On the path integral representation for Wilson loops and the non-Abelian Stokes theorem II

TL;DR

This paper revises the path integral approach for Wilson loops, demonstrating that a specific character expansion yields more accurate results and challenges previous claims about the Wilson loop's value.

Contribution

It applies a recommended character expansion to evaluate gauge path integrals, correcting prior approximations and disputing earlier results on Wilson loop calculations.

Findings

The new expansion retains previous results.

The earlier regularization method predicts zero Wilson loop.

The revised approach improves accuracy of gauge path integral evaluations.

Abstract

This paper is a revised version of our recent publication Faber et al., Phys. Rev. D62 (2000) 025019, hep-th/9907048. The main revision concerns the expansion into group characters that we have used for the evaluation of path integrals over gauge degrees of freedom. In the present paper we apply the expansion recommended by Diakonov and Petrov in hep-lat/0008004. Our former expansion was approximate and in the region of the particular values of parameters violated the completeness condition by 1.4%. We show that by using the expansion into characters recommended by Diakonov and Petrov in hep-lat/0008004 our previous results are retained and the path integral over gauge degrees of freedom for Wilson loops derived by Diakonov and Petrov (Phys. Lett. B224 (1989) 131 and hep-lat/0008004) by using a special regularization is erroneous and predicts zero value for the Wilson loop. We give comments on the paper hep-lat/0008004.