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When applied to one-loop (cut) Feynman integrals, it can be given a diagrammatic representation purely in terms of pinches and cuts of the edges of the graph. The coaction encodes the algebraic structure of these integrals, and offers ways to extract important properties of complicated integrals from simpler functions. In particular, it gives direct access to discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they satisfy, which we illustrate in the case of the pentagon. We present a new formula for the coaction of a large class of integrals. When applied to one-loop (cut) Feynman integrals, it can be given a diagrammatic representation purely in terms of pinches and cuts of the edges of the graph. The coaction encodes the algebraic structure of these integrals, and offers ways to extract important properties of complicated integrals from simpler functions. In particular, it gives direct access to discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they satisfy, which we illustrate in the case of the pentagon. 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var affiliation = $(this).data('affiliation') + '</br>'; var contribution = $(this).data('contribution') + '</br>'; $.magnificPopup.open({ items: { src: '<div id="ovelary-mathjax" class="overlay-white oc-content overlay-white-500">' + author + affiliation + contribution + '</div>', type: 'inline' }, callbacks: { open: function() { var div = document.getElementById("overlay-mathjax") MathJax.Hub.Queue(["Typeset", MathJax.Hub, div]); }, } }) }) }); </script> <tr><td class="formatRecordLabel"> Report number </td><td style="padding-left:5px;"><a href="http://arxiv.org/abs/arXiv:1803.05894">arXiv:1803.05894</a> ; CERN-TH-2018-002 ; CP3-18-01 ; Edinburgh 2018/1 ; FR-PHENO-2018-001 ; EDINBURGH-2018-1</td></tr> <tr><td class="formatRecordLabel"> Title </td><td style="padding-left:5px;"><b>The diagrammatic coaction and the algebraic structure of cut Feynman integrals</b></td></tr> <tr><td class="formatRecordLabel"><span style="white-space:nowrap;"> Author(s) </span> </td><td style="padding-left:5px;"><a href="https://cds.cern.ch/search?f=author&p=Abreu%2C%20Samuel&ln=ru">Abreu, Samuel</a> (Freiburg U.) ; <a href="https://cds.cern.ch/search?f=author&p=Britto%2C%20Ruth&ln=ru">Britto, Ruth</a> (Trinity Coll., Dublin ; IPhT, Saclay) ; <a href="https://cds.cern.ch/search?f=author&p=Duhr%2C%20Claude&ln=ru">Duhr, Claude</a> (CERN ; Louvain U., CP3) ; <a href="https://cds.cern.ch/search?f=author&p=Gardi%2C%20Einan&ln=ru">Gardi, Einan</a> (Edinburgh U.)</td></tr> <tr><td class="formatRecordLabel"> Publication </td><td style="padding-left:5px;">SISSA, 2018-03-15</td></tr> <tr><td class="formatRecordLabel"> Imprint </td><td style="padding-left:5px;">2018-03-15</td></tr> <tr><td class="formatRecordLabel"> Number of pages </td><td style="padding-left:5px;">10</td></tr> <tr><td class="formatRecordLabel"> Note </td><td style="padding-left:5px;">10 pages. Talk at RADCOR 2017, the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), 25-29 September, 2017, St. Gilgen, Austria</td></tr> <tr><td class="formatRecordLabel"> In: </td><td style="padding-left:5px;"><a href="http://dx.doi.org/10.22323/1.290.0002"><i>PoS</i> RADCOR (2018) 002</a> </a></td></tr> <tr><td class="formatRecordLabel"> In: </td><td style="padding-left:5px;"><a href="https://cds.cern.ch/record/2674862">13th International Symposium on Radiative Corrections : Application of Quantum Field Theory to Phenomenology</a>, St. Gilgen, Austria, 24 - 29 Sep 2017, pp.002</td></tr> <tr><td class="formatRecordLabel"> DOI </td><td style="padding-left:5px;"><a href="http://dx.doi.org/10.22323/1.290.0002" title="DOI" target="_blank">10.22323/1.290.0002</a> <tr><td class="formatRecordLabel"> Subject category </td><td style="padding-left:5px;">hep-ph ; Particle Physics - Phenomenology ; hep-th ; Particle Physics - Theory</td></tr> <tr><td class="formatRecordLabel"> Abstract </td><td style="padding-left:5px;">We present a new formula for the coaction of a large class of integrals. When applied to one-loop (cut) Feynman integrals, it can be given a diagrammatic representation purely in terms of pinches and cuts of the edges of the graph. The coaction encodes the algebraic structure of these integrals, and offers ways to extract important properties of complicated integrals from simpler functions. In particular, it gives direct access to discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they satisfy, which we illustrate in the case of the pentagon.</td></tr> <tr><td class="formatRecordLabel"> Copyright/License </td><td style="padding-left:5px;">preprint: (License: <a href="http://arxiv.org/licenses/nonexclusive-distrib/1.0/">arXiv nonexclusive-distrib 1.0</a>)</td></tr> </table> <br/>Corresponding record in: <a href="http://inspirehep.net/record/1662714">Inspire</a> <small> </small> <br/> <br/><br/><div align="right"><div style="padding-bottom:2px;padding-top:30px;"><span class="moreinfo" style="margin-right:10px;"> <a href="" class="moreinfo">Back to search</a> </span></div></div> <div class="bottom-left-folded"><div class="recordlastmodifiedbox" style="position:relative;margin-left:1px"> Запись создана 2018-03-16, последняя модификация 2023-11-30</div></div> <div class="bottom-right-folded" style="text-align:right;padding-bottom:2px;"> <span class="moreinfo" style="margin-right:10px;"><a href="/search?ln=ru&p=recid%3A2308774&rm=wrd" class="moreinfo">Подобные записи</a></span></div> </div> </div> </div> <br/> <br /> <div class="detailedrecordminipanel"> <div class="top-left"></div><div class="top-right"></div> <div class="inside"> <div id="detailedrecordminipanelfile" style="width:33%;float:left;text-align:center;margin-top:0"> <div><small class="detailedRecordActions">Полный текст:</small> <br /><em>1803.05894</em> - <a href="/record/2308774/files/1803.05894.pdf"><img style="border:none" src="/img/file-icon-text-12x16.gif" alt="Загрузка полного текста"/>PDF</a><br /><em>PoS(RADCOR2017)002</em> - <a href="/record/2308774/files/PoS(RADCOR2017)002.pdf"><img style="border:none" src="/img/file-icon-text-12x16.gif" alt="Загрузка полного текста"/>PDF</a><br /></div><small class="detailedRecordActions">%(x_sitename) ссылка:</small><br /><small><a href="https://pos.sissa.it/290/002/pdf"><img style="border:none" src="/img/file-icon-text-12x16.gif" alt="Загрузка полного текста"/>PoS server</a></small> </div> <div id="detailedrecordminipanelreview" style="width:30%;float:left;text-align:center"> </div> <div id="detailedrecordminipanelactions" style="width:36%;float:right;text-align:right;"> <ul class="detailedrecordactions"> <li><a href="/yourbaskets/add?ln=ru&recid=2308774">Добавить в личную книжную полку</a></li> <li>Экспортировать как <a style="text-decoration:underline;font-weight:normal" href="/record/2308774/export/hx?ln=ru">BibTeX</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2308774/export/hm?ln=ru">MARC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2308774/export/xm?ln=ru">MARCXML</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2308774/export/xd?ln=ru">DC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2308774/export/xe?ln=ru">EndNote</a>,  <a style="text-decoration:underline;font-weight:normal" href="/record/2308774/export/xn?ln=ru">NLM</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2308774/export/xw?ln=ru">RefWorks</a> </li> </ul> <div style='padding-left: 13px;'>  <div id="bookmark"></div> <div id="bookmark_sciencewise"></div> <style type="text/css"> #bookmark_sciencewise, #bookmark {float: left;} #bookmark_sciencewise li {padding: 2px; width: 25px;} #bookmark_sciencewise ul, #bookmark ul {list-style-image: none;} </style> <script type="text/javascript" src="/js/jquery.bookmark.min.js"></script> <style type="text/css">@import "/css/jquery.bookmark.css";</style> <script type="text/javascript">// <![CDATA[ $.bookmark.addSite('sciencewise', 'ScienceWise.info', 'https://cds.cern.ch/img/sciencewise.png', 'en', 'bookmark', 'http://sciencewise.info/bookmarks/1803.0589/add'); $('#bookmark_sciencewise').bookmark({sites: ['sciencewise']}); $('#bookmark').bookmark({ sites: ['facebook', 'twitter', 'linkedin', 'google_plusone'], icons: '/img/bookmarks.png', url: 'https://cds.cern.ch/record/2308774', addEmail: true, title: "The diagrammatic coaction and the algebraic structure of cut Feynman integrals", description: "We present a new formula for the coaction of a large class of integrals. 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