Axial-Anomaly in Noncommutative QED and Pauli-Villars Regularization

TL;DR

This paper investigates the axial anomaly in noncommutative QED across two and four dimensions, employing a modified path integral approach with Pauli-Villars regularization to clarify the anomaly calculation.

Contribution

It introduces a Pauli-Villars regularization within a modified path integral framework to compute the axial anomaly in noncommutative QED unambiguously.

Findings

Successful calculation of the axial anomaly in noncommutative QED

Establishment of a clear connection between regularization and Ward identities

Extension of anomaly analysis to both two and four dimensions

Abstract

We calculate the $U(1)$ axial-anomaly in two and four dimensions using a modified path integral method coupled to a Pauli-Villars regulator field in the noncommutative QED. Pauli-Villars regularization method provides us with unambiguous way to connect the modified path integral formalism with perturbative axial Ward identities at each step of calculations.