Abelian Anomalies in Nonlocal Regularization

TL;DR

This paper demonstrates that nonlocal regularization of QED exhibits an axial anomaly similar to other methods, clarifying symmetry violations and measure contributions, and discusses challenges in fully gauged chiral theories.

Contribution

It explicitly constructs the Noether current in nonlocal regularization and analyzes the anomaly and symmetry violations, providing new insights into chiral gauge theories.

Findings

Nonlocal regularization reproduces the axial anomaly.

Symmetries are violated at the current level but preserved in measure contributions.

Quantization of fully gauged chiral invariant theories faces barriers.

Abstract

Nonlocal regularization of QED is shown to possess an axial anomaly of the same form as other regularization schemes. The Noether current is explicitly constructed and the symmetries are shown to be violated, whereas the identities constructed when one properly considers the contribution from the path integral measure are respected. We also discuss the barrier to quantizing the fully gauged chiral invariant theory, and consequences.