Anomalies for Nonlocal Dirac Operators

TL;DR

This paper computes anomalies for a broad class of nonlocal Dirac operators using zeta-function and Wigner transformation techniques, showing that axial anomalies can be expressed in the standard form despite nonlocality.

Contribution

It introduces a method to compute anomalies for nonlocal Dirac operators and demonstrates that axial anomalies can be reformulated in the standard minimal Bardeen's form.

Findings

Anomalies for nonlocal Dirac operators are explicitly computed.

Nonlocal contributions can be absorbed into the standard anomaly form.

The techniques can be extended to other nonlocal operator analyses.

Abstract

The anomalies of a very general class of non local Dirac operators are computed using the $\zeta$-function definition of the fermionic determinant and an asymmetric version of the Wigner transformation. For the axial anomaly all new terms introduced by the non locality can be brought to the standard minimal Bardeen's form. Some extensions of the present techniques are also commented.