Nonlocal Regularization For Non-Abelian Gauge Theories For Arbitrary Gauge Parameter

TL;DR

This paper investigates nonlocal regularization methods for non-abelian gauge theories across different gauge parameters, proposing an improved approach that ensures gauge parameter independence of physical observables.

Contribution

The authors introduce a simplified nonlocal regularization procedure that guarantees gauge parameter independence of S-matrix elements in non-abelian gauge theories.

Findings

Original localization method fails to produce gauge-independent results.

The new procedure yields gauge-independent S-matrix elements.

The approach simplifies nonlocal regularization in gauge theories.

Abstract

We study the nonlocal regularization for the non-abelian gauge theories for an arbitrary value of the gauge parameter (\xi). We show that the procedure for the nonlocalization of field theories established earlier by the original authors, when applied in that form to the Faddeev-Popov effective action in a linear gauge cannot lead to a (\xi)-independent result for the observables. We then show that an alternate procedure which is simpler can be used and that it leads to the S-matrix elements (where they exist) independent of (\xi).