{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T19:44:13Z","timestamp":1771875853161,"version":"3.50.1"},"reference-count":44,"publisher":"American Physical Society (APS)","issue":"1","license":[{"start":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T00:00:00Z","timestamp":1767657600000},"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\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/04564\/2025"],"award-info":[{"award-number":["UID\/04564\/2025"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. D"],"accepted":{"date-parts":[[2025,12,17]]},"abstract":"<jats:p>\n                    The infrared properties of QED are investigated within the framework of the Dyson-Schwinger equations. Our study finds that, independently of the value of the coupling constant, requiring the photon self-energy to be finite for any momenta, combined with a smooth behavior for the photon-fermion vertex, is equivalent to stating that the photon is massless and that the photon propagator diverges at low momenta as\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <a:mn>1<\/a:mn>\n                      <a:mo>\/<\/a:mo>\n                      <a:msup>\n                        <a:mi>k<\/a:mi>\n                        <a:mn>2<\/a:mn>\n                      <\/a:msup>\n                    <\/a:math>\n                    . Furthermore, the Schwinger mechanism to generate, in a gauge invariant way, a photon mass is investigated and the form factors that can be at the origin of a possible photon mass are identified. For the Schwinger mechanism the link between the finiteness of the photon self-energy and the masslessness of the photon is lost. The infrared behavior of the fermion gap equation and the vertex equation are found to be infrared safe integral equations.\n                  <\/jats:p>","DOI":"10.1103\/7x24-vxr6","type":"journal-article","created":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T16:31:42Z","timestamp":1765989102000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Infrared divergences and the photon mass in QED"],"prefix":"10.1103","volume":"113","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":[[2026,1,6]]},"reference":[{"key":"7x24-vxr6Cc1R1","doi-asserted-by":"publisher","DOI":"10.1093\/ptep\/ptac097","type":"journal-article"},{"key":"7x24-vxr6Cc2R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.030001","type":"journal-article"},{"key":"7x24-vxr6Cc3R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.52.54","type":"journal-article"},{"key":"7x24-vxr6Cc4R1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(61)90151-8","type":"journal-article"},{"key":"7x24-vxr6Cc5R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1724268","type":"journal-article"},{"key":"7x24-vxr6Cc6R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.133.B1549","type":"journal-article"},{"key":"7x24-vxr6Cc7R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.140.B1110","type":"journal-article"},{"key":"7x24-vxr6Cc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.173.1527","type":"journal-article"},{"key":"7x24-vxr6Cc9R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.174.1882","type":"journal-article"},{"key":"7x24-vxr6Cc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.175.1624","type":"journal-article"},{"key":"7x24-vxr6Cc11R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01066485","type":"journal-article"},{"key":"7x24-vxr6Cc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.96.085002","type":"journal-article"},{"key":"7x24-vxr6Cc13R1","volume-title":"Lectures on the Infrared Structure of Gravity and Gauge Theory","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":"2026","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":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"016004"}}