Axial Anomaly from the BPHZ regularized BV master equation

TL;DR

This paper demonstrates how the BPHZ regularized BV master equation can be used to compute axial anomalies in QED, reproducing the known anomalous divergence of the axial current within this formalism.

Contribution

It extends the BPHZ regularized BV framework to calculate global anomalies, specifically the axial anomaly in QED, showing its effectiveness beyond gauge anomalies.

Findings

Reproduces the axial Ward identity anomaly in QED using BPHZ BV formalism.

Shows the applicability of the BPHZ regularized BV master equation to global anomalies.

Validates the framework by matching known anomaly results in standard QED.

Abstract

A BPHZ renormalized form for the master equation of the field antifiled (or BV) quantization has recently been proposed by De Jonghe, Paris and Troost. This framework was shown to be very powerful in calculating gauge anomalies. We show here that this equation can also be applied in order to calculate a global anomaly (anomalous divergence of a classically conserved Noether current), considering the case of QED. This way, the fundamental result about the anomalous contribution to the Axial Ward identity in standard QED (where there is no gauge anomaly) is reproduced in this BPHZ regularized BV framework.