Identical Relations among Transverse Parts of Variant Green Functions and the Full Vertices in Gauge Theories

TL;DR

This paper derives exact relations among the transverse parts of vertex functions in gauge theories, combining them with Ward-Takahashi identities to fully determine the three-point vertex functions in momentum space.

Contribution

It introduces a method to derive complete sets of constraint relations for vertex functions by combining transverse relations with Ward-Takahashi identities.

Findings

Exact full vector, axial-vector, and tensor vertex functions obtained.

Transverse relations are coupled and form a complete set of constraints.

Method enhances understanding of vertex functions in gauge theories.

Abstract

The identical relations among the transverse parts of variant vertex functions are derived by computing the curl of the time-ordered products of three-point Green functions involving the vector, the axial-vector and the tensor current operators, respectively. These transverse relations are coupled each other. Combining these transverse relations with the normal (longitudinal) Ward-Takahashi identities forms a complete set of constraint relations for three-point vertex functions. As a consequence, the full vector, the full axial-vector and the full tensor vertex functions in the momentum space are exactly obtained.