alan
/
zotero
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
zotero/storage/QK55TMP9/2010.html

373 lines
87 KiB
HTML
Executable File
Raw Permalink Blame History

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns=http://www.w3.org/1999/xhtml xml:lang=en style lang=en><!--
Page saved with SingleFile
url: https://arxiv.org/abs/2010.10345
saved date: Wed May 22 2024 02:24:08 GMT-0400 (Eastern Daylight Time)
--><meta charset=utf-8>
<title>[2010.10345] The Unpublished Feynman Diagram IIc</title>
<meta name=viewport content="width=device-width, initial-scale=1">
<meta name=msapplication-TileColor content=#da532c>
<meta name=theme-color content=#ffffff>
<style media=screen>body{margin:0;padding:0;background-color:#fff;color:#000;font-family:"Lucida Grande",helvetica,arial,verdana,sans-serif}a:link,a:visited,a:active{text-decoration:none;font-weight:normal}a:hover{text-decoration:underline}img{border:0}em{font-weight:bold;font-style:normal}.primary-subject{font-weight:bold}#cu-identity{font-family:verdana,arial,helvetica,sans-serif;font-size:63.125%;color:#fff;background-color:#222;width:100%;display:flex;justify-content:space-between}#cu-logo{position:relative;left:10px;top:2px;width:300px;height:49px}#cu-logo a img{width:200px}#support-ack{top:12px;right:0%;margin:0 12px 0 0;padding:8px 0;text-align:right;font-size:120%;font-weight:normal;font-family:"Lucida Grande",helvetica,arial,verdana,sans-serif;color:#fff}#support-ack-url{max-width:400px;float:right;display:block}#support-ack-url a{color:#fff;border:none;text-decoration:underline}#support-ack-url a:hover{color:#1e8bc3}#header{background-color:#b31b1b;color:#fff;margin:0;padding:10px 0 10px 0;border-bottom:2px solid #ccc;position:relative;overflow:auto}#header .header-breadcrumbs{margin:0;font-size:1em;padding:10px 0 .2em 10px;font-style:normal;float:left;display:inline-flex;align-items:center}#header .header-breadcrumbs span{margin-right:5px;margin-left:5px}#header a,#header a:visited{color:#fff;text-decoration:none}#header a:hover{text-decoration:underline}#header form{margin:0 12px 0 0;padding:0;text-align:right;font-size:.8em;line-height:100%}#header form input,#header form select{margin:0;padding:0}@media screen and (max-width:768px){.search-block.level-right{clear:both!important}#header .header-breadcrumbs{float:none;text-align:center}}main{flex-grow:1}.flex-wrap-footer{display:flex;min-height:100vh;flex-direction:column}footer ul li{display:flex;align-items:center;font-size:14px}footer ul li a{font-size:13.5px}footer{background-color:hsl(0,0%,95%);color:#000;padding:1em 2em;font-size:0.9rem;-webkit-font-smoothing:antialiased;margin-top:6rem}footer a,footer a:visited{color:#000;text-decoration:none;border-bottom:1px solid transparent;line-height:1.75em}footer a:hover,footer a:active{color:#005e9d;border-bottom:1px dotted #005e9d;text-decoration:none}footer ul{padding:0;margin:0}footer .sorry-app-links .help{font-size:0.75rem;margin-bottom:0;line-height:1.75em}footer .sorry-app-links .help a,footer .sorry-app-links .help a:visited{border-bottom:1px dotted #000}footer .sorry-app-links .help a:hover,footer .sorry-app-links .help a:active{border-bottom:1px dotted #005e9d}footer .sorry-app-links svg.icon{margin-bottom:-2px!important}footer .sorry-app-links .icon.filter-black:hover,footer .sorry-app-links .icon.filter-black:active,footer .sorry-app-links a:hover .icon.filter-black,footer .sorry-app-links a:hover .icon.filter-black{fill:#005e9d!important}footer .sorry-app-links .a11y-main-link{font-size:110%;border-bottom:1px solid transparent!important;padding:0;margin:0}@media screen and (max-width:768px){footer .sorry-app-links.column{padding:0}}.endorsers .help{position:relative;top:4rem}@media screen and (min-width:990px){.endorsers .help{top:5rem}}@media screen and (min-width:769px){.columns{display:flex;flex-direction:row}}.icon{width:.9rem;margin-right:.45em;margin-top:-.15rem}.help{font-family:"Lucida Grande","Helvetica Neue",Helvetica,Arial,sans-serif;display:block;font-size:0.75rem;margin-top:0.25rem}#content,#content-inner{margin:.7em;font-size:90%}#abs-outer,#abs{margin:-0.7em}#abs-outer .leftcolumn{margin:0 0 1em 0;padding:0px;width:calc(100% - 18em);float:left}#abs-outer .extra-services{float:right;margin:0;width:18em}#abs-outer .extra-services span.bib-cite-button{color:rgb(0,0,238);font-weight:bold;padding:.35em;display:block;text-transform:capitalize}#abs-outer .extra-services span.bib-cite-button:hover,#abs-outer .extra-services span.bib-cite-button:focus{text-decoration:underline;cursor:pointer}#labstabs{clear:both;margin:1em 1.5em}#labstabs .labstabs{display:flex;flex-wrap:wrap;white-space:normal;justify-content:flex-start}#labstabs .labstabs>label{order:1;display:block;padding:.75em 1.5em;font-size:.85em;color:#4a4a4a;margin-right:0.2rem;cursor:pointer;font-weight:bold;transition:background ease 0.2s;border-radius:6px 6px 0 0;background-color:#eef5f9}#labstabs .labstabs .tab{order:99;flex-grow:1;width:100%;display:none;padding:1rem;border:1px solid #828282;z-index:1;top:-1px;position:relative}#labstabs .labstabs .tab h1{font-size:1.25em;font-weight:normal}#labstabs .labstabs input[type="radio"]:checked+label{background:#ffffff;border:1px solid #828282;border-bottom:0;z-index:2;color:black}#labstabs .labstabs input[type="radio"]:checked+label+.tab{display:block}@media (max-width:45em){#labstabs{padding-bottom:1em;margin:1em}#labstabs .labstabs .tab,#labstabs .labstabs label{order:initial;width:100%;margin-right:0;margin-top:0.2rem;border-radius:0}#labstabs .labstabs>label{font-size:.8em}#labstabs .labstabs .tab{margin-top:-10px!important;border:2px solid #b8b8b8;border-top:0px;background-color:#ffffff}#labstabs .labstabs label{background-color:#eef5f9;color:black;padding:1em .5em}#labstabs .labstabs .labs-display-bib label{background:transparent;color:black;padding:0}#labstabs .labstabs input[type="radio"]:checked+label{background-color:#acd2e8;color:black;border:2px solid #b8b8b8;border-bottom:0px;padding:1em .5em}}#labstabs .toggle{border:1px dotted #c7d3db;padding:.5em;background-color:#eef5f9}#labstabs .toggle .columns.lab-row{align-items:center}#labstabs .toggle .columns.lab-row .column{padding:.5rem .25rem}#labstabs .column.lab-name{flex-basis:auto;flex-grow:0;font-size:.75rem}#labstabs .tab a{display:inline}#labstabs .column.lab-name em{font-size:11px;color:black}#labstabs .column.lab-name em a{line-height:18px;text-decoration:none;padding:0;border:0;font-style:normal;font-size:11px}#labstabs .column.lab-switch{flex-grow:0}#labstabs .toggle .lab-switch label.switch{position:relative;display:inline-block;width:38px;height:20px;padding:0;background-color:transparent;margin:0}#labstabs .toggle .lab-switch .slider{position:absolute;cursor:pointer;top:0;left:0;right:0;bottom:0;border-radius:24px;background-color:#ccc;-webkit-transition:.4s;transition:.4s}#labstabs .toggle .lab-switch .slider:before{position:absolute;content:"";height:16px;width:16px;left:2px;bottom:2px;border-radius:50%;background-color:white;-webkit-transition:.4s;transition:.4s}#abs-outer .subheader{background-color:#eee;color:#000;padding:.25em 0;border-bottom:1px solid #ccc}#abs-outer .subheader h1{margin:0;font-size:1.1em;padding:0 0 .2em 20px;font-weight:bold;font-style:normal}#abs h1.title{margin:.5em 0 .5em 20px;font-size:x-large;font-weight:bold;line-height:120%}#abs .authors{margin:.5em 0 .5em 20px;font-size:medium;line-height:150%}#abs .authors a{font-size:medium}#abs .dateline{margin:.5em 0 .5em 20px;font-style:italic;font-size:small}#abs blockquote.abstract{line-height:1.55;font-size:1.05em;margin-bottom:1.5em}#abs .metatable{font-size:0.92em;line-height:1.5;margin:0 0 1.5em 20px}#abs .tablecell{padding:.1em .5em 0em 0em;vertical-align:top}#abs .arxivid a{font-weight:normal}#abs-outer .submission-history{margin:1.5em 0 1.5em 20px;font-size:90%;line-height:1.5em}#abs-outer .submission-history h2{font-size:120%;margin:0 0 .25em 0;font-weight:bold}#abs-outer .endorsers{margin:1em 0 1.5em 20px;font-size:small;font-style:italic;clear:both}#abs-outer #abs .dateline{margin-top:15px;margin-bottom:0}#abs-outer #abs h1.title{margin-top:.25em}.endorsers .help{display:inline-block}@media screen and (max-width:768px){#abs-outer .extra-services h2{font-size:15px;margin-bottom:.5em}#abs-outer .extra-services h3{font-size:14px}#abs-outer .leftcolumn,#abs-outer .extra-services{width:100%;float:left}#abs-outer .extra-services,#abs-outer .extra-services .full-text,#abs-outer .extra-services .browse,#abs-outer .extra-services .extra-ref-cite{border:0px;font-size:12px}#abs-outer .extra-services{-webkit-box-shadow:inset 0px 8px 15px 0px rgba(173,173,173,1);-moz-box-shadow:inset 0px 8px 15px 0px rgba(173,173,173,1);box-shadow:inset 0px 8px 15px 0px rgba(173,173,173,1);background-color:#E6E6E6;margin:0 0 1em 0;padding:1em 0}#abs-outer .extra-ref-cite ul li{float:left}#abs-outer .extra-services .full-text ul,#abs-outer .extra-services .extra-ref-cite ul{list-style:none;margin:0;padding:0}#abs-outer .extra-services .full-text ul li,#abs-outer .extra-services .extra-ref-cite ul li{display:inline-block;margin:0 0 .25em 0;padding:0}#abs-outer .extra-services .bookmarks{margin:1em 0 0 0;border-left:0;padding:.25em .5em 0 1em;border-top:2px solid #cccccc;font-size:1em}#abs-outer .extra-services .bookmarks .abs-button-small{margin-top:.25em}#abs-outer .extra-services .browse{margin-top:.5em;border-top:2px solid #cccccc;padding-top:1em}#abs-outer .extra-services .prevnext{margin-top:.5em}#abs-outer .extra-services .browse .current{color:#AB4B02;display:inline}.abs-switch-cat{margin:0 0 1em 0}.browse .abs-switch-cat .switch{display:inline}.browse .abs-switch-cat .switch a{font-weight:bold}.abs-button{display:inline-block;border-radius:5px;border:1px solid #046BAF;font-size:1.25em;color:#046BAF!important;padding:.5em;background:#E6E6E6;margin-right:.3em}.abs-button-small{font-size:1em;padding:.25em 1em;margin:.75em .5em 0 0}.abs-button-grey{border:1px solid #666666;color:#666666!important}#abs-outer .extra-services span.bib-cite-button{margin:.5em .5em 0 0;display:inline-block!important;border-radius:5px;background:#E6E6E6;border:1px solid #046BAF;font-size:1em!important;padding:.25em 1em;font-weight:normal;text-transform:capitalize}#abs-outer .extra-services .extra-ref-cite ul li{margin:.5em 0;padding:0;height:auto}#abs-outer .extra-services .extra-ref-cite ul li a{margin:.25em .5em .25em 0}#abs-outer .subheader{background-color:#fefefe;padding:.25em 0;border-bottom:1px solid #ccc}#abs-outer .subheader h1{margin:0;font-size:.75em;padding:.2em 0 .2em 1em;font-weight:normal;font-style:normal;color:#b55c06}#abs-outer #abs .dateline{color:#767676;font-size:.85em;font-style:normal;margin:2em 0 0 1em}#abs-outer .submission-history{padding:1em;margin:0;background-color:#f5f5f5;-webkit-box-shadow:inset 0px -6px 15px 0px rgba(219,219,219,1);-moz-box-shadow:inset 0px -6px 15px 0px rgba(219,219,219,1);box-shadow:inset 0px -6px 15px 0px rgba(219,219,219,1)}#abs-outer #abs h1.title{margin:0 .25em 0 .5em;font-size:1.5em}#abs-outer #abs .authors{margin:1em .25em 0 1em;font-size:.9em;line-height:1.5em}#abs-outer #abs .authors a{font-size:inherit}#abs-outer #abs blockquote.abstract{margin:0 1em}#abs-outer #abs .metatable{margin:.75em 0 1.5em 1.5em}#abs-outer #abs a,#abs-outer a,#abs-outer .endorsers a{color:#1777bc}#abs-outer .submission-history a,#abs-outer .abs-switch-cat .switch a,#abs-outer .extra-services .full-text .abs-license a{color:#046BAF}#abs-outer .endorsers{display:block;float:left;border:1px solid #eee;padding:1em;margin:1em}#abs-outer .endorsers .help{display:none}}.extra-services{border-bottom:.35em solid #ddd}.extra-services h3{font-size:medium;font-weight:normal;margin:0 0 0.3em 0;padding-top:0.3em}.full-text{margin:0;padding:.5em 1em .5em 1em;font-size:110%;font-weight:normal;border-bottom:medium solid #ddd;border-left:.35em solid #ddd}.full-text h2{font-size:140%;font-weight:bold;margin:0.1em 0 0 0}.full-text ul{margin:.3em 0 0 1em;padding:0}.extra-ref-cite{margin:0;padding:0 1em 0 1em;font-size:90%;border-bottom:medium solid #ddd;border-left:.35em solid #ddd}.extra-ref-cite ul{font-weight:normal;margin:0.3em 0 0 20px;padding-left:0;padding-bottom:0.3em}.browse{padding:0 1em 0 1em;font-size:90%;border-bottom:medium solid #ddd;border-left:.35em solid #ddd}.browse .current{padding:0;font-weight:bold}.browse .prevnext{padding:0.2em 0 0 0}.browse .list{padding:0.2em 0 0.5em 0;font-weight:normal}.browse .switch{font-weight:normal;padding:.2em 0em .7em 0em}.bookmarks{clear:both;margin:0;padding:0 1em .5em 1em;font-size:90%;border-left:.35em solid #ddd}.abs-license{font-size:xx-small;padding-top:0.3em}@media screen and (max-width:768px){#cu-identity{flex-direction:column}#support-ack,#cu-logo{text-align:center;width:100%;left:0px}}@media screen and (max-width:768px){.is-hidden-mobile{display:none!important}.columns.is-mobile{display:flex}}.is-sr-only{border:none!important;clip:rect(0,0,0,0)!important;height:0.01em!important;overflow:hidden!important;padding:0!important;position:absolute!important;white-space:nowrap!important;width:0.01em!important}.button{border-width:1px;cursor:pointer;justify-content:center;padding-bottom:calc(0.5em - 1px);padding-left:1em;padding-right:1em;padding-top:calc(0.5em - 1px);text-align:center;white-space:nowrap}.column{display:block;flex-basis:0;flex-grow:1;flex-shrink:1;padding:0.75rem}.columns.is-vcentered{align-items:center}@media screen and (min-width:769px),print{.columns:not(.is-desktop){display:flex}}@media screen and (min-width:1024px){.columns.is-desktop{display:flex}}svg.icon{height:1em!important}.icon.filter-black{fill:#000000}.filter-dark_grey{fill:#cccccc}a .icon{transition:fill 0.3s ease}a:hover .icon.filter-black,a:hover .icon.filter-grey,a:hover .icon.filter-blue,a:hover .icon.filter-red{fill:#ffffff}.search-block.level-right{display:flex;justify-content:flex-end;clear:right}@media screen and (max-width:768px){.search-block.level-right{justify-content:center;clear:left}.search-block form.level-item{margin-left:12px!important}}.search-block form.level-item,.field.has-addons{display:flex}.search-block p.help{margin-bottom:0}.search-block .input,.search-block select,.search-block .button{font-size:0.75rem;line-height:1.5;height:2.25em;border-radius:2px;border:1px solid transparent}.search-block .button{margin-left:0}.search-block .input{border-color:transparent;box-shadow:inset 0 1px 2px rgba(10,10,10,0.1);border-bottom-right-radius:0;border-top-right-radius:0;border:0;width:100%;max-width:100%}.search-block .control{position:relative}.search-block .select::after{position:absolute;display:block;z-index:4;top:50%;right:.65em;width:0.5em;height:0.5em;content:" ";border:3px solid #0068AC;border-radius:2px;border-right:0;border-top:0;transform:rotate(-45deg);transform-origin:center;pointer-events:none;margin-top:-1.125em}.search-block .select.is-small select{-webkit-appearance:none;-moz-appearance:none;display:block;width:100%;max-width:220px;height:27px;float:right;margin:0px;background-color:#ffffff;background-image:none;-ms-word-break:normal;word-break:normal;border-color:#ccc;box-shadow:inset 0 1px 2px rgba(10,10,10,0.1);border-radius:0}.search-block .button{background-color:#711111;color:#FFF;border-color:transparent}.search-block .button:hover,.search-block .button:focus{background-color:#440A0A;color:#FFF}#header form select,#header form input{padding:0 0.5em}</style>
<link rel=canonical href=https://arxiv.org/abs/2010.10345><meta property=og:type content=website>
<meta property=og:site_name content=arXiv.org>
<meta property=og:title content="The Unpublished Feynman Diagram IIc">
<meta property=og:url content=https://arxiv.org/abs/2010.10345v1>
<meta property=og:image content=/static/browse/0.3.4/images/arxiv-logo-fb.png>
<meta property=og:image:secure_url content=/static/browse/0.3.4/images/arxiv-logo-fb.png>
<meta property=og:image:width content=1200>
<meta property=og:image:height content=700>
<meta property=og:image:alt content="arXiv logo">
<meta property=og:description content="Quantum Electrodynamics (QED) is considered the most accurate theory in the history of science. However, this precision is limited to a single experimental value: the anomalous magnetic moment of the electron (g-factor). The calculation of the electron g-factor was carried out in 1950 by Karplus and Kroll. Seven years later, Petermann detected and corrected a serious error in the calculation of a Feynman diagram; however, neither the original calculation nor the subsequent correction was ever published.Therefore, the entire prestige of QED depends on the calculation of a single Feynman diagram (IIc) that has never been published and cannot be independently verified.">
<meta name=twitter:site content=@arxiv>
<meta name=twitter:card content=summary>
<meta name=twitter:title content="The Unpublished Feynman Diagram IIc">
<meta name=twitter:description content="Quantum Electrodynamics (QED) is considered the most accurate theory in the history of science. However, this precision is limited to a single experimental value: the anomalous magnetic moment of...">
<meta name=twitter:image content=https://static.arxiv.org/icons/twitter/arxiv-logo-twitter-square.png>
<meta name=twitter:image:alt content="arXiv logo">
<style media=screen>.visually-hidden{clip-path:inset(100%);clip:rect(1px,1px,1px,1px);height:1px;overflow:hidden;position:absolute;white-space:nowrap;width:1px}.button-and-tooltip{position:relative;display:inline}.button-and-tooltip button{background:transparent;border:none;box-shadow:none;position:relative;padding:0 0 0 6px}td.tablecell.arxivdoi{display:inline-flex;align-items:center}.arrow{width:0;height:0;border-left:8px solid transparent;border-right:8px solid transparent}@-webkit-keyframes pulsate{0%{-webkit-transform:scale(.1);transform:scale(.1);opacity:0}30%{opacity:1}60%{-webkit-transform:scale(.8);transform:scale(.8);opacity:0}}@keyframes pulsate{0%{-webkit-transform:scale(.1);transform:scale(.1);opacity:0}30%{opacity:1}60%{-webkit-transform:scale(.8);transform:scale(.8);opacity:0}}</style>
<meta name=citation_title content="The Unpublished Feynman Diagram IIc"><meta name=citation_author content="Consa, Oliver"><meta name=citation_date content=2020/10/18><meta name=citation_online_date content=2020/10/18><meta name=citation_pdf_url content=http://arxiv.org/pdf/2010.10345><meta name=citation_arxiv_id content=2010.10345><meta name=citation_abstract content="Quantum Electrodynamics (QED) is considered the most accurate theory in the history of science. However, this precision is limited to a single experimental value: the anomalous magnetic moment of the electron (g-factor). The calculation of the electron g-factor was carried out in 1950 by Karplus and Kroll. Seven years later, Petermann detected and corrected a serious error in the calculation of a Feynman diagram; however, neither the original calculation nor the subsequent correction was ever published.Therefore, the entire prestige of QED depends on the calculation of a single Feynman diagram (IIc) that has never been published and cannot be independently verified.">
<style>#MathJax_Message{position:fixed;left:1px;bottom:2px;background-color:#E6E6E6;border:1px solid #959595;margin:0px;padding:2px 8px;z-index:102;color:black;font-size:80%;width:auto;white-space:nowrap}</style><link rel=icon type=image/png sizes=32x32 href="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAMAAABEpIrGAAAABGdBTUEAALGPC/xhBQAAACBjSFJNAAB6JgAAgIQAAPoAAACA6AAAdTAAAOpgAAA6mAAAF3CculE8AAACr1BMVEUAAACzICWzICSyrKazrKWzqaKzraazR0mzTE6zaGizBQiz49uzZmSzEBazHySzsam0ICmzICWzICWzICWzICWzICWzICWzICWzICWzICWzICWzICWzICWzICWzICWzICWzrKWzrKWzICWzICWzICWzICWzICWzrKWzrKWzrKWzrKWzICWzICWzICWzICWzICWzrKWzrKWzrKWzrKWzICWzICWzICWzICWzrKWzrKWzrKWzrKWzICWzICWzICWzrKWzrKWzrKWzrKWzICWzICWzICWzICWzrKWzrKWzrKWzICWzICWzICWzHySz4dWzrKWzrKWzrKWzICWzICWzHySzgX2zrqezrKWzrKWzICWzPD+zrKWzrKWzrKWzICWzHySzjYmzr6izraazT1CzLjKzMDSzQUOzrKWzrqezgH2zKi6zHySzICWzrKWzrKWzcW+zICWzICWzrKWzrKWzYWGzICWzrKWzUVKzICWzrKWzrKWznZezQkSzICWzICWzrKWzraazkY2zHiOzICWzICWzjYmzm5WzhIGzODuzAACzHySzHSKzOz6zrqazs6yzICWzICWzODuzrKWzrKWzrKWzICWzICWzODuzo5yzrKWzrKWzICWzICWzICWzGyCzr6ezrKWzrKWzICWzICWzrKWzrKWzrKWzrKWzICWzICWzICWzrKWzrKWzrKWzrKWzICWzICWzICWzrKWzrKWzrKWzrKWzrKWzICWzICWzICWzrKWzrKWzrKWzrKWzICWzICWzICWzrKWzrKWzrKWzICWzICWzrKWzrKWzrKWzrKWzrKWzrKWzrKWzrKWzrKWzrKWzrKWzrKWzrKWzrKWzICWzrKWzHySzkYyzrqezHiOzODuzJCmzqaOzISazraazpZ6zNTizkIuzi4ezraX///8A/VYjAAAA1HRSTlMAAAAAAAAAAAAAAAAAAAAAAAGA95kOB7X6kQ9W8fyaEQIBA3z9oRUllnUKDJz+qBgwxuwxGbquHD3SpQwt1CBL3cEeR+e7JFvm1mX0wSgEbO5HBYXFkfPyYaX++n0EHsH9lwtO8/NRJrr8/ttFGb7+3jpk/v6ecv6sK9j+/vVcQNf+8nUGSfD7dQMHivyVCmr2/vl3A0np28zvWS7V0joht+HJMR2vzCcLvygYp7IVc7QhFJ/9lQkSzhoRl/t2lu0UDY9XDSoLhvjgOwh89a4GB4L2i8A61lMAAAABYktHROQvYjspAAAAB3RJTUUH5wETDS455INCLAAAAgZJREFUOMt10/dfTXEYB/Dz6Ilst3lFueWmjDIysmdkF0Kyyd7Ze5WZcc2ErIhKISops6zs73Pda1zrH/EcoXPqe8+vn/fre57z+T5HURQwuHt4eoHi9AFvH2Fs6gu1nAJo1lz4+beAqkNc0BSAGhHY0ijMQa3+C8TgkNZttKJtOyFCw9r/FYgdOlKncC2Azl2EEF27/RGIEd2JevRE3Ri9erPw6cMCA/r2I+o/AFE/6MBBLCIHg6tpSBTR0HB9rophw1mMGDlqdDRRVEz1nMWYsX4sxsWOJ5owsWbOwjeOgXXSR1v85CmSnF8ydZpVCPun6TNm1pY2Wsdt1mwW1oQ5devJcsS58+YvUMXCRSC7Oly8hGjpZxZi2XKJQFyRSPRl5VcGYpVBBlYTkePbGvWItYGSd+C69arYsNEuNm2WDYG4ZauDyLbt+/YdO6X7Vb9BUjILx67dexpKe2i0d9/+HzYWKQcay3IwHDxkP/yT57AcOSq7Cjh2nIs+cfIXUeopyWVC2mn+vjNn08/xGecjaojKpbtwEVwvZbC4fKWagEx/zq9eA0DMyuZKc67rN65JrlGIvBtqP4g3b+VT4u07uqUtKBTmsKLK/hDvFt8jS4lJu/fepfc9H1T9OA8fxVPqY80YAE/KMjX9Y/nTZ/T8hWwz/4mXFa/o9RvnQMG3795/UKf4DUwCyzJ9eBcsAAAAJXRFWHRkYXRlOmNyZWF0ZQAyMDIzLTAxLTE5VDEzOjQ2OjU3KzAwOjAwqJ4w4AAAACV0RVh0ZGF0ZTptb2RpZnkAMjAyMy0wMS0xOVQxMzo0Njo1NyswMDowMNnDiFwAAABXelRYdFJhdyBwcm9maWxlIHR5cGUgaXB0YwAAeJzj8gwIcVYoKMpPy8xJ5VIAAyMLLmMLEyMTS5MUAxMgRIA0w2QDI7NUIMvY1MjEzMQcxAfLgEigSi4A6hcRdPJCNZUAAAAASUVORK5CYII="><style>.sf-hidden{display:none!important}</style><meta http-equiv=content-security-policy content="default-src 'none'; font-src 'self' data:; img-src 'self' data:; style-src 'unsafe-inline'; media-src 'self' data:; script-src 'unsafe-inline' data:; object-src 'self' data:;"><style>img[src="data:,"],source[src="data:,"]{display:none!important}</style></head>
<body class=with-cu-identity><div id=MathJax_Message style=display:none></div>
<div class=flex-wrap-footer>
<header>
<a href=#content class=is-sr-only>Skip to main content</a>
<div class="columns is-vcentered is-hidden-mobile" id=cu-identity>
<div class=column id=cu-logo>
<a href=https://www.cornell.edu/><img src=data:image/svg+xml;base64,<?xml version="1.0" encoding="utf-8"?>
<!-- Generator: Adobe Illustrator 22.1.0, SVG Export Plug-In . SVG Version: 6.00 Build 0)  -->
<svg version="1.1" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
	 viewBox="0 0 200.7 45" style="enable-background:new 0 0 200.7 45;" xml:space="preserve">
<style type="text/css">
	.st0{fill:#FFFFFF;}
	.st1{fill:#FFFFFF;stroke:#000000;stroke-width:0.1561;}
	.st2{fill:#FFFFFF;stroke:#000000;}
</style>
<g id="Layer_2_1_">
</g>
<g>
	<g id="Layer_1_1_">
		<path class="st0" d="M22.4,45C10,45,0,34.8,0,22.4S10,0,22.4,0s22.4,10,22.4,22.4C44.9,34.8,34.8,45,22.4,45z M22.4,2.5
			c-11,0-20,9-20,20s9,20,20,20s20-9,20-20C42.4,11.4,33.5,2.5,22.4,2.5z"/>
		<path class="st1" d="M17.2,24.9"/>
		<path class="st0" d="M22.4,42.3l-0.4-0.1c-0.5-0.2-13.2-5.8-13.2-15.9V8.1h27.2v18.4c0,9.7-12.6,15.3-13.2,15.6L22.4,42.3z
			 M10.8,9.9v16.3c0,8.1,9.7,13.1,11.8,14.1c2-1,11.8-6.1,11.8-13.7V10H10.8C10.8,10,10.8,9.9,10.8,9.9z"/>
		<path class="st0" d="M16.7,18.8l-0.2-0.1c0,0-1.5-0.9-2.3-1.5c-0.7-0.5-1.1-1.1-1.2-1.6c0-0.1,0-1.6,0-4.5v-0.6h7.7V11
			c0,2.9,0,4.4,0,4.5c0,0.6-0.4,1.1-1.1,1.6c-1,0.6-2.3,1.5-2.4,1.5L16.7,18.8z M14,11.5c0,1.6,0,3.7,0,3.9c0,0.1,0.2,0.5,0.6,0.7
			c0.6,0.4,1.5,1,2,1.2c0.5-0.2,1.5-0.9,2.1-1.2c0.2-0.1,0.6-0.4,0.6-0.6c0-0.2,0-2.2,0-3.9H14L14,11.5L14,11.5z"/>
		<path class="st0" d="M28.7,18.8l-0.2-0.1c0,0-1.5-0.9-2.3-1.5c-0.7-0.5-1.1-1.1-1.2-1.6c0-0.1,0-1.6,0-4.5v-0.6h7.7V11
			c0,2.9,0,4.4,0,4.5c0,0.6-0.4,1.1-1.1,1.6c-1,0.6-2.3,1.5-2.4,1.5L28.7,18.8z M26,11.5c0,1.6,0,3.7,0,3.9c0,0.1,0.2,0.5,0.6,0.7
			c0.6,0.4,1.5,1,2,1.2c0.5-0.2,1.5-0.9,2.1-1.2c0.2-0.1,0.6-0.4,0.6-0.6c0-0.2,0-2.2,0-3.9H26L26,11.5L26,11.5z"/>
		<rect x="9.3" y="19.1" class="st0" width="26.5" height="1.6"/>
		<g>
			<g>
				<path class="st0" d="M22.4,35.2c-0.5,0-0.7-0.4-0.9-0.5c-0.1-0.1-0.2-0.2-0.4-0.2c-0.7,0-1.2,0-1.8,0.1c-0.6,0-1.2,0.1-2.2,0.1
					s-1.7,0-1.7,0h-0.7V22.3h0.7c0.5,0,1.1,0,2.1,0c0.5,0,1-0.1,1.6-0.1c0.4,0,0.7-0.1,1.1-0.1c0.9-0.1,1.6,0.1,1.7,0.1
					c0.2,0,0.4,0.1,0.6,0.2c0.1-0.1,0.4-0.1,0.6-0.2c0,0,0.9-0.1,1.7-0.1c0.4,0,0.7,0.1,1.1,0.1c0.6,0.1,1.1,0.1,1.6,0.1
					c1,0,1.6,0,2.1,0h0.7v12.4h-0.7c0,0-0.7,0-1.7,0c-1,0-1.6-0.1-2.2-0.1c-0.6,0-1.1-0.1-1.8-0.1c-0.2,0-0.2,0-0.4,0.2
					C23.2,35,22.9,35.2,22.4,35.2z M21.2,33.1c0.6,0,1.1,0.2,1.4,0.5c0.2-0.2,0.7-0.5,1.4-0.5c0.7,0,1.4,0,2,0.1
					c0.6,0,1.2,0.1,2.1,0.1c0.4,0,0.6,0,0.9,0v-9.5c-0.4,0-0.9,0-1.4,0c-0.5,0-1.1-0.1-1.7-0.1c-0.4,0-0.7-0.1-1.1-0.1
					c-0.6-0.1-1.2,0-1.2,0c-0.1,0-0.2,0.1-0.2,0.1s0,0,0.1-0.1l-0.7-0.1l-0.7,0.1c0,0.1,0,0.1,0.1,0.1c0,0,0,0-0.2-0.1l0,0
					c0,0-0.6-0.1-1.2,0c-0.4,0-0.7,0.1-1.1,0.1c-0.6,0.1-1.2,0.1-1.7,0.1c-0.6,0-1,0-1.4,0v9.5c0.2,0,0.6,0,0.9,0
					c0.9,0,1.5-0.1,2.1-0.1C19.9,33.1,20.4,33.1,21.2,33.1z"/>
			</g>
		</g>
		<rect x="13.4" y="12.8" class="st0" width="6.4" height="1.1"/>
		<rect x="21.8" y="19.5" class="st0" width="1.5" height="21.8"/>
		<polygon class="st0" points="31.4,15.2 28.6,13.4 26,15.2 25.3,14.3 28.6,12 32,14.3 		"/>
		<path class="st2" d="M28.5,15.3"/>
		<rect x="17.2" y="25.1" class="st0" width="3.2" height="1.1"/>
		<rect x="17.2" y="27.7" class="st0" width="3.2" height="1.1"/>
		<rect x="17.2" y="30.3" class="st0" width="3.2" height="1.1"/>
		<rect x="24.3" y="25.1" class="st0" width="3.2" height="1.1"/>
		<rect x="24.3" y="27.7" class="st0" width="3.2" height="1.1"/>
		<rect x="24.3" y="30.3" class="st0" width="3.2" height="1.1"/>
	</g>
	<g id="Layer_3">
		<g>
			<path class="st0" d="M65.1,28.7c-1.1,0.7-3.1,1.1-4.3,1.1c-4.7,0-7.8-2.7-7.8-7.1c0-2.2,0.9-4,2.4-5.3c1.5-1.2,3.4-1.8,5.6-1.8
				c1.8,0,3.6,0.5,4.5,0.9c-0.2,1-0.4,2-0.4,2.9h-0.6v-1.5c0-0.5-0.7-0.9-1.7-1.2c-0.6-0.2-1.5-0.4-2.2-0.4c-3.7,0-5.6,2.7-5.6,6
				c0,3.9,2.6,6.4,6.5,6.4c1.5,0,3.1-0.5,3.9-1.2l0.1,0.2L65.1,28.7z"/>
			<path class="st0" d="M70,29.7c-2.4,0-4.2-2-4.2-4.5c0-2.9,1.8-5,5-5c2.4,0,4.4,2,4.4,4.4c0,2.9-2.1,5.2-5.2,5.2L70,29.7L70,29.7
				L70,29.7L70,29.7z M67.7,24.3c0,2.1,0.7,4.8,3.3,4.8c1.8,0,2.6-1.8,2.6-3.6c0-2.6-1.2-4.7-3.1-4.7C68.3,20.7,67.7,22.4,67.7,24.3
				z"/>
			<path class="st0" d="M76.8,22.9c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.7v-0.5c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1v2l0,0
				l1.1-1.2c0.5-0.6,1.1-0.9,1.6-0.9c0.4,0,0.7,0.1,0.9,0.2l-0.1,2.3h-0.4c-0.2-0.5-0.6-0.9-1.4-0.9c-0.9,0-1.7,0.9-1.7,2.2v3.4
				c0,0.5,0,1,0.1,1.1c0.1,0.1,0.4,0.2,0.9,0.2h1v0.6c-1,0-1.8,0-2.8,0c-1,0-1.7,0-2.4,0v-0.6h0.9c0.4,0,0.5-0.1,0.6-0.2
				c0.1-0.2,0.1-0.6,0.1-1.1L76.8,22.9L76.8,22.9L76.8,22.9L76.8,22.9L76.8,22.9z"/>
			<path class="st0" d="M85.8,27.3c0,0.5,0,1,0.1,1.1c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0s-1.7,0-2.4,0v-0.6h0.9
				c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1v-4.4c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.6v-0.5
				c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1v1.7l0,0l1.5-1.2c0.5-0.4,0.9-0.5,1.6-0.5c2.3,0,3.2,1.2,3.2,3.4v3.8c0,0.5,0,1,0.1,1.1
				c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.5,0-1.1,0-1.6,0c-0.5,0-1.1,0-1.6,0v-5.5c0-1.6-1-2.4-2.2-2.4c-1.2,0-2.4,1-2.4,1.8
				L85.8,27.3L85.8,27.3z"/>
			<path class="st0" d="M101.9,23.7c0,0.2,0,0.5,0,0.9c-1.2,0.2-2.3,0.2-3.6,0.2h-2.8c0,2.3,1.1,3.9,3.6,3.9c1,0,1.7-0.5,2.4-1
				l0.2,0.2l-0.4,0.6c-0.1,0.2-1.8,1.1-3.2,1.1c-2.9,0-4.5-1.8-4.5-4.5c0-2,0.5-3.1,1.5-3.8c0.4-0.2,0.7-0.6,1.2-0.7
				c0.7-0.4,1.2-0.5,2-0.5C100.3,20.1,101.9,21.5,101.9,23.7z M95.5,23.8V24c0.9,0.1,1.7,0.1,2.4,0.1c0.7,0,1.5,0,2.2,0
				c0-1.8-0.6-3.3-2.1-3.3C96.6,20.7,95.5,21.8,95.5,23.8z"/>
			<path class="st0" d="M103.7,17.2c0-0.5,0-0.9-0.5-0.9h-1.1v-0.5c1-0.1,2.1-0.4,3.1-0.7l0.1,0.1v12.1c0,0.5,0,1,0.1,1.1
				c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0s-1.7,0-2.4,0v-0.6h0.9c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1
				L103.7,17.2L103.7,17.2z"/>
			<path class="st0" d="M108.7,17.2c0-0.5,0-0.9-0.5-0.9H107v-0.5c1-0.1,2.1-0.4,3.1-0.7l0.1,0.1v12.1c0,0.5,0,1,0.1,1.1
				c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0c-1,0-1.7,0-2.4,0v-0.6h0.9c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1
				L108.7,17.2L108.7,17.2z"/>
			<path class="st0" d="M117.8,18.2c0-0.7,0-1.2-0.1-1.5s-0.4-0.2-0.9-0.2h-1v-0.6c1,0,2,0,2.9,0c0.9,0,1.8,0,2.8,0v0.6h-1
				c-0.5,0-0.7,0.1-0.9,0.2c-0.1,0.2-0.1,0.7-0.1,1.5v6.7c0,2.8,1.5,3.6,4,3.6c2.1,0,4-0.9,4-4v-6.3c0-0.7,0-1.2-0.1-1.5
				c-0.1-0.2-0.4-0.2-0.9-0.2h-0.9v-0.6c0.7,0,1.6,0,2.3,0c0.7,0,1.5,0,2.3,0v0.6h-0.9c-0.5,0-0.7,0.1-0.9,0.2
				c-0.1,0.2-0.1,0.7-0.1,1.5v5.6c0,4.2-1.6,5.9-5.5,5.9c-3.3,0-5.3-1-5.3-4.5L117.8,18.2L117.8,18.2L117.8,18.2z"/>
			<path class="st0" d="M133.2,27.3c0,0.5,0,1,0.1,1.1c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0c-1,0-1.7,0-2.4,0v-0.6
				h0.9c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1v-4.4c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.7v-0.5
				c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1v1.7l0,0l1.5-1.2c0.5-0.4,0.9-0.5,1.6-0.5c2.3,0,3.2,1.2,3.2,3.4v3.8c0,0.5,0,1,0.1,1.1
				c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.5,0-1.1,0-1.6,0c-0.5,0-1.1,0-1.6,0v-5.5c0-1.6-1-2.4-2.2-2.4c-1.2,0-2.4,1-2.4,1.8
				L133.2,27.3L133.2,27.3L133.2,27.3L133.2,27.3z"/>
			<path class="st0" d="M144.9,27.3c0,0.5,0,1,0.1,1.1c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0c-1,0-1.7,0-2.4,0v-0.6
				h0.9c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1v-4.4c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.7v-0.5
				c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1L144.9,27.3L144.9,27.3L144.9,27.3L144.9,27.3z M145.1,16.9c0,0.6-0.5,1.1-1.1,1.1
				c-0.6,0-1.1-0.5-1.1-1.1s0.5-1.1,1.1-1.1C144.6,15.8,145.1,16.3,145.1,16.9z"/>
			<path class="st0" d="M152.3,27.3c-0.4,0.7-0.5,1.5-0.9,2.1h-1l-3.4-8c-0.1-0.2-0.2-0.6-0.6-0.6h-0.6v-0.5c0.7,0,1.5,0,2.3,0
				c0.7,0,1.5,0,2.3,0v0.5h-1c-0.4,0-0.5,0.1-0.5,0.4c0,0.1,0,0.4,0.1,0.7l2.3,5.6c0.4-0.9,0.9-1.8,1.2-2.7l0.9-2.1
				c0.2-0.6,0.4-1.1,0.4-1.5c0-0.4-0.1-0.5-0.5-0.5h-0.9v-0.5c0.6,0,1.2,0,1.8,0c0.6,0,1.2,0,1.8,0v0.5h-0.6c-0.5,0-0.9,0.7-1.1,1.4
				L152.3,27.3z"/>
			<path class="st0" d="M164.1,23.7c0,0.2,0,0.5,0,0.9c-1.2,0.2-2.3,0.2-3.6,0.2h-2.8c0,2.3,1.1,3.9,3.6,3.9c1,0,1.7-0.5,2.4-1
				l0.2,0.2l-0.4,0.6c-0.1,0.2-1.8,1.1-3.2,1.1c-2.9,0-4.5-1.8-4.5-4.5c0-2,0.5-3.1,1.5-3.8c0.4-0.2,0.7-0.6,1.2-0.7
				c0.7-0.4,1.2-0.5,2-0.5C162.5,20.1,164.1,21.5,164.1,23.7z M157.6,23.8V24c0.9,0.1,1.7,0.1,2.4,0.1s1.5,0,2.2,0
				c0-1.8-0.6-3.3-2.1-3.3C158.8,20.7,157.6,21.8,157.6,23.8z"/>
			<path class="st0" d="M166.3,22.9c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.7v-0.5c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1v2l0,0
				l1.1-1.2c0.5-0.6,1.1-0.9,1.6-0.9c0.4,0,0.7,0.1,0.9,0.2l-0.1,2.3h-0.4c-0.2-0.5-0.6-0.9-1.4-0.9c-0.9,0-1.7,0.9-1.7,2.2v3.4
				c0,0.5,0,1,0.1,1.1c0.1,0.1,0.4,0.2,0.9,0.2h1v0.6c-1,0-1.8,0-2.8,0c-1,0-1.7,0-2.4,0v-0.6h0.9c0.4,0,0.5-0.1,0.6-0.2
				c0.1-0.2,0.1-0.6,0.1-1.1L166.3,22.9L166.3,22.9L166.3,22.9L166.3,22.9z"/>
			<path class="st0" d="M173,26.5v0.9c0,1.2,1.4,1.7,2.6,1.7c1.2,0,2.3-0.7,2.3-1.8c0-0.6-0.4-1.1-1-1.3c-0.9-0.2-2-0.5-2.9-0.7
				c-1-0.4-1.7-1-1.7-2.1c0-2.1,1.8-2.8,3.7-2.8c1,0,1.7,0.2,2.6,0.5c0,0.7-0.1,1.5-0.1,2.2h-0.5v-0.5c0-1-1.1-1.6-2.3-1.6
				c-1.7,0-2,1-2,1.6c0,0.9,0.6,1.4,2.1,1.6c2.3,0.4,3.4,1,3.4,2.4c0,2.2-2.2,3.3-4.3,3.3c-1,0-1.8-0.1-2.7-0.5
				c0.2-0.9,0.2-1.8,0.2-2.7h0.6L173,26.5L173,26.5L173,26.5L173,26.5z"/>
			<path class="st0" d="M183.2,27.3c0,0.5,0,1,0.1,1.1c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0c-1,0-1.7,0-2.4,0v-0.6
				h0.9c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1v-4.4c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.7v-0.5
				c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1L183.2,27.3L183.2,27.3L183.2,27.3L183.2,27.3z M183.4,16.9c0,0.6-0.5,1.1-1.1,1.1
				c-0.6,0-1.1-0.5-1.1-1.1s0.5-1.1,1.1-1.1C182.8,15.8,183.4,16.3,183.4,16.9z"/>
			<path class="st0" d="M184.5,22v-0.4l1.5-0.7v-1.3c0-0.5,0-1-0.1-1.6c0.7-0.2,1.4-0.5,1.7-0.7l0.2,0.2c-0.1,0.9-0.2,2-0.2,2.8V21
				l2.7-0.1l-0.1,1.1h-2.4v5.2c0,0.9,0.2,1.4,1.1,1.4c0.5,0,0.9-0.2,1.1-0.4l0.2,0.4l-1,1c-0.1,0.2-0.9,0.2-1.2,0.2
				c-1,0-2-0.5-2-2.1v-5.7L184.5,22z"/>
			<path class="st0" d="M198.3,22c0.1-0.2,0.1-0.4,0.1-0.5c0-0.4-0.2-0.5-0.9-0.5H197v-0.5c0.6,0,1.2,0,1.8,0c0.6,0,1.2,0,1.8,0V21
				h-0.5c-0.5,0-0.9,0.6-1.6,2.3l-3.9,9.2c-0.6,1.5-1.3,2.4-2.9,2.4c-0.4,0-0.7-0.1-1-0.2l0.5-1.5h0.2c0.2,0.2,0.7,0.5,1,0.5l0,0
				c1.1-0.1,1.7-1.7,2.1-2.6l0.5-1.2l-3.2-8c-0.4-0.7-0.6-1-1-1h-0.4v-0.5c0.7,0,1.5,0,2.3,0c0.7,0,1.5,0,2.3,0V21h-0.7
				c-0.4,0-0.6,0.1-0.6,0.5c0,0.2,0,0.5,0.1,0.7l2.2,5.4L198.3,22z"/>
		</g>
	</g>
</g>
</svg>
 alt="Cornell University"></a>
</div><div class=column id=support-ack>
<span id=support-ack-url>We gratefully acknowledge support from the Simons Foundation, <a href=https://info.arxiv.org/about/ourmembers.html>member institutions</a>, and all contributors. <a href=https://info.arxiv.org/about/donate.html>Donate</a></span>
</div>
</div>
<div id=header class=is-hidden-mobile>
<a aria-hidden=true href="https://arxiv.org/abs/%7Burl_path('ignore_me')%7D"></a>
<div class="header-breadcrumbs is-hidden-mobile">
<a href=https://arxiv.org/><img src=data:image/svg+xml;base64,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 alt="arxiv logo" style=height:40px></a> <span>&gt;</span> <a href=https://arxiv.org/list/physics/recent>physics</a> <span>&gt;</span> arXiv:2010.10345
</div>
<div class="search-block level-right">
<form class="level-item mini-search" method=GET action=https://arxiv.org/search>
<div class="field has-addons">
<div class=control>
<input class="input is-small" name=query placeholder=Search... aria-label="Search term or terms" value type=text>
<p class=help><a href=https://info.arxiv.org/help>Help</a> | <a href=https://arxiv.org/search/advanced>Advanced Search</a></p>
</div>
<div class=control>
<div class="select is-small">
<select name=searchtype aria-label="Field to search">
<option value=all selected>All fields</option>
<option value=title>Title</option>
<option value=author>Author</option>
<option value=abstract>Abstract</option>
<option value=comments>Comments</option>
<option value=journal_ref>Journal reference</option>
<option value=acm_class>ACM classification</option>
<option value=msc_class>MSC classification</option>
<option value=report_num>Report number</option>
<option value=paper_id>arXiv identifier</option>
<option value=doi>DOI</option>
<option value=orcid>ORCID</option>
<option value=author_id>arXiv author ID</option>
<option value=help>Help pages</option>
<option value=full_text>Full text</option>
</select>
</div>
</div>
<button class="button is-small is-cul-darker">Search</button>
</div>
</form>
</div>
</div>
<div class="mobile-header sf-hidden">
<div class="columns is-mobile sf-hidden">
<div class="column logo-cornell sf-hidden"><a href=https://www.cornell.edu/ class=sf-hidden>
<picture class=sf-hidden>
<source media="(min-width: 501px)" srcset="data:image/svg+xml;base64,<?xml version="1.0" encoding="utf-8"?>
<!-- Generator: Adobe Illustrator 22.1.0, SVG Export Plug-In . SVG Version: 6.00 Build 0)  -->
<svg version="1.1" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
	 viewBox="0 0 200.7 45" style="enable-background:new 0 0 200.7 45;" xml:space="preserve">
<style type="text/css">
	.st0{fill:#FFFFFF;}
	.st1{fill:#FFFFFF;stroke:#000000;stroke-width:0.1561;}
	.st2{fill:#FFFFFF;stroke:#000000;}
</style>
<g id="Layer_2_1_">
</g>
<g>
	<g id="Layer_1_1_">
		<path class="st0" d="M22.4,45C10,45,0,34.8,0,22.4S10,0,22.4,0s22.4,10,22.4,22.4C44.9,34.8,34.8,45,22.4,45z M22.4,2.5
			c-11,0-20,9-20,20s9,20,20,20s20-9,20-20C42.4,11.4,33.5,2.5,22.4,2.5z"/>
		<path class="st1" d="M17.2,24.9"/>
		<path class="st0" d="M22.4,42.3l-0.4-0.1c-0.5-0.2-13.2-5.8-13.2-15.9V8.1h27.2v18.4c0,9.7-12.6,15.3-13.2,15.6L22.4,42.3z
			 M10.8,9.9v16.3c0,8.1,9.7,13.1,11.8,14.1c2-1,11.8-6.1,11.8-13.7V10H10.8C10.8,10,10.8,9.9,10.8,9.9z"/>
		<path class="st0" d="M16.7,18.8l-0.2-0.1c0,0-1.5-0.9-2.3-1.5c-0.7-0.5-1.1-1.1-1.2-1.6c0-0.1,0-1.6,0-4.5v-0.6h7.7V11
			c0,2.9,0,4.4,0,4.5c0,0.6-0.4,1.1-1.1,1.6c-1,0.6-2.3,1.5-2.4,1.5L16.7,18.8z M14,11.5c0,1.6,0,3.7,0,3.9c0,0.1,0.2,0.5,0.6,0.7
			c0.6,0.4,1.5,1,2,1.2c0.5-0.2,1.5-0.9,2.1-1.2c0.2-0.1,0.6-0.4,0.6-0.6c0-0.2,0-2.2,0-3.9H14L14,11.5L14,11.5z"/>
		<path class="st0" d="M28.7,18.8l-0.2-0.1c0,0-1.5-0.9-2.3-1.5c-0.7-0.5-1.1-1.1-1.2-1.6c0-0.1,0-1.6,0-4.5v-0.6h7.7V11
			c0,2.9,0,4.4,0,4.5c0,0.6-0.4,1.1-1.1,1.6c-1,0.6-2.3,1.5-2.4,1.5L28.7,18.8z M26,11.5c0,1.6,0,3.7,0,3.9c0,0.1,0.2,0.5,0.6,0.7
			c0.6,0.4,1.5,1,2,1.2c0.5-0.2,1.5-0.9,2.1-1.2c0.2-0.1,0.6-0.4,0.6-0.6c0-0.2,0-2.2,0-3.9H26L26,11.5L26,11.5z"/>
		<rect x="9.3" y="19.1" class="st0" width="26.5" height="1.6"/>
		<g>
			<g>
				<path class="st0" d="M22.4,35.2c-0.5,0-0.7-0.4-0.9-0.5c-0.1-0.1-0.2-0.2-0.4-0.2c-0.7,0-1.2,0-1.8,0.1c-0.6,0-1.2,0.1-2.2,0.1
					s-1.7,0-1.7,0h-0.7V22.3h0.7c0.5,0,1.1,0,2.1,0c0.5,0,1-0.1,1.6-0.1c0.4,0,0.7-0.1,1.1-0.1c0.9-0.1,1.6,0.1,1.7,0.1
					c0.2,0,0.4,0.1,0.6,0.2c0.1-0.1,0.4-0.1,0.6-0.2c0,0,0.9-0.1,1.7-0.1c0.4,0,0.7,0.1,1.1,0.1c0.6,0.1,1.1,0.1,1.6,0.1
					c1,0,1.6,0,2.1,0h0.7v12.4h-0.7c0,0-0.7,0-1.7,0c-1,0-1.6-0.1-2.2-0.1c-0.6,0-1.1-0.1-1.8-0.1c-0.2,0-0.2,0-0.4,0.2
					C23.2,35,22.9,35.2,22.4,35.2z M21.2,33.1c0.6,0,1.1,0.2,1.4,0.5c0.2-0.2,0.7-0.5,1.4-0.5c0.7,0,1.4,0,2,0.1
					c0.6,0,1.2,0.1,2.1,0.1c0.4,0,0.6,0,0.9,0v-9.5c-0.4,0-0.9,0-1.4,0c-0.5,0-1.1-0.1-1.7-0.1c-0.4,0-0.7-0.1-1.1-0.1
					c-0.6-0.1-1.2,0-1.2,0c-0.1,0-0.2,0.1-0.2,0.1s0,0,0.1-0.1l-0.7-0.1l-0.7,0.1c0,0.1,0,0.1,0.1,0.1c0,0,0,0-0.2-0.1l0,0
					c0,0-0.6-0.1-1.2,0c-0.4,0-0.7,0.1-1.1,0.1c-0.6,0.1-1.2,0.1-1.7,0.1c-0.6,0-1,0-1.4,0v9.5c0.2,0,0.6,0,0.9,0
					c0.9,0,1.5-0.1,2.1-0.1C19.9,33.1,20.4,33.1,21.2,33.1z"/>
			</g>
		</g>
		<rect x="13.4" y="12.8" class="st0" width="6.4" height="1.1"/>
		<rect x="21.8" y="19.5" class="st0" width="1.5" height="21.8"/>
		<polygon class="st0" points="31.4,15.2 28.6,13.4 26,15.2 25.3,14.3 28.6,12 32,14.3 		"/>
		<path class="st2" d="M28.5,15.3"/>
		<rect x="17.2" y="25.1" class="st0" width="3.2" height="1.1"/>
		<rect x="17.2" y="27.7" class="st0" width="3.2" height="1.1"/>
		<rect x="17.2" y="30.3" class="st0" width="3.2" height="1.1"/>
		<rect x="24.3" y="25.1" class="st0" width="3.2" height="1.1"/>
		<rect x="24.3" y="27.7" class="st0" width="3.2" height="1.1"/>
		<rect x="24.3" y="30.3" class="st0" width="3.2" height="1.1"/>
	</g>
	<g id="Layer_3">
		<g>
			<path class="st0" d="M65.1,28.7c-1.1,0.7-3.1,1.1-4.3,1.1c-4.7,0-7.8-2.7-7.8-7.1c0-2.2,0.9-4,2.4-5.3c1.5-1.2,3.4-1.8,5.6-1.8
				c1.8,0,3.6,0.5,4.5,0.9c-0.2,1-0.4,2-0.4,2.9h-0.6v-1.5c0-0.5-0.7-0.9-1.7-1.2c-0.6-0.2-1.5-0.4-2.2-0.4c-3.7,0-5.6,2.7-5.6,6
				c0,3.9,2.6,6.4,6.5,6.4c1.5,0,3.1-0.5,3.9-1.2l0.1,0.2L65.1,28.7z"/>
			<path class="st0" d="M70,29.7c-2.4,0-4.2-2-4.2-4.5c0-2.9,1.8-5,5-5c2.4,0,4.4,2,4.4,4.4c0,2.9-2.1,5.2-5.2,5.2L70,29.7L70,29.7
				L70,29.7L70,29.7z M67.7,24.3c0,2.1,0.7,4.8,3.3,4.8c1.8,0,2.6-1.8,2.6-3.6c0-2.6-1.2-4.7-3.1-4.7C68.3,20.7,67.7,22.4,67.7,24.3
				z"/>
			<path class="st0" d="M76.8,22.9c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.7v-0.5c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1v2l0,0
				l1.1-1.2c0.5-0.6,1.1-0.9,1.6-0.9c0.4,0,0.7,0.1,0.9,0.2l-0.1,2.3h-0.4c-0.2-0.5-0.6-0.9-1.4-0.9c-0.9,0-1.7,0.9-1.7,2.2v3.4
				c0,0.5,0,1,0.1,1.1c0.1,0.1,0.4,0.2,0.9,0.2h1v0.6c-1,0-1.8,0-2.8,0c-1,0-1.7,0-2.4,0v-0.6h0.9c0.4,0,0.5-0.1,0.6-0.2
				c0.1-0.2,0.1-0.6,0.1-1.1L76.8,22.9L76.8,22.9L76.8,22.9L76.8,22.9L76.8,22.9z"/>
			<path class="st0" d="M85.8,27.3c0,0.5,0,1,0.1,1.1c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0s-1.7,0-2.4,0v-0.6h0.9
				c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1v-4.4c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.6v-0.5
				c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1v1.7l0,0l1.5-1.2c0.5-0.4,0.9-0.5,1.6-0.5c2.3,0,3.2,1.2,3.2,3.4v3.8c0,0.5,0,1,0.1,1.1
				c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.5,0-1.1,0-1.6,0c-0.5,0-1.1,0-1.6,0v-5.5c0-1.6-1-2.4-2.2-2.4c-1.2,0-2.4,1-2.4,1.8
				L85.8,27.3L85.8,27.3z"/>
			<path class="st0" d="M101.9,23.7c0,0.2,0,0.5,0,0.9c-1.2,0.2-2.3,0.2-3.6,0.2h-2.8c0,2.3,1.1,3.9,3.6,3.9c1,0,1.7-0.5,2.4-1
				l0.2,0.2l-0.4,0.6c-0.1,0.2-1.8,1.1-3.2,1.1c-2.9,0-4.5-1.8-4.5-4.5c0-2,0.5-3.1,1.5-3.8c0.4-0.2,0.7-0.6,1.2-0.7
				c0.7-0.4,1.2-0.5,2-0.5C100.3,20.1,101.9,21.5,101.9,23.7z M95.5,23.8V24c0.9,0.1,1.7,0.1,2.4,0.1c0.7,0,1.5,0,2.2,0
				c0-1.8-0.6-3.3-2.1-3.3C96.6,20.7,95.5,21.8,95.5,23.8z"/>
			<path class="st0" d="M103.7,17.2c0-0.5,0-0.9-0.5-0.9h-1.1v-0.5c1-0.1,2.1-0.4,3.1-0.7l0.1,0.1v12.1c0,0.5,0,1,0.1,1.1
				c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0s-1.7,0-2.4,0v-0.6h0.9c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1
				L103.7,17.2L103.7,17.2z"/>
			<path class="st0" d="M108.7,17.2c0-0.5,0-0.9-0.5-0.9H107v-0.5c1-0.1,2.1-0.4,3.1-0.7l0.1,0.1v12.1c0,0.5,0,1,0.1,1.1
				c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0c-1,0-1.7,0-2.4,0v-0.6h0.9c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1
				L108.7,17.2L108.7,17.2z"/>
			<path class="st0" d="M117.8,18.2c0-0.7,0-1.2-0.1-1.5s-0.4-0.2-0.9-0.2h-1v-0.6c1,0,2,0,2.9,0c0.9,0,1.8,0,2.8,0v0.6h-1
				c-0.5,0-0.7,0.1-0.9,0.2c-0.1,0.2-0.1,0.7-0.1,1.5v6.7c0,2.8,1.5,3.6,4,3.6c2.1,0,4-0.9,4-4v-6.3c0-0.7,0-1.2-0.1-1.5
				c-0.1-0.2-0.4-0.2-0.9-0.2h-0.9v-0.6c0.7,0,1.6,0,2.3,0c0.7,0,1.5,0,2.3,0v0.6h-0.9c-0.5,0-0.7,0.1-0.9,0.2
				c-0.1,0.2-0.1,0.7-0.1,1.5v5.6c0,4.2-1.6,5.9-5.5,5.9c-3.3,0-5.3-1-5.3-4.5L117.8,18.2L117.8,18.2L117.8,18.2z"/>
			<path class="st0" d="M133.2,27.3c0,0.5,0,1,0.1,1.1c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0c-1,0-1.7,0-2.4,0v-0.6
				h0.9c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1v-4.4c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.7v-0.5
				c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1v1.7l0,0l1.5-1.2c0.5-0.4,0.9-0.5,1.6-0.5c2.3,0,3.2,1.2,3.2,3.4v3.8c0,0.5,0,1,0.1,1.1
				c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.5,0-1.1,0-1.6,0c-0.5,0-1.1,0-1.6,0v-5.5c0-1.6-1-2.4-2.2-2.4c-1.2,0-2.4,1-2.4,1.8
				L133.2,27.3L133.2,27.3L133.2,27.3L133.2,27.3z"/>
			<path class="st0" d="M144.9,27.3c0,0.5,0,1,0.1,1.1c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0c-1,0-1.7,0-2.4,0v-0.6
				h0.9c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1v-4.4c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.7v-0.5
				c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1L144.9,27.3L144.9,27.3L144.9,27.3L144.9,27.3z M145.1,16.9c0,0.6-0.5,1.1-1.1,1.1
				c-0.6,0-1.1-0.5-1.1-1.1s0.5-1.1,1.1-1.1C144.6,15.8,145.1,16.3,145.1,16.9z"/>
			<path class="st0" d="M152.3,27.3c-0.4,0.7-0.5,1.5-0.9,2.1h-1l-3.4-8c-0.1-0.2-0.2-0.6-0.6-0.6h-0.6v-0.5c0.7,0,1.5,0,2.3,0
				c0.7,0,1.5,0,2.3,0v0.5h-1c-0.4,0-0.5,0.1-0.5,0.4c0,0.1,0,0.4,0.1,0.7l2.3,5.6c0.4-0.9,0.9-1.8,1.2-2.7l0.9-2.1
				c0.2-0.6,0.4-1.1,0.4-1.5c0-0.4-0.1-0.5-0.5-0.5h-0.9v-0.5c0.6,0,1.2,0,1.8,0c0.6,0,1.2,0,1.8,0v0.5h-0.6c-0.5,0-0.9,0.7-1.1,1.4
				L152.3,27.3z"/>
			<path class="st0" d="M164.1,23.7c0,0.2,0,0.5,0,0.9c-1.2,0.2-2.3,0.2-3.6,0.2h-2.8c0,2.3,1.1,3.9,3.6,3.9c1,0,1.7-0.5,2.4-1
				l0.2,0.2l-0.4,0.6c-0.1,0.2-1.8,1.1-3.2,1.1c-2.9,0-4.5-1.8-4.5-4.5c0-2,0.5-3.1,1.5-3.8c0.4-0.2,0.7-0.6,1.2-0.7
				c0.7-0.4,1.2-0.5,2-0.5C162.5,20.1,164.1,21.5,164.1,23.7z M157.6,23.8V24c0.9,0.1,1.7,0.1,2.4,0.1s1.5,0,2.2,0
				c0-1.8-0.6-3.3-2.1-3.3C158.8,20.7,157.6,21.8,157.6,23.8z"/>
			<path class="st0" d="M166.3,22.9c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.7v-0.5c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1v2l0,0
				l1.1-1.2c0.5-0.6,1.1-0.9,1.6-0.9c0.4,0,0.7,0.1,0.9,0.2l-0.1,2.3h-0.4c-0.2-0.5-0.6-0.9-1.4-0.9c-0.9,0-1.7,0.9-1.7,2.2v3.4
				c0,0.5,0,1,0.1,1.1c0.1,0.1,0.4,0.2,0.9,0.2h1v0.6c-1,0-1.8,0-2.8,0c-1,0-1.7,0-2.4,0v-0.6h0.9c0.4,0,0.5-0.1,0.6-0.2
				c0.1-0.2,0.1-0.6,0.1-1.1L166.3,22.9L166.3,22.9L166.3,22.9L166.3,22.9z"/>
			<path class="st0" d="M173,26.5v0.9c0,1.2,1.4,1.7,2.6,1.7c1.2,0,2.3-0.7,2.3-1.8c0-0.6-0.4-1.1-1-1.3c-0.9-0.2-2-0.5-2.9-0.7
				c-1-0.4-1.7-1-1.7-2.1c0-2.1,1.8-2.8,3.7-2.8c1,0,1.7,0.2,2.6,0.5c0,0.7-0.1,1.5-0.1,2.2h-0.5v-0.5c0-1-1.1-1.6-2.3-1.6
				c-1.7,0-2,1-2,1.6c0,0.9,0.6,1.4,2.1,1.6c2.3,0.4,3.4,1,3.4,2.4c0,2.2-2.2,3.3-4.3,3.3c-1,0-1.8-0.1-2.7-0.5
				c0.2-0.9,0.2-1.8,0.2-2.7h0.6L173,26.5L173,26.5L173,26.5L173,26.5z"/>
			<path class="st0" d="M183.2,27.3c0,0.5,0,1,0.1,1.1c0.1,0.1,0.2,0.2,0.6,0.2h0.9v0.6c-0.7,0-1.5,0-2.4,0c-1,0-1.7,0-2.4,0v-0.6
				h0.9c0.4,0,0.5-0.1,0.6-0.2c0.1-0.2,0.1-0.6,0.1-1.1v-4.4c0-0.6,0-1.1-0.1-1.2c-0.1-0.1-0.4-0.2-0.7-0.2h-0.7v-0.5
				c1.1-0.1,2.3-0.5,3.1-0.9l0.1,0.1L183.2,27.3L183.2,27.3L183.2,27.3L183.2,27.3z M183.4,16.9c0,0.6-0.5,1.1-1.1,1.1
				c-0.6,0-1.1-0.5-1.1-1.1s0.5-1.1,1.1-1.1C182.8,15.8,183.4,16.3,183.4,16.9z"/>
			<path class="st0" d="M184.5,22v-0.4l1.5-0.7v-1.3c0-0.5,0-1-0.1-1.6c0.7-0.2,1.4-0.5,1.7-0.7l0.2,0.2c-0.1,0.9-0.2,2-0.2,2.8V21
				l2.7-0.1l-0.1,1.1h-2.4v5.2c0,0.9,0.2,1.4,1.1,1.4c0.5,0,0.9-0.2,1.1-0.4l0.2,0.4l-1,1c-0.1,0.2-0.9,0.2-1.2,0.2
				c-1,0-2-0.5-2-2.1v-5.7L184.5,22z"/>
			<path class="st0" d="M198.3,22c0.1-0.2,0.1-0.4,0.1-0.5c0-0.4-0.2-0.5-0.9-0.5H197v-0.5c0.6,0,1.2,0,1.8,0c0.6,0,1.2,0,1.8,0V21
				h-0.5c-0.5,0-0.9,0.6-1.6,2.3l-3.9,9.2c-0.6,1.5-1.3,2.4-2.9,2.4c-0.4,0-0.7-0.1-1-0.2l0.5-1.5h0.2c0.2,0.2,0.7,0.5,1,0.5l0,0
				c1.1-0.1,1.7-1.7,2.1-2.6l0.5-1.2l-3.2-8c-0.4-0.7-0.6-1-1-1h-0.4v-0.5c0.7,0,1.5,0,2.3,0c0.7,0,1.5,0,2.3,0V21h-0.7
				c-0.4,0-0.6,0.1-0.6,0.5c0,0.2,0,0.5,0.1,0.7l2.2,5.4L198.3,22z"/>
		</g>
	</g>
</g>
</svg>
 400w" sizes=400w>
<source srcset="data:image/svg+xml;base64,<?xml version="1.0" encoding="utf-8"?>
<!-- Generator: Adobe Illustrator 19.2.1, SVG Export Plug-In . SVG Version: 6.00 Build 0)  -->
<svg version="1.1" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
	 viewBox="0 0 120 120" style="enable-background:new 0 0 120 120;" xml:space="preserve">
<g>
	<path d="M45.9,91.7c6.8,5.3,13.5,8.2,13.8,8.3l0.5,0.2l0.5-0.2c0.3-0.1,6.9-3,13.7-8.3c9.1-7.1,13.9-15.2,13.9-23.5l0-37.6l-56.4,0
		l0,37C31.9,76.1,36.7,84.5,45.9,91.7z M58.8,80.1c-0.3-0.1-0.6-0.2-1-0.2c0,0,0,0-0.1,0c-1.4,0-2.4,0.1-3.5,0.2
		c-1.1,0.1-2.2,0.2-3.8,0.2c-0.7,0-1.4,0-1.9,0V62.7c0.1,0,0.2,0,0.2,0c0.7,0,1.5,0,2.6,0c0.9,0,1.9-0.1,3-0.2
		c0.6-0.1,1.3-0.1,2-0.2c1.2-0.1,2.2,0.1,2.2,0.1c0.1,0,0.2,0.1,0.3,0.1C58.8,62.4,58.8,80.1,58.8,80.1z M85.6,68.2
		c0,15.4-18.9,25.8-24.5,28.6v-14c0.1-0.1,0.2-0.2,0.3-0.3c0.3-0.3,0.5-0.5,1-0.5c1.3,0,2.3,0.1,3.4,0.2c1.1,0.1,2.2,0.2,3.9,0.2
		c1.7,0,3,0,3,0l0.9,0l0-5.2h2.2v-2.8h-2.2l0-5.1h2.2v-2.8h-2.2l0-5.7l-1,0c-0.4,0-0.8,0-1.3,0c-0.7,0-1.5,0-2.5,0
		c-0.8,0-1.7-0.1-2.8-0.2c-0.6-0.1-1.3-0.1-2-0.2c-1.5-0.2-2.8,0.1-2.9,0.1c0,0,0,0-0.1,0V55h24.5L85.6,68.2z M61.1,80.2V62.5
		c0.1-0.1,0.3-0.1,0.5-0.2c0,0,1.1-0.2,2.3-0.1c0.7,0.1,1.4,0.1,2,0.2c1.1,0.1,2.1,0.2,3,0.2c0.9,0,1.6,0,2.3,0c0.2,0,0.4,0,0.5,0
		l0,17.7c-0.5,0-1.2,0-1.9,0c-1.6,0-2.7-0.1-3.8-0.2c-1.1-0.1-2.1-0.2-3.5-0.2C61.9,80,61.5,80.1,61.1,80.2z M34.6,33.3l51,0l0,19.1
		h-51L34.6,33.3z M34.6,55h24.3v5.3c-0.4-0.1-1.5-0.2-2.7-0.1c-0.7,0.1-1.4,0.1-2,0.2c-1.1,0.1-2,0.2-2.8,0.2c-1,0-1.8,0-2.5,0
		c-0.5,0-0.9,0-1.3,0l-1,0v5.1h-2.4v2.8h2.4v5.1h-2.4v2.8h2.4v5.7l0.9,0c0.1,0,1.4,0.1,3,0c1.7,0,2.9-0.1,3.9-0.2
		c1.1-0.1,2-0.2,3.3-0.2c0.5,0,0.7,0.2,0.9,0.5c0,0,0.1,0.1,0.1,0.1v14.1C53,93.8,34.6,83.5,34.6,67.6L34.6,55z"/>
	<path d="M55.9,35.2H41.6v1c0,3.1,0,8.4,0,8.6c0.1,1.1,0.8,2.1,2.2,3c1.7,1.2,4.3,2.7,4.4,2.7l0.5,0.3l0.5-0.3
		c0.1-0.1,2.9-1.6,4.6-2.7c2-1.3,2.1-2.6,2.1-3c0-0.2,0-4.8,0-8.6V35.2z M43.6,37.2h10.2c0,0.8,0,1.7,0,2.6H43.6
		C43.6,38.9,43.6,38,43.6,37.2z M53.9,44.7c0,0.5-0.7,1-1.2,1.4c-1.2,0.8-3.1,1.9-4,2.4c-0.8-0.5-2.6-1.5-3.8-2.4
		c-0.8-0.5-1.3-1.1-1.3-1.5c0-0.1,0-1.3,0-2.9h10.2C53.9,43.3,53.9,44.5,53.9,44.7z"/>
	<path d="M80.1,34.8H65.6v1c0,3.9,0,8.6,0,8.9c0.1,1.1,0.8,2.1,2.2,3c1.8,1.2,4.4,2.7,4.5,2.8l0.5,0.3l0.5-0.3
		c0.1-0.1,3-1.6,4.7-2.8c2.1-1.4,2.1-2.6,2.1-3c0-0.2,0-4.9,0-8.8L80.1,34.8z M78.1,44.5c0,0.5-0.7,1.1-1.2,1.4
		c-1.3,0.8-3.2,1.9-4.1,2.4c-0.9-0.5-2.6-1.6-3.9-2.4c-0.4-0.3-1.3-0.9-1.3-1.5c0-0.1,0-0.2,0-0.5l5-3.6l5.5,3.7
		C78.1,44.3,78.1,44.5,78.1,44.5z M72.6,37.8l-5,3.6c0-1.4,0-3.2,0-4.7h10.6c0,1.6,0,3.3,0,4.8L72.6,37.8z"/>
	<path d="M63.7,66.5l1,0.1c0.6,0.1,1.2,0.1,1.7,0.1l2.9,0.1l0-2l-2.9-0.1c-0.4,0-0.9-0.1-1.5-0.1l-1-0.1c-0.3,0-0.5,0-0.7,0l0.1,2
		C63.4,66.4,63.6,66.4,63.7,66.5z"/>
	<path d="M66.4,70.2c-0.4,0-0.9-0.1-1.5-0.1c-0.3,0-0.7-0.1-1-0.1c-0.3,0-0.5,0-0.7,0l0,2c0.1,0,0.3,0,0.5,0c0.4,0,0.7,0.1,1,0.1
		c0.6,0.1,1.1,0.1,1.6,0.1c0.6,0,1.5,0,2.2,0l0.8,0l0-2l-0.8,0C67.9,70.3,67,70.2,66.4,70.2z"/>
	<path d="M66.4,75.8c-0.4,0-0.9-0.1-1.5-0.1c-0.3,0-0.7-0.1-1-0.1c-0.3,0-0.5,0-0.7,0l0.1,2c0.1,0,0.3,0,0.5,0c0.4,0,0.7,0.1,1,0.1
		c0.6,0.1,1.2,0.1,1.6,0.1l0.8,0c0.8,0,1.8,0,2.1,0.1l0-2c-0.3,0-1.3,0-2.1-0.1L66.4,75.8z"/>
	<path d="M53.8,66.7c0.5,0,1-0.1,1.7-0.1c0.3,0,0.6-0.1,1-0.1c0.2,0,0.3,0,0.5,0l0-2c-0.2,0-0.4,0-0.7,0c-0.4,0-0.7,0.1-1,0.1
		c-0.6,0.1-1.1,0.1-1.5,0.1l-2.9,0.1l0,2L53.8,66.7z"/>
	<path d="M55.3,70.1c-0.6,0.1-1.1,0.1-1.5,0.1l-2.9,0.1l0,2l2.9-0.1c0.5,0,1-0.1,1.7-0.1l0.9-0.1c0.2,0,0.3,0,0.4,0l0.1-2
		c-0.2,0-0.4,0-0.7,0L55.3,70.1z"/>
	<path d="M55.3,75.6c-0.6,0.1-1.1,0.1-1.6,0.1c-0.9,0-2.4,0.1-2.8,0.1l0,2c0.4,0,1.9-0.1,2.9-0.1c0.5,0,1-0.1,1.7-0.1l1-0.1
		c0.1,0,0.3,0,0.4,0l0-2c-0.2,0-0.4,0-0.7,0L55.3,75.6z"/>
	<path d="M9.3,60.3c2.5,0,4-1.6,4.2-4.4c0-0.5,0-1.2-0.1-1.9l0-0.2l-2.1,0l0.2,0.4c0.1,0.3,0.2,1,0.2,1.6c-0.1,1.4-1.2,2.3-2.7,2.2
		c-1.6-0.1-2.5-1.1-2.5-2.5c0-0.5,0.1-1,0.5-1.5l0.3-0.4l-2-0.3l-0.1,0.2c-0.3,0.6-0.4,1.3-0.5,1.9c-0.2,2.9,1.4,4.8,4.3,4.9
		C9.1,60.3,9.2,60.3,9.3,60.3z"/>
	<path d="M9.7,50.5c0.6,0.2,1.1,0.2,1.6,0.2c1.9,0,3.3-1.1,3.9-3c0.3-1.2,0.2-2.2-0.3-3.2c-0.6-1-1.6-1.7-2.9-2.1
		c-0.5-0.2-1.1-0.2-1.5-0.2c-1.9,0-3.3,1.1-3.9,3C5.8,47.7,7,49.7,9.7,50.5z M8.3,45.8c0.3-1.1,1.2-1.3,1.9-1.3
		c0.3,0,0.7,0.1,1.1,0.2c0.9,0.3,1.6,0.7,1.9,1.3c0.2,0.4,0.3,0.8,0.1,1.3c-0.3,1.1-1.2,1.3-1.9,1.3c-0.4,0-0.7-0.1-1.1-0.2
		C9.1,48,7.9,47.1,8.3,45.8z"/>
	<path d="M18.3,39.3l-2.9-1.6l0.1-0.2c0.3-0.5,0.5-0.5,0.9-0.4l2.9,0.4l1.1-2.1l-3.8-0.4c-0.3,0-0.5,0-0.7,0c0-0.8-0.4-1.6-1.2-2
		c-0.4-0.2-0.8-0.3-1.2-0.3c-1.4,0-2.1,1.4-2.8,2.7l-1,1.9l7.6,4.1L18.3,39.3z M13.8,36.6l-0.1,0.2l-1.4-0.7l0.1-0.2
		c0.3-0.6,0.7-1.2,1.3-0.9c0.2,0.1,0.3,0.2,0.4,0.4C14.2,35.8,14,36.3,13.8,36.6z"/>
	<polygon points="23,31.7 19.1,28.5 24.7,29.8 26.2,27.9 19.6,22.4 18.2,24 22.2,27.3 16.6,26 15,27.9 21.7,33.4 	"/>
	<polygon points="32.7,22.4 31.5,21 29.1,22.9 28,21.6 30.2,19.8 29,18.4 26.8,20.2 26,19.1 28.4,17.2 27.2,15.7 23.1,19 28.5,25.7 
			"/>
	<polygon points="39.8,18.1 38.9,16.5 36.2,18 32.9,12.1 31,13.2 35.2,20.7 	"/>
	<polygon points="47.1,15.3 46.4,13.6 43.6,14.6 41.3,8.3 39.2,9 42.1,17.1 	"/>
	<path d="M55.8,13.9c0.2,0,0.3,0,0.5,0c1.2-0.1,2.1-0.5,2.6-1.1c0.5-0.6,0.7-1.5,0.6-2.5l-0.4-5.4L56.9,5l0.4,4.9
		c0.1,1.7-0.6,2-1.2,2.1c-0.1,0-0.1,0-0.2,0c-0.5,0-1.2-0.2-1.4-1.9l-0.4-4.9l-2.2,0.2l0.4,5.4C52.7,12.8,53.8,13.9,55.8,13.9z"/>
	<polygon points="65.7,8.8 67.5,14.1 70,14.5 71.1,5.9 69,5.6 68.3,10.7 66.5,5.3 64.1,5 62.9,13.5 65,13.8 	"/>
	<polygon points="77.6,7.8 75.5,7.1 72.9,15.3 75,16 	"/>
	<polygon points="88.4,12.6 86.5,11.6 82.3,15.9 83.2,10 81.1,8.9 79.8,18 82,19 	"/>
	<polygon points="90.6,25 91.7,23.5 89.3,21.6 90.3,20.3 92.5,22 93.7,20.5 91.5,18.8 92.3,17.7 94.7,19.6 95.9,18.1 91.7,14.9 
		86.4,21.7 	"/>
	<path d="M94.2,28.6l2.5-2.2l0.1,0.2c0.3,0.4,0.3,0.5,0.1,1l-1.4,2.6l1.6,1.8l1.7-3.4c0.1-0.1,0.2-0.4,0.2-0.7
		c0.7,0.3,1.6,0.2,2.3-0.4c1.9-1.6,0.4-3.3-0.7-4.6l-1.4-1.6L92.7,27L94.2,28.6z M99.3,24.1l0.1,0.2c0.3,0.4,0.6,0.8,0.6,1.1
		c0,0.2-0.1,0.3-0.3,0.4C99.6,26,99.4,26,99.3,26c-0.4,0-0.8-0.4-1-0.7l-0.1-0.2L99.3,24.1z"/>
	<path d="M102.2,35.5c-0.4,0.3-1-0.2-1.2-0.6c-0.3-0.5-0.4-1-0.4-1.7l0-0.5l-2,0.9l0.1,0.4c0.2,0.7,0.3,1.1,0.7,1.8
		c0.7,1.2,1.6,1.8,2.6,1.8c0.5,0,0.9-0.1,1.4-0.4c1.5-0.9,1.3-2.3,1.1-3.4c-0.1-0.7-0.2-1.2,0.1-1.4c0.2-0.1,0.3-0.1,0.4-0.1
		c0.4,0,0.7,0.4,0.8,0.5c0.3,0.4,0.4,0.9,0.5,1.4l0.1,0.4l1.8-0.8l0-0.2c-0.1-0.6-0.4-1.2-0.8-1.9c-0.9-1.6-2.5-2.1-3.9-1.2
		c-1.5,0.9-1.3,2.3-1.1,3.3C102.5,34.8,102.6,35.3,102.2,35.5z"/>
	<rect x="102.5" y="39.6" transform="matrix(0.9259 -0.3777 0.3777 0.9259 -7.4559 43.3568)" width="8.6" height="2.2"/>
	<polygon points="111.2,46.2 104.7,47.8 105.2,49.9 111.8,48.3 112.3,50.5 114.1,50.1 112.5,43.5 110.7,44 	"/>
	<polygon points="106.2,56.6 106.3,58.8 109.7,58.6 115.1,61.4 115,59 111.8,57.5 114.8,55.6 114.6,53 109.6,56.5 	"/>
	<polygon points="11,76.4 12.8,75.9 12.1,73.3 13.4,72.9 14.2,75.7 16,75.1 14.6,70.3 6.3,72.7 6.9,74.8 10.3,73.8 	"/>
	<path d="M18.7,83.6c0.3-1,0.2-2.1-0.3-3.2c-0.8-1.6-2-2.4-3.6-2.4c-0.7,0-1.5,0.2-2.3,0.6c-1.3,0.6-2.1,1.5-2.5,2.6
		c-0.3,1-0.2,2.1,0.3,3.2c0.8,1.5,2,2.4,3.6,2.4c0.7,0,1.5-0.2,2.3-0.6C17.5,85.5,18.4,84.7,18.7,83.6z M15.3,84.1
		c-0.5,0.3-1.1,0.4-1.6,0.4c-0.8,0-1.3-0.3-1.6-1c-0.2-0.5-0.3-0.9-0.1-1.3c0.2-0.6,0.8-1.2,1.6-1.6c0.5-0.2,1-0.4,1.5-0.4
		c0.8,0,1.3,0.3,1.6,1c0.2,0.5,0.3,0.9,0.1,1.3C16.6,83.1,16.1,83.7,15.3,84.1z"/>
	<path d="M24.7,90.3l-3.9,3.1c-1,0.8-1.8,0.9-2.4,0.2c-0.2-0.3-0.3-0.6-0.3-0.9c0.1-0.4,0.4-0.9,1-1.4l3.9-3.1l-1.4-1.7l-4.3,3.4
		c-0.9,0.7-1.4,1.5-1.4,2.4c0,0.8,0.3,1.6,1,2.5c0.8,1.1,1.7,1.6,2.7,1.6c0.7,0,1.4-0.3,2.1-0.9L26,92L24.7,90.3z"/>
	<polygon points="32,97.3 28.8,101.3 30,95.7 28.1,94.1 22.6,100.8 24.3,102.2 27.5,98.2 26.3,103.8 28.2,105.4 33.7,98.7 	"/>
	<path d="M38.4,101.4l-2.2-1.1l-3.9,7.7l2.2,1.1c1.1,0.5,2,0.8,2.9,0.8c1.5,0,2.7-0.8,3.5-2.4C42.2,104.9,41.3,102.9,38.4,101.4z
		 M38.8,106.5c-0.4,0.9-1.2,1.4-2.1,1.4c-0.4,0-0.7-0.1-1.1-0.3l-0.5-0.3l2.2-4.4l0.5,0.3c0.6,0.3,1,0.8,1.2,1.3
		C39.2,105.2,39.1,105.8,38.8,106.5z"/>
	<polygon points="43.2,112.8 48.3,114.2 48.8,112.4 45.8,111.6 46.2,110 49,110.7 49.5,108.9 46.7,108.2 47,106.8 50.1,107.6 
		50.5,105.8 45.4,104.5 	"/>
	<path d="M55.9,106.5l-2.5-0.1l-0.5,8.6l2.5,0.1c0.2,0,0.4,0,0.6,0c2.9,0,4.4-1.4,4.6-4.1c0.1-1.3-0.2-2.4-0.9-3.2
		C58.9,107.1,57.7,106.6,55.9,106.5z M55.8,113.3l-0.6,0l0.3-4.9l0.6,0c1.2,0.1,2.3,1,2.2,2.6C58.2,112.6,57,113.3,55.8,113.3z"/>
	<path d="M68.2,105.8l-1.5,9.1l2.3-0.5l0.3-1.9l2.8-0.6l1.1,1.7l2.4-0.5l-5.1-7.7L68.2,105.8z M69.6,110.6l0.3-2.3l1.2,1.9
		L69.6,110.6z"/>
	<polygon points="76.4,110.3 77.2,112.4 79.2,111.6 78.5,109.6 	"/>
	<path d="M80.6,101.6l-2.2,1.2l4.1,7.6l2.2-1.2c2.9-1.6,3.6-3.6,2.3-6.1C85.7,100.5,83.5,100,80.6,101.6z M84.1,107.4l-0.5,0.3
		l-2.3-4.3l0.5-0.3c0.3-0.2,0.7-0.3,1.1-0.3c0.9,0,1.6,0.5,2.1,1.3C85.8,105.5,85.1,106.8,84.1,107.4z"/>
	<polygon points="88.7,104.3 89.9,106.1 91.7,104.8 90.5,103 	"/>
	<polygon points="92.1,93.2 91.7,96.6 93.6,96.9 93.8,95.5 97.9,99.6 99.5,98.1 93.4,91.9 	"/>
	<path d="M103.8,88.7c-0.7-0.5-1.5-0.6-2.4-0.3c0-0.8-0.4-1.6-1-2c-1.1-0.8-2.5-0.3-3.6,1.1c-1,1.4-0.9,2.8,0.3,3.7
		c0.6,0.4,1.4,0.5,2.1,0.3c-0.1,0.9,0.2,1.6,0.9,2.1c0.5,0.4,1,0.5,1.5,0.5c0.9,0,1.7-0.5,2.5-1.5c0.6-0.8,0.9-1.6,0.8-2.4
		C104.8,89.7,104.4,89.2,103.8,88.7z M99.7,89.3c-0.3,0.2-0.6,0.4-0.9,0.4c-0.1,0-0.3,0-0.4-0.1c-0.4-0.3-0.2-0.8,0-1.1
		c0.1-0.2,0.3-0.3,0.5-0.3c0.1,0,0.3,0.1,0.5,0.2C99.7,88.6,99.8,89,99.7,89.3z M102.7,91.7c-0.3,0.4-0.8,0.5-1.2,0.2
		c-0.3-0.3-0.5-0.6-0.4-1.2c0.6-0.4,1.1-0.5,1.5-0.2c0.2,0.1,0.3,0.3,0.3,0.5C102.9,91.2,102.8,91.5,102.7,91.7z"/>
	<path d="M107.7,80.3c-1.5-0.7-2.9-0.3-3.6,1.1c-0.2,0.4-0.3,0.8-0.2,1.2c-0.5-0.4-1-1.1-0.6-2c0.2-0.4,0.5-0.7,0.8-1l0.3-0.2
		l-1.6-1.1l-0.2,0.2c-0.4,0.4-0.8,0.9-1.1,1.5c-0.4,0.9-0.5,1.7-0.2,2.5c0.5,1.4,1.9,2.4,3,2.9c1,0.5,1.8,0.7,2.5,0.7
		c1.1,0,1.9-0.5,2.5-1.6C110.1,82.7,109.5,81.2,107.7,80.3z M107.7,83.5c-0.1,0.3-0.4,0.4-0.7,0.4c-0.2,0-0.5-0.1-0.7-0.2
		c-0.4-0.2-0.7-0.5-0.8-0.7c-0.1-0.2,0-0.3,0-0.5c0.1-0.3,0.3-0.4,0.7-0.4c0.2,0,0.5,0.1,0.8,0.2c0.4,0.2,0.6,0.4,0.7,0.7
		C107.8,83.2,107.7,83.4,107.7,83.5z"/>
	<path d="M110.8,71.5c-1.7-0.5-3.1,0.3-3.6,1.9c0,0.2-0.1,0.3-0.1,0.4l-1-0.3l0.9-3l-1.7-0.5l-1.5,5l4.8,1.5l0-0.4
		c0-0.5,0.1-0.9,0.2-1.4c0.1-0.4,0.6-1.4,1.5-1.2c1,0.3,0.8,1.4,0.7,1.7c-0.2,0.6-0.5,1-0.8,1.4l-0.3,0.3l2,0.7l0.1-0.2
		c0.3-0.6,0.6-1.3,0.8-1.8c0.3-1,0.3-1.9-0.1-2.7C112.3,72.3,111.6,71.8,110.8,71.5z"/>
	<path d="M16.3,60c0,24,19.5,43.6,43.5,43.6c24,0,43.5-19.5,43.5-43.6c0-24-19.5-43.5-43.5-43.5C35.9,16.4,16.3,36,16.3,60z
		 M59.9,17.9c23.2,0,42,18.9,42,42c0,23.2-18.9,42-42,42c-23.2,0-42-18.9-42-42C17.8,36.8,36.7,17.9,59.9,17.9z"/>
	<path d="M59.9,0.4C27,0.4,0.3,27.1,0.3,60c0,32.8,26.7,59.6,59.6,59.6c32.8,0,59.6-26.7,59.6-59.6C119.4,27.1,92.7,0.4,59.9,0.4z
		 M59.9,118c-32,0-58-26-58-58c0-32,26-58,58-58c32,0,58,26,58,58C117.9,92,91.9,118,59.9,118z"/>
</g>
</svg>
 2x">
</picture>
</a></div>
</div>
</div>
</header>
<main>
<div id=content>
<div id=abs-outer>
<div class=leftcolumn>
<div class=subheader>
<h1>Physics &gt; History and Philosophy of Physics</h1>
</div>
<div class="header-breadcrumbs-mobile sf-hidden">
(physics)
</div>
<style>#abs{font-family:"Lucida Grande",Helvetica,Arial,sans-serif!important}#abs h1.title{display:block;font-size:1.8em!important;font-weight:700;margin-block-end:12px;margin-block-start:12px;margin-bottom:12px;margin-inline-end:0px;margin-inline-start:20px;margin-left:20px;margin-right:0px;margin-top:12px}#abs div.authors{font-size:1.2em;line-height:24px;margin-bottom:8px;margin-left:20px;margin-right:0px;margin-top:8px}#abs div.dateline{font-size:0.9em;font-style:italic;margin-bottom:6.5px;margin-left:20px;margin-right:0px;margin-top:6.5px}#abs blockquote.abstract{font-size:1.05em;margin-block-end:21.6px;margin-block-start:14.4px;margin-bottom:21.6px;margin-inline-end:40px;margin-inline-start:40px;background-color:white;border-left:0px;padding:0px}#abs div.metatable{font-size:0.95em!important;margin-bottom:19px;margin-left:20px;margin-right:0px;margin-top:0px;border:0px;padding:0px}#abs div.metatable tbody{vertical-align:middle}#abs tr{margin-top:0px;margin-bottom:0px}#abs td.tablecell{padding-top:0px;padding-bottom:0px;padding-right:6.5px;padding-left:0px;vertical-align:top;font-size:0.95em!important;margin-top:0px;margin-bottom:0px;border:0px}#abs td.tablecell.label{font-weight:400!important}#abs span.primary-subject{font-weight:700}#abs span.arxivid{font-weight:700}</style>
<div id=content-inner>
<div id=abs>
<div class=dateline>
[Submitted on 18 Oct 2020]</div>
<h1 class="title mathjax"><span class="descriptor sf-hidden">Title:</span>The Unpublished Feynman Diagram IIc</h1>
<div class=authors><span class="descriptor sf-hidden">Authors:</span><a href="https://arxiv.org/search/physics?searchtype=author&amp;query=Consa,+O">Oliver Consa</a></div> <div id=download-button-info class=sf-hidden hidden>View a PDF of the paper titled The Unpublished Feynman Diagram IIc, by Oliver Consa</div>
<a class="mobile-submission-download sf-hidden" href=https://arxiv.org/pdf/2010.10345>View PDF</a>
<blockquote class="abstract mathjax">
<span class="descriptor sf-hidden">Abstract:</span>Quantum Electrodynamics (QED) is considered the most accurate theory in the history of science. However, this precision is limited to a single experimental value: the anomalous magnetic moment of the electron (g-factor). The calculation of the electron g-factor was carried out in 1950 by Karplus and Kroll. Seven years later, Petermann detected and corrected a serious error in the calculation of a Feynman diagram; however, neither the original calculation nor the subsequent correction was ever published.Therefore, the entire prestige of QED depends on the calculation of a single Feynman diagram (IIc) that has never been published and cannot be independently verified.
</blockquote>
<div class=metatable>
<table summary="Additional metadata"> <tbody><tr>
<td class="tablecell label">Comments:</td>
<td class="tablecell comments mathjax">5 pages, 2 figures</td>
</tr>
<tr>
<td class="tablecell label">Subjects:</td>
<td class="tablecell subjects">
<span class=primary-subject>History and Philosophy of Physics (physics.hist-ph)</span></td>
<tr>
<td class="tablecell label">Cite as:</td>
<td class="tablecell arxivid"><span class=arxivid><a href=https://arxiv.org/abs/2010.10345>arXiv:2010.10345</a> [physics.hist-ph]</span></td>
</tr>
<tr>
<td class="tablecell label">&nbsp;</td>
<td class="tablecell arxividv">(or <span class=arxivid>
<a href=https://arxiv.org/abs/2010.10345v1>arXiv:2010.10345v1</a> [physics.hist-ph]</span> for this version)
</td>
</tr> <tr>
<td class="tablecell label">&nbsp;</td>
<td class="tablecell arxivdoi">
<a href=https://doi.org/10.48550/arXiv.2010.10345>https://doi.org/10.48550/arXiv.2010.10345</a>
<div class=button-and-tooltip>
<button class=more-info aria-describedby=more-info-desc-1>
<svg height=15 role=presentation xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512"><path fill=currentColor d="M256 8C119.043 8 8 119.083 8 256c0 136.997 111.043 248 248 248s248-111.003 248-248C504 119.083 392.957 8 256 8zm0 110c23.196 0 42 18.804 42 42s-18.804 42-42 42-42-18.804-42-42 18.804-42 42-42zm56 254c0 6.627-5.373 12-12 12h-88c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h12v-64h-12c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h64c6.627 0 12 5.373 12 12v100h12c6.627 0 12 5.373 12 12v24z"></path></svg>
<span class=visually-hidden>Focus to learn more</span>
</button>
<div role=tooltip id=more-info-desc-1 class=sf-hidden>
arXiv-issued DOI via DataCite
</div>
</div>
</td>
</tr> <tr>
<td class="tablecell label">Journal&nbsp;reference:</td>
<td class="tablecell jref">Progress In Physics, Volume 16, Issue 2 (October, 2020)</td>
</tr>
</table>
</div>
</div>
</div>
<div class=submission-history>
<h2>Submission history</h2> From: Oliver Consa [<a href=https://arxiv.org/show-email/880ea844/2010.10345>view email</a>] <br> <strong>[v1]</strong>
Sun, 18 Oct 2020 09:37:27 UTC (63 KB)<br>
</div>
</div>
<div class=extra-services> <div class=full-text>
<a name=other></a>
<span class="descriptor sf-hidden">Full-text links:</span>
<h2>Access Paper:</h2>
<ul>
<div id=download-button-info class=sf-hidden hidden>
View a PDF of the paper titled The Unpublished Feynman Diagram IIc, by Oliver Consa</div><li><a href=https://arxiv.org/pdf/2010.10345 aria-describedby=download-button-info accesskey=f class="abs-button download-pdf">View PDF</a><li><a href=https://arxiv.org/src/2010.10345 class="abs-button download-eprint">TeX Source</a><li><a href=https://arxiv.org/format/2010.10345 class="abs-button download-format">Other Formats</a></ul>
<div class=abs-license><a href=http://arxiv.org/licenses/nonexclusive-distrib/1.0/ title="Rights to this article">view license</a></div>
</div>
<div class=browse>
Current browse context: <div class=current>physics.hist-ph</div>
<div class=prevnext>
<span class=arrow>
<a class="abs-button prev-url" href="https://arxiv.org/prevnext?id=2010.10345&amp;function=prev&amp;context=physics.hist-ph" accesskey=p title="previous in physics.hist-ph (accesskey p)">&lt;&nbsp;prev</a>
</span>
<span class=is-hidden-mobile>&nbsp; | &nbsp;</span> <span class=arrow>
<a class="abs-button next-url" href="https://arxiv.org/prevnext?id=2010.10345&amp;function=next&amp;context=physics.hist-ph" accesskey=n title="next in physics.hist-ph (accesskey n)">next&nbsp;&gt;</a>
</span><br>
</div><div class=list>
<a class="abs-button abs-button-grey abs-button-small context-new" href=https://arxiv.org/list/physics.hist-ph/new>new</a>
<span class=is-hidden-mobile> | </span>
<a class="abs-button abs-button-grey abs-button-small context-recent" href=https://arxiv.org/list/physics.hist-ph/recent>recent</a>
<span class=is-hidden-mobile> | </span>
<a class="abs-button abs-button-grey abs-button-small context-id" href=https://arxiv.org/list/physics.hist-ph/2010>2010</a>
</div><div class=abs-switch-cat>
Change to browse by:
<div class="switch context-change">
<a href="https://arxiv.org/abs/2010.10345?context=physics">physics</a><br class=is-hidden-mobile>
</div>
</div>
</div>
<div class=extra-ref-cite>
<h3>References &amp; Citations</h3>
<ul>
<li><a class="abs-button abs-button-small cite-ads" href=https://ui.adsabs.harvard.edu/abs/arXiv:2010.10345>NASA ADS</a><li><a class="abs-button abs-button-small cite-google-scholar" href="https://scholar.google.com/scholar_lookup?arxiv_id=2010.10345" target=_blank rel=noopener>Google Scholar</a></li>
<li><a class="abs-button abs-button-small cite-semantic-scholar" href=https://api.semanticscholar.org/arXiv:2010.10345 target=_blank rel=noopener>Semantic Scholar</a></li>
</ul>
<div style=clear:both></div>
</div>
<div class=extra-ref-cite>
<a id=bib-cite-css href=https://arxiv.org/static/browse/0.3.4/css/cite.css class=sf-hidden hidden>a</a>
<span id=bib-cite-trigger class="bib-cite-button abs-button">export BibTeX citation</span>
<span id=bib-cite-loading class=sf-hidden hidden>Loading...</span>
</div>
<div id=bib-cite-modal class="bib-modal sf-hidden" hidden>
</div><div class=bookmarks>
<div><h3>Bookmark</h3></div><a class="abs-button abs-button-grey abs-button-small" href="http://www.bibsonomy.org/BibtexHandler?requTask=upload&amp;url=https://arxiv.org/abs/2010.10345&amp;description=The%20Unpublished%20Feynman%20Diagram%20IIc" title="Bookmark on BibSonomy">
<img src=data:image/png;base64,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 alt="BibSonomy logo">
</a>
<a class="abs-button abs-button-grey abs-button-small" href="https://reddit.com/submit?url=https://arxiv.org/abs/2010.10345&amp;title=The%20Unpublished%20Feynman%20Diagram%20IIc" title="Bookmark on Reddit">
<img src="data:image/png;base64,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" alt="Reddit logo">
</a>
</div> </div>
<div id=labstabs>
<div class=labstabs><input name=tabs id=tabone checked class=sf-hidden type=radio>
<label for=tabone>Bibliographic Tools</label>
<div class="tab labs-display-bib">
<h1>Bibliographic and Citation Tools</h1>
<div class=toggle>
<div class="columns is-mobile lab-row">
<div class="column lab-switch">
<label class=switch>
<input id=bibex-toggle class="lab-toggle sf-hidden" type=checkbox>
<span class=slider></span>
<span class=is-sr-only>Bibliographic Explorer Toggle</span>
</label>
</div>
<div class="column lab-name">
<span id=label-for-bibex>Bibliographic Explorer</span> <em>(<a href=https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer>What is the Explorer?</a>)</em>
</div>
</div>
<div class="columns is-mobile lab-row">
<div class="column lab-switch">
<label class=switch>
<input id=litmaps-toggle class="lab-toggle sf-hidden" data-script-url=/static/browse/0.3.4/js/litmaps.js?20210617 aria-labelledby=label-for-litmaps type=checkbox>
<span class=slider></span>
<span class=is-sr-only>Litmaps Toggle</span>
</label>
</div>
<div class="column lab-name">
<span id=label-for-litmaps>Litmaps</span> <em>(<a href=https://www.litmaps.co/ target=_blank>What is Litmaps?</a>)</em>
</div>
</div>
<div class="columns is-mobile lab-row">
<div class="column lab-switch">
<label class=switch>
<input id=scite-toggle class="lab-toggle sf-hidden" data-script-url=/static/browse/0.3.4/js/scite.js?20210617 aria-labelledby=label-for-scite type=checkbox>
<span class=slider></span>
<span class=is-sr-only>scite.ai Toggle</span>
</label>
</div>
<div class="column lab-name">
<span id=label-for-scite>scite Smart Citations</span> <em>(<a href=https://www.scite.ai/ target=_blank>What are Smart Citations?</a>)</em>
</div>
</div>
</div>
<div class="labs-content-placeholder labs-display" style=display:none></div>
<div style=min-height:15px id=litmaps-open-in></div>
<div style=min-height:15px id=scite-open-in></div>
</div>
<input name=tabs id=tabtwo class=sf-hidden type=radio>
<label for=tabtwo>Code, Data, Media</label>
<div class="tab sf-hidden">
</div>
<input name=tabs id=labstabs-demos-input class=sf-hidden type=radio>
<label for=labstabs-demos-input id=labstabs-demos-label>Demos</label>
<div class="tab sf-hidden">
</div>
<input name=tabs id=tabfour class=sf-hidden type=radio>
<label for=tabfour>Related Papers</label>
<div class="tab sf-hidden">
</div>
<input name=tabs id=tabfive class=sf-hidden type=radio>
<label for=tabfive>
About arXivLabs
</label>
<div class="tab sf-hidden">
</div>
</div>
</div>
<div class=endorsers>
<a href=https://arxiv.org/auth/show-endorsers/2010.10345 class=endorser-who>Which authors of this paper are endorsers?</a> |
<a id=mathjax_toggle>Disable MathJax</a> (<a href=https://info.arxiv.org/help/mathjax.html>What is MathJax?</a>)
<span class=help style=font-style:normal;float:right;margin-top:0;margin-right:1em></span>
</div>
</div>
</div>
</main>
<footer style=clear:both>
<div class="columns is-desktop" role=navigation aria-label=Secondary style="margin:-0.75em -0.75em 0.75em -0.75em">
<div class=column style=padding:0>
<div class=columns>
<div class=column>
<ul style=list-style:none;line-height:2>
<li><a href=https://info.arxiv.org/about>About</a></li>
<li><a href=https://info.arxiv.org/help>Help</a></li>
</ul>
</div>
<div class=column>
<ul style=list-style:none;line-height:2>
<li>
<svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512" class="icon filter-black" role=presentation><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"></path></svg>
<a href=https://info.arxiv.org/help/contact.html> Contact</a>
</li>
<li>
<svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512" class="icon filter-black" role=presentation><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"></path></svg>
<a href=https://info.arxiv.org/help/subscribe> Subscribe</a>
</li>
</ul>
</div>
</div>
</div>
<div class=column style=padding:0>
<div class=columns>
<div class=column>
<ul style=list-style:none;line-height:2>
<li><a href=https://info.arxiv.org/help/license/index.html>Copyright</a></li>
<li><a href=https://info.arxiv.org/help/policies/privacy_policy.html>Privacy Policy</a></li>
</ul>
</div>
<div class="column sorry-app-links">
<ul style=list-style:none;line-height:2>
<li><a href=https://info.arxiv.org/help/web_accessibility.html>Web Accessibility Assistance</a></li>
<li>
<p class=help>
<a class=a11y-main-link href=https://status.arxiv.org/ target=_blank>arXiv Operational Status <svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 256 512" class="icon filter-dark_grey" role=presentation><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"></path></svg></a><br>
Get status notifications via
<a class=is-link href=https://subscribe.sorryapp.com/24846f03/email/new target=_blank><svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512" class="icon filter-black" role=presentation><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"></path></svg>email</a>
or <a class=is-link href=https://subscribe.sorryapp.com/24846f03/slack/new target=_blank><svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 448 512" class="icon filter-black" role=presentation><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"></path></svg>slack</a>
</p>
</li>
</ul>
</div>
</div>
</div>
</div>
</footer>
</div>
Reference in New Issue View Git Blame Copy Permalink