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.