Product Integral Formalism and Non-Abelian Stokes Theorem

TL;DR

This paper introduces a surface product integral representation for the Wilson loop operator, extending Stokes' theorem to non-abelian gauge theories using product integrals.

Contribution

It provides a novel non-abelian Stokes' theorem formulation based on product integral properties, advancing the mathematical understanding of Wilson loops.

Findings

Surface product integral representation for Wilson loop

Non-abelian Stokes' theorem formulation

Mathematical insight into gauge theory Wilson loops

Abstract

We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes' theorem.