We relate an -loop Feynman integral to a sum of phase space integrals, where the integrands are determined by the spanning trees of the original -loop graph. Causality requires that the propagators of the trees have a modified prescription, and we present a simple formula for the correct prescription.
{ "_oai": { "updated": "2022-03-04T10:31:27Z", "id": "oai:repo.scoap3.org:46283", "sets": [ "PRL" ] }, "authors": [ { "raw_name": "Robert Runkel", "affiliations": [ { "country": "Germany", "value": "PRISMA Cluster of Excellence, Institut f\u00fcr Physik, Johannes Gutenberg-Universit\u00e4t Mainz, D-55099 Mainz, Germany" } ], "surname": "Runkel", "given_names": "Robert", "full_name": "Runkel, Robert" }, { "raw_name": "Zolt\u00e1n Sz\u0151r", "affiliations": [ { "country": "Germany", "value": "PRISMA Cluster of Excellence, Institut f\u00fcr Physik, Johannes Gutenberg-Universit\u00e4t Mainz, D-55099 Mainz, Germany" } ], "surname": "Sz\u0151r", "given_names": "Zolt\u00e1n", "full_name": "Sz\u0151r, Zolt\u00e1n" }, { "raw_name": "Juan Pablo Vesga", "affiliations": [ { "country": "Germany", "value": "PRISMA Cluster of Excellence, Institut f\u00fcr Physik, Johannes Gutenberg-Universit\u00e4t Mainz, D-55099 Mainz, Germany" } ], "surname": "Vesga", "given_names": "Juan Pablo", "full_name": "Vesga, Juan Pablo" }, { "raw_name": "Stefan Weinzierl", "affiliations": [ { "country": "Germany", "value": "PRISMA Cluster of Excellence, Institut f\u00fcr Physik, Johannes Gutenberg-Universit\u00e4t Mainz, D-55099 Mainz, Germany" } ], "surname": "Weinzierl", "given_names": "Stefan", "full_name": "Weinzierl, Stefan" } ], "titles": [ { "source": "APS", "title": "Causality and Loop-Tree Duality at Higher Loops" } ], "dois": [ { "value": "10.1103/PhysRevLett.122.111603" } ], "publication_info": [ { "journal_volume": "122", "journal_title": "Physical Review Letters", "material": "article", "journal_issue": "11", "year": 2019 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2020-06-29T15:38:16.983364", "source": "APS", "method": "APS", "submission_number": "bca49440b8c511eaad8602163e01809a" }, "page_nr": [ 6 ], "license": [ { "url": "https://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "Published by the American Physical Society", "year": "2019" } ], "control_number": "46283", "record_creation_date": "2019-03-22T13:30:17.170626", "_files": [ { "checksum": "md5:9b5652bd0a6c396a79cb00a5e4c056c5", "filetype": "pdf", "bucket": "749e9338-f05c-4e83-aae7-617008521221", "version_id": "5a273a29-f936-429a-b0fc-99b2cca5856e", "key": "10.1103/PhysRevLett.122.111603.pdf", "size": 272374 }, { "checksum": "md5:99ef064881f8caae7587e8baf7d9d46b", "filetype": "xml", "bucket": "749e9338-f05c-4e83-aae7-617008521221", "version_id": "32f7bfdc-9e92-4173-a383-f0b7d4d69d75", "key": "10.1103/PhysRevLett.122.111603.xml", "size": 145030 } ], "collections": [ { "primary": "HEP" }, { "primary": "Citeable" }, { "primary": "Published" } ], "arxiv_eprints": [ { "categories": [ "hep-ph", "hep-th" ], "value": "1902.02135" } ], "abstracts": [ { "source": "APS", "value": "We relate an <math><mi>l</mi></math>-loop Feynman integral to a sum of phase space integrals, where the integrands are determined by the spanning trees of the original <math><mi>l</mi></math>-loop graph. Causality requires that the propagators of the trees have a modified <math><mi>i</mi><mi>\u03b4</mi></math> prescription, and we present a simple formula for the correct <math><mi>i</mi><mi>\u03b4</mi></math> prescription." } ], "imprints": [ { "date": "2019-03-22", "publisher": "APS" } ] }