{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T07:55:24Z","timestamp":1771919724731,"version":"3.50.1"},"reference-count":66,"publisher":"American Physical Society (APS)","issue":"7","license":[{"start":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:00:00Z","timestamp":1760054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04564\/2020"],"award-info":[{"award-number":["UIDB\/04564\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDP\/04564\/2020"],"award-info":[{"award-number":["UIDP\/04564\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2022\/05328-3"],"award-info":[{"award-number":["2022\/05328-3"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. D"],"accepted":{"date-parts":[[2025,9,19]]},"abstract":"<jats:p>We investigate the Dyson-Schwinger equation for the photon-fermion one-particle irreducible vertex in QED in linear covariant gauges. The longitudinal component of this vertex is described using the Ball-Chiu basis, while its transverse part is expressed with the K\ud835\udea4z\ud835\udea4lersu-Reenders-Pennington basis. Combining the vertex Ward-Takahashi identity with the vertex equation, we derive a set of exact, nonlinear integral equations governing the transverse vertex. These equations hold for any linear covariant gauge and must be solved self-consistently. We discuss several approximations to the exact equations, generalizing results previously obtained at the perturbative one-loop level. Various kinematical configurations are also examined. Furthermore, we compute the perturbative solution of the transverse vertex Dyson-Schwinger equations for all transverse form factors and derive their perturbative asymptotic expressions.<\/jats:p>","DOI":"10.1103\/cvsn-k4q5","type":"journal-article","created":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:15:58Z","timestamp":1760105758000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["QED photon-fermion vertex from its Dyson-Schwinger equation in 4D: The full vertex, the transverse form factors, and the perturbative solution"],"prefix":"10.1103","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8266-3796","authenticated-orcid":true,"given":"Orlando","family":"Oliveira","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04z8k9a98","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Coimbra"}]}],"member":"16","published-online":{"date-parts":[[2025,10,10]]},"reference":[{"key":"cvsn-k4q5Cc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.030001","type":"journal-article"},{"key":"cvsn-k4q5Cc2R1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198834625.001.0001","type":"book","volume-title":"Quantum Field Theory and Critical Phenomena","author":"Jean Zinn-Justin","year":"2021"},{"key":"cvsn-k4q5Cc3R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(76)90572-1","type":"journal-article"},{"key":"cvsn-k4q5Cc4R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02724229","type":"journal-article"},{"key":"cvsn-k4q5Cc5R1","doi-asserted-by":"publisher","DOI":"10.1016\/0370-2693(85)91254-7","type":"journal-article"},{"key":"cvsn-k4q5Cc6R1","doi-asserted-by":"publisher","DOI":"10.1016\/0370-2693(87)91335-9","type":"journal-article"},{"key":"cvsn-k4q5Cc7R1","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.81.426","type":"journal-article"},{"key":"cvsn-k4q5Cc8R1","doi-asserted-by":"publisher","DOI":"10.1140\/epjc\/s10052-024-13231-5","type":"journal-article"},{"key":"cvsn-k4q5Cc9R1","doi-asserted-by":"crossref","DOI":"10.1142\/6200","type":"book","volume-title":"Lectures on QED and QCD","author":"A. 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All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92025 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"076009"}}