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arXiv · 2507.06880

The QED photon-fermion vertex from its Dyson-Schwinger equation in 4D: the full vertex, the transverse form factors and the perturbative solution

Orlando Oliveira
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Abstract

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 Kızılersu-Reenders-Pennington basis. Combining the vertex Ward-Takahashi identity with the vertex equation, we derive a set of exact, non-linear 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.

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Orlando Oliveira. 2025-10-08. The QED photon-fermion vertex from its Dyson-Schwinger equation in 4D: the full vertex, the transverse form factors and the perturbative solution. https://arxiv.org/abs/2507.06880

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