays, really.'3
Schwinger blended well with the dynamic group of young theoreticians associated with Oppenheimer, who included David Bohm, Herbert C. Corben, Sidney Dancoff, Edward Gerjuoy, Phillip Morrison, William Rarita, Leonard Schiff, Robert Serber, Harland Snyder, and George Volkov. He quickly began to collaborate on several projects and, even before the first two months were over, he and Oppenheimer sent their first joint paper for publication. It was a letter to the Physical Review 'On pair emission in the proton bombardment of fluorine.' [15]
This letter addressed a complication which had arisen in interpreting the data from an ongoing Berkeley cyclotron experiment of Fowler and Lauritsen,5 in which the capture of a proton by fluorine produced an unstable neon nucleus which disintegrated into oxygen via the emission of a very low-energy alphaparticle. Some time after this emission, a substantial excess of energy was

58 CLIMBING THE MOUNTAIN
released in the form of monochromatic gamma radiation. The reason why the reaction had to go through a double-step process instead of the alphaparticle taking the entire available energy was explained by the selection rules that involved angular momentum and parity conservation. What was puzzling was that sometimes, instead of the gamma radiation process, 'it produced an excited oxygen nucleus which strangely decayed into [a stable oxygen nucleus accompanied by the emission of] an electron and positron, and of course everybody was theorizing about new forces and so forth.'3 Why this reaction appeared to be strange was because the relative frequency of its outcome indicated that the pairs must have been produced directly, not by internal conversion. On the other hand, in order to forbid long-range alpha-particle emission, the excited oxygen level was believed to be of odd parity, while the ground state must be of even parity, which would bar any such pair production process. Oppenheimer believed that electrodynamics would break down at the nuclear scale and suggested that a new kind of non-electromagnetic exchange interaction coupling of the electrons to nucleons might be responsible for this effect. He gave the problem to Leonard Schiff, who could not find a satisfactory explanation for this dilemma. 'Schiff was then Oppenheimer's assistant in Berkeley,* and the problem got handed down from one to the next. Oppenheimer was interested in this, so Schiff said, "Hey, Schwinger, why don't you look into this?" So I did. And obviously it got done in a day or so.'3
Typically, Schwinger took a totally conservative approach and refused to engage in any speculation about a new force before ruling out all the more natural reasons on the grounds of existing theory. 'I think I realized that it just was something in the electromagnetic interaction of the forbidden transition that could not radiate light but could proceed by vacuum polarization:3 that is, through the production of electron-positron pairs. The simplest explanation was to assume that the initial oxygen level is of even, not odd, parity. Then the energy could be released only by the emission of two quanta via an intermediate energy level or directly through vacuum polarization. He calculated the probability amplitudes for pair production and double-photon emission via a virtual intermediate state of oxygen. The ratio of respective emission probabilities was
* Ed Gerjuoy, who by this point was a graduate student of Oppenheimer's, recalled that when Schiff gave one of his frequent talks at Oppenheimer's seminar, Oppenheimer was very mean and caustic in his remarks to him, often leaving the gentle Schiff on the verge of tears. However, Gerjuoy realized immediately that the same would not happen to Schwinger, who became Oppenheimer's assistant the following year, because from the first Schwinger could answer all of Oppenheimer's questions until the leader was forced to lapse into silence.6

SCHWINGER GOES TO BERKELEY 59
greater than one, and the quanta from the two-photon process would form a weak continuous spectrum which would not have been observed, thus providing a very simple explanation of the phenomenon. An experimental prediction ensued: if the excited state of oxygen is even rather than odd, then the production of high-energy alpha-particles would also be large at the energies where pair production was large. 'We should expect the resonance yield oflong-range alpha-particles to be comparable with, and probably considerably greater than, the yield of pairs! [15]
The paper on pair emission was written by Oppenheimer and, besides its physical importance in demonstrating the reality of vacuum polarization, is of historical interest as an illustration of the differences between Schwinger's and Oppenheimer's treatments of experimental information, which would create some friction if the two had to collaborate closely. Schwinger believed that no piece of data explainable by established theory should serve as the starting point for a search for departure from that theory. That would be speculation, or worse, a search of the last resort for a magical solution by a person lacking adequate mathematical skill. Therefore, when he was presented with the problem of explaining a strange energy level that decayed through electronpositron production, he first looked for a process of pair production consistent with the conventional electrodynamic interaction. Once the figures agreed, that was it. On the other hand, while writing about this result, Oppenheimer felt compelled to conclude that 'if [the predicted high yield of long-range alphaparticles] is not so, the pair emission itself would seem to provide strong evidence for non-electromagnetic coupling between electrons and heavy particles: [15] Schwinger felt uneasy about Oppenheimer's unsupported comment about other possible explanations of this effect, and complained: 'He wrote that letter to the Physical Review incorporating whatever calculations and ideas I had but at the same time mentioning other possibilities. To me it was a purely electrodynamic process and exactly what was to be expected. On the other hand he, in the spirit of the time, was convinced that electrodynamics had broken down and so in the letter there is still a reference to the possibility of some new short-range force between electrons and protons, which I had no great stock in, but there it was:3
Schwinger later recalled that the experience of this particular calculation dealing with the direct conversion of energy into a pair left him with a deep conviction that vacuum polarization was an entirely real, observable effect. 'Vacuum polarization did not occur to me [as a new phenomenon]. Out of the decaying nucleus there comes an electron-positron pair. Vacuum polarization is just a handy word meaning that there are phenomena in which electronpositron pairs are created. It is just a catchword for indicating that class of phenomena. You can't get rid of it. The phrase vacuum polarization means no

60 CLIMBING THE MOUNTAIN
more than the fact that an electron-positron combination is coupled to the electromagnetic field and it may show itself as real or virtual.''
Years later, while working on the foundations of quantum electrodynamics, the understanding of this fact would give him a definite edge over Richard Feynman who chose to ignore such processes entirely in the first version of his theory. On the other hand, Schwinger felt compelled to include them in spite of all the problems with the divergent calculations of this effect. This would be an important step in his invention of mass renormalization.
Schwinger could have arrived at this discovery as early as 1939. That year Oppenheimer suggested to Sidney Dancoff to try to compute the second-order relativistic electrodynamic correction to electron scattering in the electrostatic field of a nucleus. Dancoff made a fatal, but at the same time quite understandable, mistake in omitting the contribution due to vacuum polarization in which a virtual electron-positron pair is created or annihilated with the necessary energy borrowed and then returned to the field. In such a process the pair creation appears as an effect disconnected from the scattering.* Effects like this were then difficult to visualize, but their omission violated relativistic invariance, leaving some otherwise cancelling terms intact, and Dancoff could not notice that the divergent electrodynamic corrections could be incorporated together into a united electromagnetic and mechanical mass. It is somewhat surprising that he made this error, because his paper includes a footnote in which he notes that Serber pointed out the importance of including 'the Coulomb interaction with the virtual pairs in the field of the scattering potential; which 'results also follow directly from formulae for "polarization of the vacuum."' But Dancoff erroneously stated that 'the conclusions drawn below are unaffected by the presence of the Coulomb interaction: 7 After Dancoff published his results, remarkably the error went unnoticed until after the war, when in 1947 Oppenheimer asked H. W. Lewis to redo Dancoff's calculation, who found that Dancoff had omitted 'certain electrostatic transitions . . . essential to the covariance of the scheme.'8 Lewis, and Schwinger shortly thereafter [43], found a finite radiative correction, thereby providing 'a satisfactory termination to a subject that has been beset with much confusion.' [43] In a different context, Ito, Koba, and Tomonaga repeated Dancoff's error as late as November 1947 and had to rescind it two months later.9
It is paradoxical that although Schwinger knew Dancoffwell and the two interacted socially at the time one of them was already including vacuum polarization in his calculations while the other was ignoring similar processes. History might
* For electron scattering, the relevant process omitted was one in which the positron and photon are virtual, rather than the positron and electron, but as Schwinger noted, all such processes arc part of a whole.

SCHWINGER GOES TO BERKELEY 61
have developed differently if the two of them had had more time to discuss their respective research interests in greater detail.
Schwinger found Oppenheimer to be dazzling and erudite. Despite some conscious dissident refusal to be influenced, during his two-year stay in Berkeley he became fascinated with Oppenheimer and even picked up certain elements of his lifestyle. Julian had always been much younger than his academic peers and had been left behind when others were undergoing the usual rituals of transition to adulthood. Now was the right time to catch up. He was on his own, earning a small salary which nonetheless seemed to be a small fortune to him, but in spite of this sudden independence he was totally inexperienced in worldly matters and needed a role model. Who could fit that role better than Oppenheimer-elegant, attractive to the opposite sex, given to driving impressive automobiles, connoisseur of good food and potent Martinis, and on top of all that an accomplished theoretician, surrounded like a saintly scholar by a circle of doting disciples?
It took no time for a real friendship to develop between these two such dissimilar characters who, to the end, remained quite different from each other; in particular, Julian's shyness and inexperience in social interactions made him feel somewhat clumsy and act accordingly. 'Oppenheimer was immensely stimulating ancl clever, learned. I liked his style and elegance. I responded to his taste in autr ,,10biles and women, should I say.' 3 As for food, they went out together in groups on many occasions. 'To my surprise, he would often ask me out to lunch at an elegant restaurant, which left me very embarrassed because I never knew whether I ought to pay my fair share, or what. But he would pick up the tab until one day, in trying to indicate to me that I was not really doing the right thing, he said, "Oh, by the way, I think I left my wallet at home. Could you possibly ... .'' And so that was a signal. I mean I didn't think of these outings as master and pupil being together so he gently informed me that a little reciprocity would be in order, which made me feel much better.'J
Although Schwinger, following Oppenheimer, was becoming a connoisseur of fine foods, at Berkeley he still remained largely a 'steak and potato' person, which he had been before. As to Oppenheimer's tastes in food, those rather gourmet habits of Mexican food and chili and so on, 'it took me quite a while to respond to that. I'm not sure that my delight with Mexican and Southwest food goes directly back to Oppenheimer, but it certainly was the beginning.'3 He had not tasted Mexican food in New York, 'and it took me a while to get accustomed to the hotness of it. The Martinis were sort of an eye-opener followed by an eye-closer, but I did my best to keep up. It was a different style of life and I appreciated it.'1
Throughout his life, Schwinger was known as a man with an uncompromising taste for fast and spectacular automobiles (his last car was a brilliant red

62 CLIMBING THE MOUNTAIN
Maserati). His fondness for cars certainly began in Berkeley where the very first thing he decided was to go first class and bought 'a red LaSalle, a charming car, just a notch below Cadillac. It was a similar car. I'm sure that Oppenheimer's interest in Cadillacs had its effect on me when I realized that this LaSalle was available. It was, of course, a used car. My income did not allow me to buy new cars, but it was in very good shape. I enjoyed it; it was a marvelous way to begin.'' Julian must have been infatuated with this car because he kept it even after, three years later, he had saved enough to acquire a Cadillac of his own.
Schwinger thrived in the stimulating atmosphere created by Oppenheimer and got along very well with the lively circle of young theorists surrounding him. Never before or later in life did he blend and fuse so tightly with any other group of people. Although he did not abandon his habit of working in seclusion and very late into the night, causing Oppenheimer to remark in a jokingly sarcastic manner that 'his wave function does not overlap' with others, in this case Corben,1 he undertook intensive and productive collaborative projects with Oppenheimer, Gerjuoy, Corben, and Rarita. He would also at least once renounce his routine to take part in an automobile trek, sharing a ride with Oppenheimer, to go to Pasadena. These trips were institutionalized by Oppenheimer who wanted to cultivate contacts with the rest of the West Coast physics research community and arranged regular work-and-some-pleasure trips by several cars to Caltech. In such transitions from Berkeley to Caltech and back Schwinger went with Oppenheimer. 'We certainly left and arrived together. I don't think we always traveled in the same car.'3
Schwinger was quickly consolidating his already considerable confidence in himself. In his career he never made a major mistake or misjudgment that he would have to rectify.* He trusted his opinions and calculations and was even becoming confrontational in the face of experimental evidence that did not agree with his preqictions. During 1940, Luis W. Alvarez and Kenneth S. Pitzer at the Radiation Laboratory in Berkeley conducted a carefully prepared experiment, involving 50 000 counts, on the scattering of slow neutrons with the thermal energy corresponding to a temperature of 20.4 K on ortho- and parahydrogen. 10 They expected to obtain more precise values of the cross sections than were already available, but instead obtained magnitudes that were substantially different from what Schwinger thought to be true based on his earlier theoretical work. [8] He corrected them by pointing out that they had not properly taken into account the effects of the thermal motion of molecules in the gaseous target they had used. But still the inferred
* A possible exception was his initially incorrect, but unpublished, first relativistic Lamb shift calculation which we will describe in Chapter 8. His foray into cold fusion, late in life, was perhaps a misjudgement, but not a technical mistake.

SCHWINGER GOES TO BERKELEY 63
experimental cross section for the scattering of neutrons on protons was 15% lower than the directly measured value of 20 barns. [11 j 'The whole idea of that scattering experiment was to measure the scattering length of neutronproton scattering in the triplet and singlet states. Previously only the orders of magnitudes were available. There was a quantitative experiment coming on line and, as a matter of fact, I got Alvarez very angry at me because I thought that the results he got were quite improbable in the light of what one anticipated and I suggested that the experiments be repeated. I don't know if they ever were, but he was quite angry. Instead of being appreciative of the experiments, I suggested that there must be a flaw somewhere, as the theorist always does, and I must have been arrogant about such things, but I think I was right.''
We recall that when Schwinger left for Berkeley, Morton Hamermesh was quite upset because their joint paper on neutron scattering by ortho- and parahydrogen and deuterium was left unfinished, only to appear a decade later [33, 38]. Only a brief abstract appeared in the Physical Review [14]. But the Alvarez-Pitzer experiment provoked Schwinger to retrieve the research notes on his work from Hamermesh. 'Suddenly there comes a telegram, please send all the calculations, and l packed up a pile of stuff about this high, and shipped it off, heard nothing till suddenly some letters appeared in the Physical Review. There were some experiments by Alvarez and Pitzer, 10 and a short note by Julian [20 j with these calculations. I just gave up on him and did a thesis quick.' 11 In fact, Schwinger modestly acknowledged Hamermesh's contributions: 'The cross section curves necessary for the evaluation . . . have been computed by Schwinger and Teller [8], with extensions and improvements by Hamermesh [14].'
Schwinger wrote a letter to the Physical Review [20], explaining his concern and the two letters of the disagreeing parties were published side by side. Schwinger's letter ended with the words: 'The consequences of these orthopara measurements are in such variance with present theoretical concepts that it would be highly desirable to repeat these measurements and search for systematic I rrors.' Alvarez and Pitzer declined to do that and politely stated that they h(l other priorities: 'The theoretical implications of these data will be discussed in a companion note by Dr. Schwinger. We had planned to repeat the work, to improve the statistical accuracy and to search for possible systematic errors, but pressure of other work now makes that impossible for some time.' 10
Mesotrons
Schwinger had arrived to work with Oppenheimer two years after what was believed to be the hard experimental evidence for the existence of Yukawa

64 CLIMBING THE MOUNTAIN
particles,12 then still called 'mesotrons: had been established. 13 Oppenheimer and Serber were the first physicists in the Western hemisphere who published on the Yukawa CT-field, although not as proponents of his idea. They published some strongly worded criticism of Yukawa's theory, pointing out that it was effectively equivalent to Heisenberg's exchange model, 14' 15 but by the time Schwinger joined Oppenheimer, the latter had already changed his mind. Everybody in Berkeley was talking about mesons, and for the second time in his young life Schwinger had the good fortune to find himself at the right place at the right time.
The essence of Yukawa's new ideas was his explanation of the nuclear force through the exchange of mesons, which in relativistic quantum mechanics led to the concept of mesonic fields. The original Yukawa scalar field had already, in the minds of many, been abandoned in favor of a vector field quantized in a manner similar to electrodynamics. Being massive and charged, it also possessed longitudinal degrees offreedom and was complex. These were unwelcome complications at a time when the methods of quantum electrodynamics were crude and the divergence problem was still unresolved. Still, in a very limited class of problems it was possible to obtain certain quantitative predictions in the lowest order of perturbation theory without totally renouncing the requirements of rigor. Schwinger was familiar with the existing literature on the subject, including the still generally unnoticed publications (in the USA) of the Bristol group of refugee physicists which included Herbert Frohlich, Walter Heitler, and Nicholas Kemmer. It is remarkable that some of this work was devoted to the explanation-on the grounds of nuclear theory-of two effects that would play a very special role in Schwinger's discoveries in quantum electrodynamics. One was an incorrect explanation of a small anomaly in the fine structure of hydrogen, now known as the Lamb shift, then freshly discovered experimentally by R. C. Williams.16 Frc,\hlich, Heitler, and Kahn hypothesized that this effect could be the result of a long-distance remnant of a short-range force associated with the virtual emission of a meson by a proton in the hydrogen nucleus. 1; Earlier the group of Frohlich etal. had suggested that this effect might also affect the magnetic moments of a proton and a neutron. They calculated the self-energy correction to the nucleon energy due to the virtual emission of a vector meson. It diverged, but in an external magnetic field the divergent self-energy could be expanded in a power series in the field strength, and the coefficient of the term linear in the field turned out to be finite. Frohlich, Heitler, and Kemmer risked the interpretation that it represented an anomalous correction to the magnetic moment. 18
Schwinger was familiar with the developments in meson theory, but he did not trust them. He felt uncomfortable with 'subtraction physics' and was always reluctant to use any procedures that he could not fully understand. Therefore

SCHWINGER GOES TO BERKELEY 65
he chose to concentrate on what he knew how to calculate rigorously with the tested methods of quantum mechanics. He returned to the old project on which he had worked at the University of Wisconsin and during his last year at Columbia, which was the inclusion of the tensor component in the potential of the nuclear force. He was prompted to return to this unfinished task by the publication in England of new results with which he did not fully agree.
In 1940, Frohlich, Heitler, and Kahn published an article 19 in which they applied the new meson theory to photoelectric nuclear processes. In particular, the deuteron photodisintegration experiments contained a wealth of useful clues about the nature of the neutron-proton interaction. Heider, Frohlich, and Kahn concluded that the exchange currents related to the strong tensor coupling, derived from the vector-meson model, were predominantly responsible for the emission of hard gamma radiation. In this particular application, they managed to arrive at finite probability amplitudes by circumventing the divergence problems arising from the short-range singularity of the tensor potential of the form 1/ r3 which was inherent in all single-meson theories. They did not do it in an entirely consistent manner, including the tensor forces in some while ignoring them in other parts of their calculations. The value of the photoproduction cross section found by Frohlich, Heitler, and Kahn was large and Schwinger suspected that this was a concealed but straightforward consequence of that very singularity and later commented that 'although this perturbation calculation gives convergent results, it is obviously a dubious procedure to include singularities which, in other aspects of the theory, imply infinities only lent significance by arbitrary methods.' [22] Therefore he finally decided to deploy his own techniques for tensor forces, which had been awaiting practical applications.
Collaboration with William Rarita
The methods used by the Bristol group had evolved from the work of Nicholas Kemmer. 20 The exact nature of the meson field was still unknown, but there existed two possible candidates to understand it: the spinless Yukawa and the spin-1 Proca fields. The interaction part of the Lagrangian density was supposed to be made up as a product of the quantized meson field and two Dirac spinors representing proton and neutron fields. Since the Lagrangian density is a relativistic scalar, the product necessarily had to be constructed in a relativistically covariant manner from the Dirac matrices in such a way that the entire expression transformed as a scalar. The algebra of Dirac matrices produces five such linearly independent products, none of which could be arbitrarily

66 CLIMBING THE MOUNTAIN
excluded. Therefore, in principle, one could have five different meson theories, with meson fields transforming under the Lorentz and reflection groups as scalars, pseudoscalars, vectors, pseudovectors, or a tensor field constructed from a vector. The actual interaction Lagrangian was believed to be a combination of several kinds of such terms and their respective coupling constants had to be determined empirically from the scattering data.
However, because of the ever-present divergences, the calculations of the scattering cross sections could only be conducted in the lowest order of approximation, including only the basic processes that involved the virtual exchange of a meson between a proton and a neutron, or the virtual creation and disintegration of a meson by a pair of nucleons. In this lowest order of approximation, the general form of solutions was essentially determined by the conservation laws and the algebraic form of the multiplier terms introduced in the interaction to make it a scalar quantity. Very similar expressions could also be derived on the grounds of conventional quantum mechanics. \Vith a proper combination of tensor and other types of nuclear potentials, involving the operators for the exchange of positions and spins of the neutron and proton, one could emulate the position and spin dependence of the leading order perturbative results characteristic of all kinds of postulated meson theories, be they scalar, vector, charged, neutral, or mixed. The only important difference was that in the quantum-mechanical approach the results depended on the overall volume of the potential well, but were relatively insensitive to the actual radial dependence of the interaction potential. Therefore the potential could be almost arbitrary. On the other hand, in vector meson theory the radial dependence was predetermined by dimensional considerations and had an unavoidable and very strong 1/r3 singularity at the origin. Therefore Schwinger decided to compute the scattering probabilities on the basis of quantum mechanics, without explicitly engaging himself in the. still murky intricacies associated with the quantization of meson fields. He was not willing to become a field theorist yet. He had tried to work on a similar problem in Wisconsin and found that, by using only the exchange potentials and central forces, it was not possible to reproduce the structure of all possible expressions obtained in field-theoretical solutions. Something was missing, and the only possible addition was a non-central force. 'I had picked up the idea of tensor forces, following it from field theory and then ignoring the field theory background.'3
In the exchange theories of nuclear forces the calculations were based on the standard Schri-jdinger equation,

SCHWINGER GOES TO BERKELEY 67
where Mis the nucleon mass (M/2 is the reduced mass of the neutron-proton system), and in which the interaction potential on the right-hand side is a product of J(r), a function of the distance r separating the nucleons, and O is the exchange operator. The role of the latter is to introduce couplings between the particles in different spin (or isospin) states by switching the position or spin variables within the wavefunction IV(r1, r2, s1, s2). The arguments r; and s; are the coordinates and spins of the interacting nucleons, respectively. One possible exchange operator O was the product of Pauli spin matrices u1, u2, which exchanged the spins of the two interacting nucleons. Such an interaction was called the Bartlett force. The other type was the mathematically identical operator, being a product of the isospin matrices -r1, -r2, which exchanged isospins, thus effectively switching the respective positions of the proton and neutron. The latter interaction was known as the Majorana force. The operator O could also be an identity operator, corresponding to no exchange, and this force was called the Wigner force. The last possibility included the product of u1, u2 and -r1, -r2 , and the interaction, known as the Heisenberg force, was associated with the exchange of both spins and positions.
No single type of the above exchange potentials satisfactorily described even the basic properties of nuclear forces, and it was recognized that combinations of at least two of them were needed. However, no combination of the four central forces would produce the structure of terms obtained in the calculations of cross-sections in meson theories. The central force operators did not form a complete set invariant under rotation and inversion (simultaneous reversal of all spatial coordinates) which was needed to describe fundamental forces, because such a set also contained even powers of u; · r/ r, where r is the vector distance between the particles. For spin-½ particles all higher even powers reduced to the quadratic term (u1•r)(u2 • r) / r2 or the identity. This non-central type of exchange potential was the tensor force that Schwinger had invented in Wisconsin.
\A/ith tensor forces, it was possible to emulate all kinds of probability amplitudes produced in the leading order of perturbative calculations in meson theories. For example, the combination of Wigner, Bartlett, and tensor forces led to solutions similar to those of the neutral meson theory. On the other hand, the combination of Heisenberg, Majorana, and tensor interactions would reproduce the results of charged meson theory, without encountering the difficul-
ties with the divergences due to the singularity of the potential at r = 0.
As Schwinger noted, 'We have avoided these difficulties by employing simplified potentials which permit exact solutions for the pertinent states of the deuteron [13 j and thus allow a consistent solution of the problem. Although the choice of these simplified interactions has been guided by the current mesotron theories, we have disregarded the detailed radial dependence of the nuclear

68 CLIMBING THE MOUNTAIN

forces, obtained from these theories by a highly questionable application of perturbation theory. Two typical forms of the interaction potential are:

1

V = -( •1 • r2) {A+ B(CT1 • CT2) + CS12} J(r),

(3.2)

3

V = - {A'+ B' CT\· CT2 + C'S12} J(r),

(3.3)

S12

=

(CT1·r)(CT2•r)

3

r 2

-

CT1 • CT2,

(3.4)

written in terms of the isotopic spin operators r1, r2 ; the spin operators CT1, CT2; and Eqns (3.2) and (3.3) are respectively analogous to the "symmetrical" and "neutral" potential now in vogue.' [221 The tensor interactions given by Eqn (3.4) are precisely those given by Schwinger in [13], and discussed in Chapter 2-see Eqns (2.5) and (2.6).
The potentials (3.2) and (3.3) included a total of six coupling constants, but Schwinger reduced their number with the help of a phenomenological analysis. He fixed the relative magnitudes of the coupling constants A and Bin Eqn (3.2)
and A' and B' in Eqn (3.3) by using the relationships between the interaction
strengths in the singlet and triplet states of given parity. Therefore there was only one coupling constant associated with the central force and one with the tensor force. The former constant was determined by the known neutron-proton cross section of 20 barns.
The relative strength of the coupling constant of the tensor force was determined from the magnitude of the deuteron quadrupole moment, which, in the absence of tensor interaction, would be zero. The postulate of the 'tensor force was not entirely speculative. The tensor force predicted that the deuteron had a quadrupole moment. . . . I was conscious of the fact that while I had predicted the quadrupole moment, I was predicting it on the basis of no quantitative information, so I could not tell whether the quadrupole moment was positive or negative. To my astonishment, when in 1938 I went to talk* about this theoretical prediction, Rabi at the same time was experimentally discovering the
quadrupole moment. [We recounted this story in the previous chapter. l Then
Rabi measured it and it was positive in some nominal sense. And so one wanted to incorporate as much quantitative information as possible, particularly how the existence of the quadrupole moment would alter the magnetic moment of

* At the same APS meeting in Chicago, Schwinger also gave an experimental talk for Willis Lamb, who 'couldn't go for some reason.' lt 'was about the scattering of neutrons that was the anticipation of the later M/\ssbauer effect: 1 Schwinger had overlapped with Lamb in his last year at Columbia. Lamb was impressed; 'Schwinger knew Dirac's book on The Principles ofQuantum Mechanics very well, and could solve problems on the basis
of having mastered it, which l could not, and l greatly admired him for that' lTelephone
interview ofWillis E. Lamb, Jr_ by fagdish Mehra, 12 March 2000.]

SCHWINGER GOES TO BERKELEY 69
the neutron as inferred from that of the proton and deuteron. This was the beginning of quantitative implications to be tested experimentally, so we were just looking around for what other implications were there.'3
Thus in 1938, Schwinger already recognized that the calculations of the problems of the bound state, partial wave scattering, and radiative capture of neutrons, were reduced to solving the standard Schrodinger equation and did not present any fundamental difficulty. In order to solve the quantum-mechanical two-body problem, Schwinger developed a technique which reduced the calculations to solving systems of simultaneous differential equations that could then be solved perturbatively by iteration. Schwinger's technique was to expand the wavefunctions into spherical harmonics and, simultaneously, in a double power series in integer powers of the distance multiplied by the logarithm of the distance variable. Once properly set up, these computations were not too sophisticated mathematically, but were extremely cumbersome. Doing them on the available mechanical calculators demanded inordinate amounts oftime. Schwinger had very little time to spare, so he temporarily shelved the problem. Tm surprised at the very slow pace of this, but I felt no great urge to publish rapidly. It was not publish or perish in those days. In any case, I was publishing a lot anyway. But when I came to Berkeley, I came with the feeling that I wanted to do some more elaborate calculations with the more realistic models of forces and so forth. Now that came down to numerical work, and while I had done some numerical work on ancient calculators of the time, I looked around for somebody who was a little more adept at this than myself.'3
As we noted at the end of the last chapter, the required help came in the person of a fellow physicist from New York, William Rarita. Rarita had also been a student of Rabi's, but only for a short time. Because of personality differences their relationship had been short-lived. After an unsuccessful attempt to find a problem suitable for a doctoral dissertation, Rarita turned to Gerald Feenberg, who had just arrived from Harvard and was actively recruiting doctoral students. This relationship proved to be much more fruitful and Rarita successfully completed his thesis without any undue difficulty. He eventually obtained a hard-to-get teaching position at Brooklyn College, and taught physics there until the late 1940s.
Rarita came to Berkeley in 1940 for a one-year sabbatical visit. Upon his arrival in California he asked Oppenheimer for guidance in finding a promising research project. Rarita's interests were mainly in nuclear physics and, to his credit, he had published an article with Richard Present on proton-proton scattering in which they had independently arrived at the conclusion that central forces alone were incapable of describing accurately the experimental protonproton scattering data.21 Quite naturally, Oppenheimer suggested to Rarita that he should concentrate on tensor forces, and then said it might be interesting to investigate the problem of photodisintegration of the deuteron and

70 CLIMBING THE MOUNTAIN
relations between tensor forces and cross sections for nuclear reactions involving photodisintegration. 1
Rarita began to read the literature, had some exchange of ideas with H. A. Nye, and then met Schwinger, who invited him to compare notes. Soon they were working together. In the initial stage of this collaboration, Rarita just did numerical work under Schwinger's strict guidance. 'Somebody told me that he [Rarita] was pretty good at calculating, and I went around and said, "Would you like to help me out?" and he did.... He became my calculating arm. I wrote the paper and told him what equations to solve and so forth, and he was very happy doing this, for in the process he learned what was going on.'3
Eventually, this uneven distribution of responsibilities became more level and a true friendship developed between Rarita and Schwinger, who spent long hours working together every day, although of course, in Rarita's words, 'Schwinger worked the night shift.' 'He got up about two in the afternoon and went to the seminar at 4 p.m. After dinner we talked and worked until IO p.m., when I went to bed. He continued to work until five in the morning.' 1
Certain outsiders initially had unfavorable impressions about the nature of this collaboration. 'Interestingly enough, [Schwinger's old friend] Joe Weinberg was there [working on his thesis with Oppenheimer]. Joe had a high sense of justice, an overly keen sense in some respects. He came to me and said, "vVhy are you exploiting Rarita?" Exploiting, meaning I was using him. I said, 'Tm not exploiting him. His name is going to be on the paper." In fact, I said, Tm probably making him." Which is exactly true.* But Joe Weinberg did not see it that way. He was very conscious oflabor and capital and-well, you know that before the war, shall we say, very idealistic communist sympathies were widespread. That's not news of course, but he was a rather rabid person of that type. He saw my collaboration with Rarita as a class struggle, exploitation of the masses. It was rather silly, because ~ach of the two gave what he was best at and ended up with a collaboration. Actually, it suited well the left-wing ideology, "From each according to his best!" He and I were perfectly good friends and he wasn't upset.'3
Indeed, with the passage of time Rarita took over an ever-increasing share of responsibility for theoretical aspects of the work. Together they started from more general aspects of the tensor interaction and properties of the bound states in which Schwinger was principally interested, and then they progressed to the process of photodisintegration, solving which had been Rarita's objective. By then, Rarita had learned enough to deliver on his own. In their first publication together [22], Rarita and Schwinger computed the cross sections for the photodisintegration of the deuteron by 17.5 MeV gamma-rays and showed that 'no significant evidence regarding the tensor interaction may be expected
* Rarita obtained a full professorship at Brooklyn College after his sabbatical.

SCHWINGER GOES TO BERKELEY 71
from rough measurements of the total cross section; the large value obtained by Frohlich, Heitler, and Kahn 19 is illusory.'
Rarita and Schwinger published altogether four papers on tensor forces, the main one of which 'On the neutron-proton interaction' [23 J included the formulation of the problem and applications to the calculations of the ground state of the deuteron, neutron-proton scattering, and then photodisintegration of the deuteron. In retrospect, the article's chief message was that pseudoscalar, not vector, meson theory which included the proper admixture of non-central force appeared best to describe the observed quantities related to these phenomena. The sequence of topics in this article reflected the actual order in which the calculations had been made; however, as we have noted, its publication was preceded by a shorter version devoted purely to photodisintegration [22], possibly to acknowledge the smaller participation of H. A. Nye. A few days before Christmas 1940, Schwinger and Rarita also drove to Pasadena to give a presentation of this paper at the meeting of the Pacific Section of the American Physical Society at Caltech [21]. It was an interesting conference involving physicists and astronomers, which included an illustrated lecture on the enormity of problems encountered during the construction of the world's then largest (200 inch) telescope on Mt Palomar.
One special consequence of the existence of tensor forces was that the deuteron's ground state, which was previously regarded as a spherically symmetric singlet state ofzero orbital angular momentum, now emerged as a super-
position of states that included eigenfunctions ofangular momentum l = 0 and
l = 2 or, in spectroscopic notation, a combination of S and D states. ln other
words, it possessed a non-zero quadrupole, but no electric dipole, moment. By using Rabi's data on the electric quadrupole moment and certain helpful spin sum-rule techniques that Schwinger had developed while working with Corben on the theory of spin- I mesons (see Appendix 1 of [24]), Rarita and Schwinger
found that the l = 2 admixture of the deuteron is about 3.9%. Another inter-
esting result was an estimate of the magnetic moment of the neutron, which, because of the smallness of the D-state admixture, was hardly different from that given by the simple difference of the moments of the deuteron and the proton, and also in agreement with experiment. However, there were significant discrepancies between the magnetic moments of the deuteron and 6 Li, which could be accounted for by the tensor force. Most of the tensor force consequences resulted from the small D-state content of the deuteron, and the magnitudes of tensor force corrections to other nuclear quantities turned out to be rather small, and this in itself Schwinger found rather surprising.
The other source of information on the nuclear force came from the data on the scattering of neutrons by protons and the radiative capture of neutrons. The inclusion of the tensor force, which violates conservation of spin,

72 CLIMBING THE MOUNTAIN
complicated the calculations of scattering cross sections by a partial wave expansion. In a partial wave expansion, the incoming and outgoing wave functions are expanded in eigenfunctions of the angular momentum. The incoming waves have zero orbital angular momentum in the direction of propagation, and therefore the total angular momentum in that direction is equal to the spin quantum number, both of which are conserved quantities in the case of purely central forces. Therefore the orbital angular momentum in the propagation direction is also conserved. In the presence of non-central forces, without spin conservation, the outgoing waves of a given angular momentum become superpositions of different spin states and corresponding states of non-zero orbital angular momentum. This proliferation of possible states complicated the application of perturbation techniques, making it necessary to use the device of spin averaging. The results of Rarita's numerical calculations related to neutron-proton interactions were very encouraging. 'This demonstrates that the spin forces of the type S1 2 are capable of at least a partial explanation of the experimental data.' [23] Previous calculations of the total neutron-proton total cross section, based on a purely central potential, had invariably produced magnitudes larger than the experimentally observed ones. The reduction in magnitude due to the tensor force was less than hoped for (only 2%); not enough to rule out any inconsistency but sufficient for the authors to conclude that 'it is difficult to decide whether a definite discrepancy exists.' [23] They were also able to pronounce with a similar degree of confidence the agreement with less certain data on the radiative capture of slow neutrons (indirectly confirming again Schwinger's value of 20 barns for the neutron-proton cross section), but not for the reactions of photodisintegration of the deuteron.
Schwinger made the calculation of the probabilities of the dissociation of the ground state of the deu~eron induced by the absorption of soft gamma-rays. The dominant mechanism for such transitions involved electric and magnetic dipole transitions to dissociated, respectively triplet and singlet, continuum states of the deuteron. Rarita carried out the numerical calculations for the case of disintegration by a well-defined, strong 2.62 MeV line of the gamma emission from ThC", that is, 208 Tl. For this energy, satisfactory experimental data on total and forward cross sections for the emission of neutrons and protons by photodisintegration were available. The theoretical cross section was 50% larger than experiment, and the forward scattering was predicted to be much larger than observed. Comparison with the data was a clear disappointment and a lesson that quantum mechanics alone was no longer an adequate tool for nuclear physics. Schwinger, who wrote the article, made a momentous statement that 'for the first time we meet a phenomenon whose explanation apparently demands a detailed application of a field theory.' [23 j

SCHWINGER GOES TO BERKELEY 73
The last article, 'On the exchange properties of the neutron-proton interaction', [24] contained a thorough numerical study of the chief experimental implications of the principal types of exchange potential. This included the calculation of the total cross section and the angular distributions of scattered particles in proton-neutron collisions, and the distributions of the nucleons produced in photodisintegration. The previous paper [23] was restricted to even parity states, while here, to study the exchange nature of the neutron-proton interaction, attention shifted to states of odd parity. These states could only be studied by high-energy processes-thus the photodisintegration considered in [23] had an energy of2.62MeV, as opposed to 17.SMeV here. This paper contained considerably more pedagogical details of the calculations, including technical appendices on spin sum-rules and the details of the modified perturbation technique used in the calculations. It clearly lacked Schwinger's characteristic style. 'Rarita was more involved in this now. He had learned the ropes and it was less a calculating problem than a theoretical one. So I forwarded his knowledge of the subject. I don't remember who did the actual work; he may have done most of it. I've always been happy to have collaborators along with me even if I do the major portion of the paper; it doesn't bother me.' Schwinger did the conceptual work anyway, and he liked to think that those associated with him had learned and grown through the process. 'It was another aspect of teaching.' 3
As the summer of 1941 approached, the interests of Schwinger and Rarita began to diverge.* Rarita was emerging from the collaboration with Schwinger with a command of techniques and a greatly increased experience in phenomenological nuclear physics. He certainly wanted to go on putting his new skills to work. For Schwinger, it meant a conclusion of earlier pursuits. After two years around Oppenheimer, his interest in nuclear phenomenology was fading. Schwinger did continue teaching nuclear physics after the war, and made further research contributions, but in 1941 he was somewhat disenchanted by the
* After Schwinger's death, Gerjuoy recalled that 'Rarita did not understand much. He was just pounding the adding machine. Julian was trying to sec if using the parameters which fit the quadrupole moment of the deuteron he could consistently understand the two-particle system. It became clear it was going to work. Rarita's year was coming to an end, and Julian had lost interest in the problem. The two-particle system was understood. In fact what I started working for Julian on was to see whether the parameters would fit the three-particle svstem-the triton, 3 He, and the alpha-particle for good measure.
One day we came in lto find that] Rarita had been chewing on this. Rarita-short and
broad-said to Julian, "Ts the paper going to get written?" Julian said, "Oh, yes, don't worry about it:' Rarita just got mad and he muscled Julian right up against the wall and said, "Julian, if you don't get that paper written, J'm going to kill you!" Two or three weeks later that famous paper got written.'5

74 CLIMBING THE MOUNTAIN
limited conceptual challenges ofa fundamental nature that it could provide and therefore he began to turn toward the more fundamental aspects of quantum field theory. In part, he was motivated by the developments in meson theory, but the influence of and friendship with Oppenheimer played a catalytic role in this transition. Oppenheimer's involvement with field theory had always been immensely serious. He had contributed to it and made an impact on the subject, and always put some of his younger associates to work on the problems of field theory. Schwinger was now entering this new phase that redefined his life and work as a physicist.
Transition to field theory
A short letter 'On a theory of particles with half-integral spin' [25] that was submitted to the Physical Review in the early summer of 1941 marked Schwinger's shift from purely quantum-mechanical methods applied to nuclear physics to field theory. It was the first paper that Schwinger published in which he did not refer to a single experimental 'number.' The paper was inspired by the earlier work ofFierz and Pauli22 on a general theory of particles of arbitrary spin which Schwinger found interesting, but in need of improvement. The short article also turned out to be a parting gift to 'vVilliam Rarita, whom Schwinger included as a co-author, although he did not contribute much to its creation. 'As a matter of fact I was reverting to being a field theorist [from having been a nuclear physicist]. This goes back to the work of Pauli and Fierz, which I had read somewhere and found very clumsy. And so, as a sideline of the development, I had been thinking if one couldn't find a better way of presenting it. It's not clear to me how Rarita came into this, because he did not really contribute anything to the idea; I did it myself. But he was my satellite and I was just thanking him for his friendship, something I have done several times. I could not thank him in money, so I thanked him by saying, "Why don't you do a little thing that was not important and then you're on the paper." '1
In the Fierz-Pauli theory, the particles of integral spin were described by tensors of corresponding rank, while the particles of fractional spin greater than one-half were spinors of appropriate multiple order. For example, wavefunctions of spin-2 bosons were tensors of the second rank, while spin-i fermions were described by wavefunctions with three spinor indices. In order to avoid problems of indefinite energy, additional conditions on the fields were necessary. For a wavefunction 1/fv1... vk of a particle of integral spin k, these conditions had the form
(3.5)

SCHWINGER GOES TO BERKELEY 75

Here the summation convention had been employed; repeated Greek indices are summed over, taking the values O through 3. The first condition was a
direct generalization of the auxiliary condition da V!a = 0 imposed on vector
fields in the Proca theory. In order to derive these supplementary conditions from a variational principle, Fierz and Pauli had to introduce auxiliary fields into the Lagrangian. Schwinger disliked the complications of the formalism associated with multiple-order spinors and auxiliary fields. He proposed an alternative, more elegant approach so simple that he was able to present it in a one-, compared with Fierz and Pauli's 22-page article. (However, he was later to see the virtues of the multispinor formalism-see, for example [153, 190].)
Schwinger proposed to describe higher fractional spin particles by fundamental quantities of mixed transformation properties of spinors and tensors.
Fractional (s = k + ½)-spin particles of mass m would then be ordinary Dirac
four-component spinors and symmetric Lorentz tensors of rank k. As ordinary spinors, they would satisfy the Dirac equation
(3.6)

In Eqn (3.6) the spinor indices of Dirac gamma matrices Ya and the wavefunction 1/Jv1... vk are suppressed. The indices v1 ... vk represent Lorentz tensor components. The positive definiteness ofthe energy still demanded that the conditions (3.5) are met, but there was no need to impose them. Instead, Schwinger postulated an algebraic rather than a differential condition

(3.7)

and then the conditions (3.5) followed as a straightforward consequence of Eqn (3.6). He showed that the number of independent components is properly
2(k+1).
Schwinger also proposed a Lagrangian for a free field of spin-~,

{,

=

-
1/1 1,(yvA,,

+

m)i/11,

-

1-
-:_;,1/1,,(YiJ\,

+

y,,A1,)1/J,,

+

1-
31/1 1,Yi,(Yrar

-

m)yvi/Jv,

(3.8)

resembling the Lagrangian of spin one-half theory, which was extremely simple compared with the artificially complex expressions in the Fierz-Pauli formulation.*

* Although not as simple as it might have been. Many years later, Stanley Deser expressed surprise21 that Schwinger had not pointed out that this Lagrangian could have been expressed much more simply using the four-dimensional Levi-Civita symbol:

/" _
J..,-

2i E

/HKA-
'1/f 11

YKYs3;,1/fv,

= where y 5 is the chirality operator, y 5 y 0y 1y 2y 3•

(3.9)

76 CLIMBING THE MOUNTAIN
Although the Rarita-Schwinger Lagrangian was not unique, it possessed great advantages when interactions were included. In the absence of the external electromagnetic field the expression for the current had the usual form,
(3.10)
and this permitted the incorporation of the interaction with electromagnetic potentials in the ordinary way reminiscent of quantum electrodynamics. Pauli and Fierz needed as many as eight auxiliary conditions to accomplish this. Moreover, in the massless case the Lagrangian (3.8) was invariant under a gauge transformation. The Rarita-Schwinger theory was to become fashionable nearly forty years later, when supergravity necessitated the appearance of the spin-~ gravitino.24
This paper dealing with the higher fractional spin was Schwinger's first article without an explicit and immediate application to an experimental problem, but not his first paper of a predominantly field-theoretical scope. A year earlier Schwinger had published an article with Herbert C. Corben on 'The electromagnetic properties of mesotrons' [18, 19]. Corben, a fresh PhD, was an Australian who, like Schwinger, had arrived in Berkeley to work with Oppenheimer with the help of a fellowship. He was a Commonwealth Fund Fellow. Before coming to Berkeley, Corben had studied meson fields with H.J. Bhabha in Cambridge, England, and published with H. S. W. Massey on the penetration properties of charged spin- I cosmic ray mesons passing through the atmosphere.25 Oppenheimer recognized that Corben's and Schwinger's respective experiences complemented each other and he suggested that they start working together.
Schwinger described Corben as 'a very smart and cheerful fellow. We had no problem getting together and working and collaborating.'3 Soon they combined their strengths, Schwinger in quantum mechanics and Corben in meson theory, and decided to inv,stigate the interaction of spin- I mesons with arbitrary magnetic moments with Coulomb fields. (Massey and Corben had already considered the case of the magnetic moment being unity, the Proca equation. So had Oppenheimer, Serber, and Snyder.26 ) The motivation for this particular subject was the still unresolved problem of substantial discrepancies between the observed interaction properties ofcosmic rays and the values obtained from the standard field theoretic calculations which worked very well for electrons and protons. We now know that the confusion had its origin in misidentifying the abundant cosmic ray mu-mesons (or muons) as the nuclear binding 'mesotrons; the Yukawa particles, which we now call pions. What was really happening in the upper atmosphere was the decay of pions into muons and neutrinos, and it was the (non-strongly interacting) muons that penetrated to sea level. At the time, this was still a completely unsolved mystery, and Corben and Schwinger tried to find an explanation ofthis discrepancy by exploring the

SCHWINGER GOES TO BERKELEY 77
consequences of assuming that the mesons had anomalous magnetic properties which affected their ionizing power. Therefore they decided to calculate the cross sections for the electromagnetic interactions of mesons of spin-0, I/2, or I, and having an arbitrary magnetic moment, with a static external Coulomb field. 'Whether that makes sense I do not know . . . . We just wanted to explore what would happen if you added a magnetic moment. It would obviously strengthen
the electromagnetic interactions and shorten the penetration llength J.'3
The preferred theory of mesotrons at the time was that they were spin1 particles. Therefore, they considered the general form of a Lagrangian for a vector meson field cf>11 of mass m coupled to the electromagnetic potential Av,
(3.11)
= where Dv is a gauge-covariant derivative, Dv<f>µ (av+ ieA,.)cf>/l' The exact
form of the Lagrangian was then dictated only by the requirement that it is a scalar quantity, therefore it was not unique; this was reflected by the presence of a numerical tensor, ,~~,which could be an arbitrary combination of three possible bilinear forms that could be constructed from metric tensors. Using the freedom to define the magnitudes of these constants, Corben and Schwinger wrote the solutions of the equations of motion as a sum of two otherwise
unrelated fields, <f>a = \Va + aa¢, of which one was a vector and the other
a scalar. They noted that the two could transform into each other under an electromagnetic perturbation. This was pure speculation and there was no evidence for any such phenomenon, but nevertheless the proposition was very intriguing. It was still an open question whether the meson fields were scalars or vectors, and the possibility of having both fields mixed and emerging from a single Lagrangian was worth mentioning.
After deriving the expressions for the symmetric stress-energy-momentum tensor, Corben and Schwinger proceeded to find stationary solutions of the equations of motion for the field in the presence of a Coulomb field. The rather complex calculation was handled efficiently and elegantly, thanks to Schwinger's mastery of spherical harmonics and spin techniques. Unfortunately, the divergent behavior of certain wavefunctions near the origin prevented them from producing a complete set of solutions for the Proca mesons in the electrostatic field of a point charge. While this was then a common occurrence in this kind of calculation, Schwinger's first foray into meson theory ended in a mild disappointment.
Without a complete set of finite wavefunctions it was not possible to achieve any meaningful results through a perturbation expansion, and therefore Corben and Schwinger were forced to turn to the Born approximation, which also could not produce a conclusive answer regarding the values of the spin or magnetic

78 CLIMBING THE MOUNTAIN
moment. Despite this drawback,, they were still able to obtain some definite results for the scattering cross sections. They concentrated on the mesonelectron scattering because of its purely electromagnetic nature. The comparison of their results with the experimental data seemed to speak in favor of the theories of spin- I mesons with the magnetic moment equal to one nuclear magneton (that is, Proca mesons) or, to a lesser degree, a theory of spin-½ mesons possessing the magnetic moment of an undetermined value, but other than one magneton. This work was described in a talk at the APS meeting [18] and in a Physical Review paper [ I9], having essentially the same abstract. Of course, we now know that the muon is a spin-½ particle with magnetic moment nearly equal to one.*
The good days are over
After Schwinger's one-year fellowship expired, Oppenheimer made him his own assistant for another year (replacing Leonard Schiff), but no further offer was forthcoming after this extension came to an end. No particular reason for the end of the partnership had to be given, but the pattern had repeated itself again; it took Julian two years of apprenticeship to grow up and match, even surpass, his master. Since Julian could be an assistant only in title, not exactly a helper of the kind Oppenheimer needed, the time had come for him to end the tutelage, move out, and establish his own territory. The assistant's job was in the meantime offered to Schwinger's future lifelong friend Robert Sachs.28
Again, characteristically, the decision regarding where to go next was not Julian's. In his eyes, his career still presented itself as a chain of small miracles; only good things had happened to him before, and there was always somebody out there who was available to take care of the details. This time it was no different. Some consultation between Rabi and Oppenheimer took place, and afterwards Julian was told that a suitable opening at Purdue University existed for him, to which he agreed, and that was that. Later on he would describe the process as 'I was shipped out to Purdue.' He recalled: 'One has to look at what was happening in the summer of 1941. I have no doubt that the planning for the uranium [atomic bomb] project had begun.' Although the Manhattan Project began in Los Alamos only in April 1943, Oppenheimer was involved in it from the beginning. 'I was not privy to all that was going on, but after all there was
* Joseph Weinberg, then Oppenheimer's student at Berkeley, remembered dropping around Julian's 'digs' at Bcrkclcy-'a magnificently appointed suite'-and while snooping around noticed three or four different versions of a tvped manuscript for Physical
Review. It was the manuscript for the paper with Corben l19]. When asked why so many
versions, Julian explained that he was trying to find the 'most compact and elegant prcscntation;2e This is a striking example of Schwinger's perfectionistic style.

SCHWINGER GOES TO BERKELEY 79
Oppenheimer in California, Rabi in New York, who I'm sure had his eye on the long range, and I suspect that they decided that maybe I had had enough of shall we say the coddled life and had to get out in the real world, because I don't recall how this happened. In effect I was told that "You're going to leave and we have a job for you as an instructor at Purdue University." Now why Purdue? It turned out that at that time Purdue had one of the best departments of theoretical physics in the country. There were many bright young people there and that was not a bad choice.'3
In the summer of 1941 Schwinger's happy stay in California was coming to an end, as was Oppenheimer's creative involvement with theoretical physics. June was a particularly busy month for Julian. Maybe sensing the impending turmoils of America joining the World War, maybe out of fear that regular faculty responsibilities would temporarily take him away from research work, Schwinger submitted one short paper and three abstracts before leaving for Purdue, all ofwhich may be regarded as 'patent applications; or progress reports of the unfinished work that could be interrupted by his departure to a new place and situation.
Three of these were brief communications delivered during the APS meeting that again took place at Caltech from 18 to 20 June. Coincidentally, the meeting was addressed by George B. Pegram, at that time the President of the Society, who had admitted Julian to Columbia with a scholarship while he was chairman of the physics department there. Out of the 35 communications presented at the meeting, three were Schwinger's. They were on nuclear phenomenology and gave a good sampling of what his research topics had been. In one [29 j, he attempted to estimate the range of nuclear forces from the value of the quadrupole moment ofthe deuteron based on the observation that its existence directly implied a lower limit to the range of the forces. In another [28], he discussed the stationary nucleonic states produced by a charged scalar meson field. The stated purpose of this calculation was to explain the 'anomalously large theoretical scattering ofcharged mesotrons by nuclear particles! Apossible mechanism was the formation of heavier states of nucleons through strong coupling of nuclei with mesons. The idea that this might be the case came from Gregor \Ventzel,29 who had envisioned states in which the nucleons became 'dressed' in clouds of mesons which produced a shielding effect that modified the strength of the effective nuclear force. Bound together, nucleons and mesons would then form atom-like stationary states of a mass somewhat larger than the known nucleons and of arbitrary charge. Wentzel's paper 'fascinated me enormously and I had begun to work on that and I discovered by doing it in my own way that Wentzel had made mistakes. I should have published the paper in which I wrote all that, but in fact I never did until it was sent to the Wentzel Festschrift 25 years later [28aj. So it was published too late to be of any use.'j

80 CLIMBING THE MOUNTAIN
Schwinger knew that his calculation was more than a technical improvement over Wentzel's work and, although he never did fully publish the results of this research, nevertheless he made a very conscious effort to establish credit for
his results. The abstract l28 J was written simultaneously with the article l26J
with Oppenheimer, which touched upon essentially the same subject, though it was enriched by an analysis of the implications on scattering. That paper was received by the journal on 19 June, the day after he delivered his talk. 'You know it was so easy to do it then that you got lazy about writing the full papers.' Oppenheimer's contribution to this was in part his interest in cosmic rays and 'that, after all, was the underlying stimulus. As to the quantum ideas, Oppenheimer certainly was adequate technically to deal with the semi-classical treatment of spin. . . . He was not adequate, or at least he never attempted to follow or join in, with the quantum treatment, which was more elaborate. But he was contributing, and when I told him about Wentzel making a mistake, he certainly did not question it. Well, he was trying to keep his hands in lots of different topics and it is very difficult to work intensively on all these subjects.' Schwinger wrote the paper essentially, but Oppenheimer was glad to put his name on it too.3
After the Pasadena meeting, Schwinger wrote a long technical letter to Oppenheimer, in which he first apologized for 'misunderstanding our writing agreement.' Apparently this had to do with the failure to complete the long article on the subject. He said 'he had worked out the quantum theory of the pseudoscalar fairly completely; which agreed with the classical theory. He said that he had started looking at the charged pseudoscalar problem, but had not gotten very far. He then described technical conversations he had with Pauli and Weisskopf, presumably at the meeting.30
Schwinger began to write the sequel [28a] which he, in the first reference of the article with Oppenheimer, promised 'to be published soon: but the plans for polishing it for publication never materialized. 'In fact, it was never finished, because I remember that when I sent it to the \Ventzel Festschrift it ended unfinished and somebody commented at that time that it was like a manuscript with the last page torn off, and it was all rather mysterious.'3 The \Ventzel Festschrift article ends with a parenthetical comment: 'The 1941 manuscript stops with this equation left incomplete, although there are sketches of the rest of the argument.' At the time of the Festschrift, Wentzel wrote Schwinger a letter of thanks for his contribution: 'It was very gratifying to me to see, at last, your unpublished paper in 1941 which no doubt was the basis of the Oppenheimer-Schwinger note in Phys. Rev. [26] and presumably known to Dancoff, Serber, and Pauli in their development and generalization of the strong-coupling method. It was only through brief letters from Pauli that I heard of these developments before the correspondence between Princeton and Switzerland was stopped early in

SCHWINGER GOES TO BERKELEY 81
1942. Later, starting in 1943 I felt I had to reconstruct what you had done because I needed problems for my doctoral students Coester, Houriet, Villars, Jost, and others. So you will appreciate how pleased I am to see your paper in my Festschrift.'31
The results of these articles helped in accommodating the puzzling paradox of the early meson theory, which was how mesons could be the agents of the extremely strong nuclear binding force, and yet deeply penetrate all kinds of absorbing media with only relatively feeble scattering effects caused by their interaction with atomic nuclei. The satisfactory explanation on the grounds of the two-meson theory, with the pi-meson being responsible for nuclear binding and the muon (with no strong interaction) abundantly present in sea-level cosmic rays, was still years away, and Schwinger and Oppenheimer [26J followed a path similar to several earlier attempts to explain this strange property.
First, in 1939 Heisenberg, working on the neutral Proca vector mesons, had discovered that a substantial part of their interaction energy might be used to increase the internal energy of a nucleon through reaction effects that converted the self-field of a nucleon into the increased inertia associated with the spin motion.32 'Oppenheimer became interested and was looking for a quantum way of doing whatever Heisenberg had suggested, . . . but he never got beyond the classical way of looking at it, which is what Heisenberg had developed.' 3 By 1940, the popular feeling among theoreticians had changed and the dominant belief was that some peculiar mechanism of quantum interference weakened the nuclear force in some, and strengthened it in other, physical situations. There existed theories supporting this idea as evidence. Bhabha11 and Heitler11 independently suggested that the weakening of the nuclear force could indeed happen in a theory of charged scalar mesons if slightly excited states of charge 2 and -1 existed side-by-side with the ordinary nucleons (neutrons and protons) of charge zero and one. The superposition of scattering effects on the ordinary and excited 'isobar' states would then lead to almost complete cancellation of interactions with the nuclei and near-zero scattering cross sections in the high-momentum limit. In contradistinction, in the low-momentum region the cross sections were not significantly affected, and therefore mesons could be responsible for nuclear binding inside the nucleus while at the same time still having very high penetration power in the atmosphere when arriving as components of highly energetic cosmic radiation. As we have noted, in 1940 and 1941, WentzeJ29 developed a model in which he explained the production of isobaric states of non-standard charge by a process in which the nuclei emitted or absorbed a charged meson. He used a scalar meson field; thus such emissions changed only the charge but not the spin of the nucleon emitting a meson.
Schwinger thought that Wentzel's calculation of the shielding effect of meson clouds was overly simplified on account of several avoidable assumptions which

82 CLIMBING THE MOUNTAIN
could possibly have a prejudicial effect on the character of expected solutions. First, Wentzel employed the perturbation scheme he had developed in inverse, rather than positive, powers of the coupling constant (thus it was a strong coupling rather than a weak coupling expansion); then he positioned the nucleons in a rigid, cubic periodic lattice, effectively assuming that they were infinitely heavy. He calculated the self-energy of the nucleons due to meson exchange in the limit of strong coupling. His results were finite only due to non-zero lattice spacing and finite lattice size. The correction to the self-energy of a single nucleon included a large negative constant term, a positive term due to the mass of the mesons present, and finally a small positive correction that was proportional to the square of the charge of the nucleon, implying that the isobars became increasingly heavy as their charge increased. However, Wentzel's results predicted much too large an energy gap between the isobaric states to produce the cancellations necessary to match the inferred observed value of the scattering cross section, and Schwinger expected that the discrepancy might be an artifact of Wentzel's approximations.
Therefore he decided to revisit the problem, first from the classical and then from the quantum point of view. He was able to carry out the calculations and rigorously solve the problem of a classical meson field coupled strongly to a continuous extended source, and then also produced a quantum calculation which also used an extended source rather than Wentzel's cubic lattice.* This calculation had to be approximate, and Schwinger conducted it in the strongcoupling limit. He also extended the calculations of Wentzel's charged scalar meson field to a neutral pseudoscalar field. However, he failed in generalizing the quantum calculations a step further to a charged pseudoscalar field. Interestingly, the formulae for strong-coupling cross-sections obtained in the classical and the quantum case turned out to agree exactly. These results permitted Oppenheimer and Schwinger to conclude that 'these methods are sufficient to decide in favor of a pseudoscalar, rather than a scalar or vector, field to fix roughly the values of the coupling constant and source size needed to make the model definite.' [26] This marked the second time that Schwinger concluded that the meson was a pseudoscalar; a correct conclusion, although here based on a false premise.
Although related to the incorrect conception of a single 'meson; these calculations represented an important piece of research for Schwinger, who then fully mastered the technique of unitary canonical transformations. It marked an important step in the development of strong coupling theory. In this particular application he used the canonical transformation for separating the
* This appears to be Schwinger's first use of a source function, a concept which became increasingly important throughout his career.

SCHWINGER GOES TO BERKELEY 83
wavefunctions of individual isobaric states, but later it would play a crucial role in many formal applications, eventually including the renormalization method of quantum electrodynamics.
The first of the three papers presented by Schwinger at the 1941 Pasadena meeting of the American Physical Society was a progress report on research with Edward Gerjuoy [27]. Recall that Gerjuoy had been an undergraduate with Schwinger at City College in 1934. Now he was one of Oppenheimer's graduate students. He recalled an amusing incident which happened one day while he, Schwinger, and Oppenheimer were talking in Oppenheimer's long office in LeConte Hall. Two other students, Chaim Richman and Bernard Peters, came in seeking a suggestion for a research problem from Oppenheimer. Schwinger listened with interest while Oppenheimer proposed calculating the cross section for the electron disintegration of the deuteron. That midnight, when Gerjuoy came to pick up Schwinger for the latter's breakfast before their all-night work session, he noted that Schwinger, while waiting for him in the lobby of the International House, had filled the backs of several telegram blanks with calculations on this problem. Schwinger stuffed the sheets in his pocket and they went to work. Six months later, Gerjuoy and Schwinger were again in Oppenheimer's office when Richman and Peters returned, beaming. They had solved the problem, and they covered the whole board with the elaborate solution. Oppenheimer looked at it, said it looked reasonable, and then said, 'Julian, didn't you tell me you worked this cross section out?' Schwinger pulled the yellowed, crumpled blanks from his pocket, stared at them a moment, and then pronounced the students' solution was okay apart from a factor of two. Oppenheimer told them to find their error, and they shuffled out, dispirited. Indeed, Schwinger was right; they found they had made a mistake, and published the paper,'5 but they were sufficiently crushed that both switched to experimental physics. 5
After their midnight repast, Gerjuoy and Schwinger would work till 3 a.m., when they would stop for lunch; then they worked in LeConte Hall until 7:30 in the morning, when Gerjuoy would have to stop to get ready for his duties as a teaching assistant. Evidently, Gerjuoy got little sleep at this time, having also been recently married. For their problem they had to evaluate some 200 spin sums; to check their results, they decided to compute them separately, and compare the results. They disagreed on only 20 terms, but in each case Schwinger was right and Gerjuoy had made a mistake. But, unlike Peters and Richman, Gerjuoy had enough faith in his own abilities, and recognition that Schwinger possessed another class ofintellect, that he did not give up theoretical physics. 5 Moreover, never 'did Julian gloat about it or in any way put me down.'3'' (At some point during their collaboration Gerjuoy taught Schwinger to play pool. 5 )

84 CLIMBING THE MOUNTAIN
They continued their work through the summer and by the end of the year submitted as a more comprehensive paper 'On tensor forces and the theory oflight nuclei' [30].* Gerjuoy stepped into the project on tensor forces where Rarita had left it, and understood the physics much better. 5 At that time, the magnitudes of the tensor and non-tensor coupling constants as well as the parameters describing the radial shape of the interaction potential were already available from the calculation of the quadrupole moment of the deuteron and other properties of the neutron-proton system. The next step in the investigation obviously had to be to reach beyond the two-body problem of the deuteron to the calculation of the wavefunctions oflight nuclei composed of three or four nucleons. The binding energies ofthe nucleons in light nuclei have an interesting pattern which at that time had no theoretical explanation: the alpha-particles 4 He are very strongly bound, while the three-nucleon nuclei of 3He and 3H are considerably less so, and the deuteron binding energy is practically zero on the nuclear scale. Schwinger suspected that this must be an effect due to the admixture of tensor forces in the interaction potential, but he could not prove it directly by an explicit calculation because the technical aspects of the nuclear three-body problem presented an immensely more difficult challenge and were much different from the deuteron problem.
First of all, the spin-orbit coupling brought in by the tensor coupling changed the classification of the energy eigenstates. The total spin of a nucleus was no longer a constant of motion and its value was not a good quantum number for identifying the state of the nucleon. Therefore the traditional spectroscopic classification developed for atomic optical spectra had to be replaced. Although this was true as well in the case of the deuteron, the situation was simpler there because the symmetry or antisymmetry of the wavefunction permitted the conservation of the total spin quantum number. Furthermore, for the two-body system parity could be µsed to eliminate certain angular momentum classifications from the ground state. These special features, of course, could not be applied to larger systems. Matters were further complicated by the greatly increased complexity of the variables needed to describe the spatial structure of the many-nucleon system. Therefore the numerical techniques that worked sufficiently well for Rarita's computations were now entirely inadequate. Instead, Gerjuoy and Schwinger turned to the variational method, which from then on became Schwinger's preferred technique for many years to come. He perfected such techniques in his war work at the MIT Radiation Laboratory a few years later, but nonetheless the paper with Gerjuoy represented an important step in the application of this technique to nuclear physics.
• Gerjuoy actually wrote this paper after Schwinger left Berkeley, and received only minor comments from Schwinger.J

SCHWINGER GOES TO BERKELEY 85

The technique was not much different from the one that had been in use for a while for estimating the ground state energy of a quantum system. In such applications, one starts by making a reasonable guess on the general form of a trial wavefunction ¢, leaving in it a free parameter, say the rate at which it decreases with the distance, and then varies the parameter in order to minimize the value of the energy,

f¢*H¢d 3 r E= f¢*cpd3r,

(3. 12)

where H is the interaction Hamiltonian. The lowest value of E generally provides a good estimate of the ground state energy.
In 1937, L. H. Thomas had pointed out17 that if the binding energy of a nucleus is known, this procedure can be reversed and modified so that it could be comfortably used, through a series of iterations, for finding wavefunctions and the parameters defining the shape of the nuclear potential. Schwinger recognized the power of the variational methods and adopted them as his favorite workhorse, especially for many-body nuclear calculations. He learned how to exploit this technique in its full capacity in his work on waveguides, and later advocated its use in his lectures on nuclear theory that he gave after World War II. It was to play a major role in his later developments of quantum electrodynamics.
As was the case with the Rarita-Schwinger papers on the deuteron, the key aspect of the work on light nuclei was to figure out the exact percentage composition of angular momentum states of the ground state. For example, the ground state of 4 He was an unknown mixture 1So, 3 Po, and 5Do states. As the trial wavefunctions for the variational method, Gerjuoy and Schwinger chose the products of the exponentials of the negative sum of squares of mutual distances between nucleons and the expressions, built of Pauli spin matrices and vector distances between nuclei, that were necessary to provide correct symmetry properties. For the shape of the interaction potential, which was less important, they substituted simple square-wells of the size and depth previously determined from the deuteron data by Rarita and Schwinger [23, 24]. Variational calculations were then conducted by minimizing the energy with respect to multiple parameters: separate rates of exponential decrease for each spin state present in the mixture, and the coefficients describing the relative amounts of these spin eigenstates in the wave function.
The results of these calculations were that the D-states admixtures of 4 He and 3 H were only about 4%, but that only about 50% of the observed binding could be accounted for in this way. This discrepancy led Gerjuoy and Schwinger to conclude that 'the assumption that the ordinary and tensor forces have the same range is not adequate.' [30] Unfortunately the calculation was eventually

86 CLIMBING THE MOUNTAIN
found to be partly incorrect. An error had been made in the choice of algebraic terms defining the spin and angular momentum of the wave functions. The tensor interaction potential introduces a spin-orbit interference which violates the conservation of total spin, while leaving the isospin degrees of freedom intact. Therefore, for describing the state of the nucleus the eigenvalues of the orbital momentum must be used together with isospin quantum numbers. The awareness of this fact came only gradually, and at the time the paper was written Gerjuoy and Schwinger did not know about it. Hence their classification of states was incomplete.38 The error affected the wavefunctions of the 4 D state of 3 H. Actually there are only three independent components of the 4 D state, but Gerjuoy and Schwinger represented it as a combination of four states, which were therefore linearly dependent and not mutually orthogonal. In any event, Schwinger continued this work with Robert Sachs when he went to Purdue, presenting calculations of the magnetic moments of 3 H and 3 He at the 1942 Baltimore APS meeting [32] and a full paper after the war [36].
Departure for Purdue University
Oppenheimer and Schwinger parted as good friends, 'I do have the feeling that Oppie appreciated me particularly. First of all it was clear from our conversations that were rather friendly and intimate even though I still did not quite know how to act in the face of His Majesty.'' Oppenheimer's high regard and respect for Schwinger continued forever. 'When [in 1947] he finally decided to leave Berkeley to go to the Institute las Director of the Institute for Advanced Study in Princeton], he very delicately explored with me the possibility of my coming to Berkeley to take over. I don't know what exactly [to take over], his professorship, his chair, or at least come to Berkeley. That didn't work out, but it certainly indicated a fairly high regard for me.'3 However, as we shall see later, this offer, which Schwinger regarded as duplicitous, left a bitter taste in Schwinger's mouth.
There was another reason why Schwinger did not regret much when he parted company with Oppenheimer after two years despite his great respect for Oppie as a scientist. 'I would have enjoyed staying on at Berkeley;3 but he increasingly felt that Oppenheimer was losing his creativity because he chose to become an organizer, a manager unwilling to be burdened with demanding details. Throughout his career, Schwinger had a deep respect for the 'theorist's manual labor: which he thought of as a key to success; he would even redo a seemingly routine calculation as pure exercise, for the purpose of speeding it up and developing a better command of the techniques. Thanks to this attitude and constant practice, he would go through monumentally complex calculations with ease, without making even the slightest error. Deep respect for detail had

SCHWINGER GOES TO BERKELEY 87
become a characteristic trait of Schwinger's entire career as a scientist. He had a rare talent for making the details actually work for him, be it as a source of approximation in a phenomenological calculation or a decisive criterion of validity and internal harmony of the theoretical logical structure. He had little respect for colleagues who would abandon the details in pursuit of more grandiose plans.
Asked how he coped with Oppenheimer's pervasive influence, Schwinger explained: 'This is not easy to answer. The resistance did come but it took a little longer. I had a feeling that I had found something more interesting in Oppenheimer than in these other people, so I wanted very much to get the feel of him, and learn something from him, of course. But . . . he was constantly on stage himself, which was a little difficult to cope with at first, but I gradually got used to his mannerisms, although I must say that his manner of speaking always left me baffled as to what he was actually saying.' The mannerisms that struck Schwinger in Oppenheimer as the actor, public figure and teacher, were 'certainly the quickness, sharpness, and acuity, plus of course his attitude of putting people off.* One got this feeling that he very much insisted on displaying that he was on top of everything, which he very often was. But as I grew to know him more and more it became clear that since he no longer concerned himselfI'm now speaking scientifically-with the details of things, it became more and more superficial, which I regretted very much. It was a lesson to me, never to lose completely your touch with the subject, otherwise it's all over.' Oppenheimer continued to act even later in life as if he was on top of everything. 'Well, he could pull it off better than most people. He did have a quick brain. There was no question about that, but I think the brain must be supplemented by long hours of practice that go into the fluidity and ease. Without the technical practice sooner or later you get lost.'3
Schwinger left for Purdue with a sense of expectation. On the way to Indiana he briefly retraced the path of his earlier journeys westward from Columbia University,t and went to participate in the Michigan Summer Symposium in Physics. Often referred to simply as the University of Michigan Summer School, the Symposium was a two-month long learning workshop intended to bring together the cream of active theoretical physicists with bright graduate students
* Gerjuoy recalled that he asked Schwinger for help on another part of his thesis one day while both were in Oppenheimer's office. Julian responded by putting the entire multipole expansion formalism on the board, and patiently explained matters to the bright student and co-worker. Just then Oppenheimer came in, glanced at the board, and put both down for wasting time on such elementary matters.5 t Schwinger drove across the country with Rarita. Of course, in accord with Schwinger's habits, they traveled mostly at night. They had only one near accident.39

88 CLIMBING THE MOUNTAIN
from all over the American continent. He had attended it as a graduate student in 1937. This time Schwinger arrived as an invited lecturer, which in itself was an unusual distinction, especially since he joined at so young an age the elite company of Wolfgang Pauli, Frederick Seitz, and Victor Weisskopf. At Ann Arbor Weisskopf and Schwinger became good friends. 1 Weisskopfhad built his career on electron and early radiation theories. After the war, their continuing friendship and frequent contacts actively influenced Schwinger when he set as his goal the quantization of relativistic electrodynamics.
At Purdue University, Schwinger was given a salary of approximately $2000 per annum, only slightly higher than what he was earning as Oppenheimer's assistant. Thanks to his earlier experiences in Wisconsin and trips to Ann Arbor he was no stranger to the new surroundings, even though 'Purdue was a strange place to have [a stimulating environment], in the middle of nowhere, particularly an engineering school by and large. So in effect I accepted. I had gotten used to the idea that somebody was guiding my life and that I didn't have to worry about myself. Indeed, Lark-Horowitz had become chairman of the department of physics, and he set out to organize the collection of bright youngsters who were available cheap in the United States.'3 There was in fact nothing to worry about.
References
1. Mentioned in S. S. Schwebcr, QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga. Princeton University Press, 1994, p. 288.
2. Barbara Grizzell, Harold Schwinger's daughter, interview with K. A. Milton in Reading, Massachusetts, 10 June 1999.
3. Julian Schwinger, conversations and interviews with Jagdish Mehra in Bel Air, California, March 1988.
4. I. I. Rabi, talk at J. Schwinger's 60th Birthday Celebration, February 1978 (AIP Archive).
5. W. A. Fowler and C. C. Lauritsen, Phys. Rev. 56,840 (1939). 6. Edward Gerjuoy, telephone interview with K. A. Milton, 25 June 1999. 7. S. M. Dancoff, Phys. Rev. 55, 959 (I 939). 8. H. W. Lewis, Phys. Rev. 73, 173 (1948). 9. D. Ito, Z. Koba, and S. Tomonaga, Prag. Theor.Phys. 2,216 (1948); errata, ibid. 217. 10. L. W. Alavarez and K. S. Pitzer, Phys. Rei·. 58, I003 (I 940). 11. M. Hamermesh, talk at J. Schwinger's 60th Birthday Celebration, February 1978
(AIP Archive). 12. H. Yukawa, Proc. Phys.-Math. Soc. Japan 17, 48 (1935). 13. S. H. Neddermeyer and C. D. Anderson, Phys. Rev. 51,884 (1937).