On the non-Abelian Stokes theorem for SU(2) gauge fields

TL;DR

This paper derives a simplified non-Abelian Stokes theorem for SU(2) gauge fields that eliminates the need for surface ordering by using the flux's instantaneous color orientation, applicable on the lattice.

Contribution

It introduces a novel formulation of the non-Abelian Stokes theorem that removes the need for surface ordering and extends it to lattice gauge theory.

Findings

Elimination of surface ordering in the non-Abelian Stokes theorem.

Derivation of the theorem on the lattice.

Analysis of terms contributing to Wilson loop traces.

Abstract

We derive a version of non-Abelian Stokes theorem for SU(2) gauge fields in which neither additional integration nor surface ordering are required. The path ordering is eliminated by introducing the instantaneous color orientation of the flux. We also derive the non-Abelian Stokes theorem on the lattice and discuss various terms contributing to the trace of the Wilson loop.