Stokes Theorem for Loop Variables of Non-Abelian Gauge Field

TL;DR

This paper provides an analytic proof of the non-Abelian Stokes theorem, demonstrating its consistency via the Bianchi identity, and explores constructing a gauge field Lagrangian using loop variables.

Contribution

It offers a new analytic proof of the non-Abelian Stokes theorem and investigates the formulation of gauge field Lagrangian in terms of loop variables.

Findings

Proof of the non-Abelian Stokes theorem

Verification of consistency via Bianchi identity

Exploration of gauge field Lagrangian construction

Abstract

A simple analytic proof of the formula known as the non-Abelian Stokes theorem is given. It is explicitly shown that the consistency of the formula is guaranteed by the Bianchi identity for the gauge field. An attempt is made to construct the Lagrangian for the gauge field in terms of loop variables.