Transverse Ward-Takahashi identities and full vertex functions in different representations of QED3 *

Abstract

Abstract We derive the transverse Ward-Takahashi identities (WTI) of N-dimensional quantum electrodynamics by means of the canonical quantization method and the path integration method, and subsequently attempt to prove that QED3 is solvable based on the transverse and longitudinal WTI, indicating that the full vector and tensor vertices functions can be expressed in terms of the fermion propagators in QED3. Further, we discuss the effect of different γ matrix representations on the full vertex function.