Identical relations among transverse parts of variant Green's functions and the full vertices in gauge theories - art. no. 025207

Identity relations among the transverse parts of variant vertex functions i n gauge theories are derived by computing the curl of the time-ordered prod ucts of three-point Green's functions involving the vector, the axial-vecto r, and the tensor current operators, respectively. Combining these transver se relations with the normal (longitudinal) Ward-Takahashi identities forms a complete set of Ward-Takahashi relations for three-point vertex function s. As a consequence, the complete solutions for the vector, the axial-vecto r. and the tensor vertex functions in the momentum space are consistently a nd exactly obtained by solving this complete set of Ward-Takahashi relation s. In the case of massless fermions, the full vector and the full axial-vec tor vertices are expressed in terms of the fermion propagators only.