Generalized Coordinate Gauge and Nonabelian Stokes Theorem

TL;DR

This paper introduces a generalized coordinate gauge for nonabelian gauge theories, providing a new proof of the nonabelian Stokes theorem and exploring gauge conditions related to contour integrals of field strength.

Contribution

It presents a novel contour gauge framework and a simplified proof of the nonabelian Stokes theorem, enhancing understanding of gauge conditions and their applications.

Findings

Contour gauge relates vector potential to field strength via contour integrals.

Special contour classes lead to simplified gauge conditions.

The paper offers a straightforward proof of the nonabelian Stokes theorem.

Abstract

A contour gauge of general type is analysed where 1-form (vector potential) is expressed as a contour integral of the 2-form (field strength) along an arbitrary contour $C$. For a special class of contours the gauge condition reduces to $k_{\mu}(x) A_{\mu}(x) = 0 $ where $k_{\mu}(x)$ is a tangent vector to the contour $C$. A simple proof of the nonabelian Stokes theorem is given demonstrating the advantage of the gauge.