On the axial anomaly in Very Special Relativity

TL;DR

This paper investigates the axial anomaly within Very Special Relativity Electrodynamics, demonstrating that standard anomalies are preserved without corrections and exploring regularization methods in different dimensions.

Contribution

It provides a detailed analysis of the axial anomaly in VSR, showing that traditional anomalies remain unchanged and illustrating how to derive the anomaly via the path integral approach.

Findings

Standard axial anomaly is preserved in VSR in 2 and 4 dimensions.

Regularization methods used do not alter the anomaly results.

Path integral approach reproduces the anomaly in VSR.

Abstract

In this paper we study the axial anomaly in Very Special Relativity Electrodynamics using Pauli-Villars and dimensional regularization of ultraviolet divergences and Mandelstam-Leibbrandt regularization of infrared divergences. We compute the anomaly in 2 and 4 dimensional space-time. We find that this procedure preserves the vector Ward identity(charge conservation) and reproduce the standard axial anomaly in 2 and 4 dimensions without corrections from VSR. Finally, we show how to obtain the anomaly in the path integral approach.