Communications in Physics 23, 11-19 (2013)

WARD-TAKAHASHI IDENTITY FOR VERTEX FUNCTIONS OF sQED

HA THANH HUNG, LE THO HUE AND HOANG NGOC LONG

Ward-Takahashi identity is an useful tool for calculating amplitude of scattering pro- cesses. 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 cal- culated 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.