Quantum anomaly of the transverse Ward-Takahashi relation for the axial-vector vertex

TL;DR

This paper investigates quantum anomalies in the transverse Ward-Takahashi relations within four-dimensional gauge theories, revealing an anomaly in the axial-vector case but not in the vector case, thus deepening understanding of gauge symmetry violations.

Contribution

It introduces the concept of a quantum anomaly in the transverse Ward-Takahashi relation for the axial-vector vertex, expanding the known anomalies in gauge theories.

Findings

Anomaly found in the axial-vector transverse Ward-Takahashi relation.

No anomaly detected for the vector vertex.

The axial-vector curl equation exhibits a quantum anomaly.

Abstract

We study the possible quantum anomaly for the transverse Ward-Takahashi relations in four dimensional gauge theories based on the method of computing the axial-vector and the vector current operator equations. In addition to the well-known anomalous axial-vector divergence equation (the Adler-Bell-Jackiw anomaly), we find the anomalous axial-vector curl equation, which leads to the quantum anomaly of the transverse Ward-Takahashi relation for the axial-vector vertex. The computation shows that there is no anomaly for the transverse Ward-Takahashi relation for the vector vertex.