On the non-Abelian Stokes theorem in SU(2) gluodynamics

TL;DR

This paper presents a formulation of the non-Abelian Stokes theorem for SU(2) gauge fields that simplifies the mathematical structure by eliminating extra variables and surface ordering, with applications to lattice gauge theory.

Contribution

It introduces a new approach to the non-Abelian Stokes theorem that avoids additional integration variables and surface ordering, and discusses its lattice implementation.

Findings

Simplified non-Abelian Stokes theorem for SU(2)

Application to lattice gauge theory

Analysis of contributions to Wilson loop trace

Abstract

We discuss the non-Abelian Stokes theorem for SU(2) gauge fields which avoids both additional integration variables and surface ordering. The idea is to introduce the instant color orientation of the flux piercing the loop. The non-Abelian Stokes theorem is also considered on the lattice and various terms contributing to the trace of the Wilson loop are discussed.