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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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Phys. Rev. D 112, 076009 – Published 10 October, 2025

DOI: https://doi.org/10.1103/cvsn-k4q5

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, 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.

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Phys. Rev. D 112, 076009– Published 10 October, 2025
  • Received 10 July 2025
  • Accepted 19 September 2025
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