Looking at QED with Dyson–Schwinger Equations: Basic Equations, Ward–Takahashi Identities and the Two-Photon-Two-Fermion Irreducible Vertex

Abstract A minimal truncated set of the integral Dyson–Schwinger equations, in Minkowski spacetime, that allows to explore QED beyond its perturbative solution is derived for general linear covariant gauges. The includes equations fermion and photon propagators, photon-fermion vertex, two-photon-two-fermion one-particle-irreducible diagram. If first three are exact, build a closed equation ignoring contribution Green functions with large number external legs. It shown vertex reproduces lowest-order result limit small coupling constant. Furthermore, this define an iterative procedure compute higher order corrections Ward–Takahashi identity irreducible solved soft limit, where one momenta vanish, low kinematics. determines longitudinal component while it proposed use determine transverse part DSE heavy considering simplified version vertices. low-energy effective discussed fermionic operators generated computed terms propagator functions.