Axial Anomaly in Noncommutative QED on R^4

TL;DR

This paper investigates the axial anomaly in noncommutative QED on four-dimensional space, demonstrating that it aligns with the classical Chern class, and compares it with the commutative case using multiple methods.

Contribution

It provides a detailed calculation of the axial anomaly in noncommutative U(1) gauge theory and establishes its equivalence to the classical Chern class, comparing with the commutative scenario.

Findings

Axial anomaly in noncommutative QED matches the classical Chern class.

Multiple methods confirm the anomaly's form.

Comparison shows consistency with the commutative case.

Abstract

The axial anomaly of the noncommutative U(1) gauge theory is calculated by a number of methods and compared with the commutative one. It is found to be given by the corresponding Chern class.