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Infrared divergences and the photon mass in QED
Authors: Oliveira, O.
Ref.: Phys. Rev. D 113(1), 016004 (2026)
Abstract: 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 1/k2. 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.
