Ward-Takahashi Identity for Vertex Functions of \(\text{sQED}\)

Abstract

Ward-Takahashi identity is an useful tool for calculatingamplitude of scattering processes. In the high-order perturbative theory of sQED, propagator and vertex functions contain many high-order corrections. By using Ward-Takahashi identity, each vertex function is separated into two parts: ``longitudinal'' and ``transverse'' part. The longitudinal part can be directly calculated from Ward-Takahashi identity. The transverse part depends on the expanding of specific orders of the theory. In this report, we present one method based on the Ward-Takahashi identity, to calculate this part of vertex functions at the one-loop order in arbitrary gauge and dimensions in sQED.