On the Point-Splitting Method of the Commutator Anomaly of the Gauss Law Operators

TL;DR

This paper examines the point-splitting method for the commutator anomaly in Gauss law operators, revealing that specific regularization kernels yield unique results that differ from previous cohomological findings.

Contribution

It demonstrates that certain regularization kernels produce unique commutator anomalies, contrasting with Faddeev's cohomological approach.

Findings

Certain regularization kernels lead to unique anomaly results

Results differ from Faddeev's cohomological conclusions

Integral conditions constrain the regularization kernels

Abstract

We analyze the generalized point-splitting method and Jo's result for the commutator anomaly. We find that certain classes of general regularization kernels satisfying integral conditions provide a unique result, which, however differs from Faddeev's cohomological result.