Nonperturbative Fermion-Boson Vertex Function in Gauge Theories

TL;DR

This paper derives a nonperturbative fermion-boson vertex function in four-dimensional Abelian gauge theories using Ward-Takahashi relations, accounting for anomalies and corrections, and expressing it in terms of the full fermion propagator.

Contribution

It provides an exact, self-consistent derivation of the fermion-boson vertex function incorporating transverse anomalies and quantum corrections, advancing understanding of gauge invariance.

Findings

Vertex function expressed in terms of full fermion propagator

Transverse axial anomaly contributes to the vertex

Inclusion of quantum corrections and anomalies

Abstract

The nonperturbative fermion-boson vertex function in four-dimensional Abelian gauge theories is self-consistently and exactly derived in terms of a complete set of normal (longitudinal) and transverse Ward-Takahashi relations for the The nonperturbative fermion-boson vertex function in four-dimensional Abelian gauge theories is self-consistently and exactly derived in terms of a complete set of normal(longitudinal) and transverse Ward-Takahashi relations for the fermion-boson and the axial-vector vertices in the case of massless fermion, in which the possible quantum anomalies and perturbative corrections are taken into account simultaneously. We find that this nonperturbative fermion-boson vertex function is expressed nonperturbatively in terms of the full fermion propagator and contains the contributions of the transverse axial anomaly and perturbative corrections. The result that the transverse axial anomaly contributes to the nonperturbative fermion-boson vertex arises from the coupling between the fermion-boson and the axial-vector vertices through the transverse Ward-Takahashi relations for them and is a consequence of gauge invariance.