Transverse Ward-Takahashi identities and full vertex functions in different representations of QED_3

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.