A Normal Coordinate Expansion for the Gauge Potential

TL;DR

This paper introduces a covariant normal coordinate expansion method for gauge potentials on curved space-time, providing a potentially useful tool for theoretical physics applications.

Contribution

It presents a fully covariant normal coordinate expansion technique for gauge potentials, filling a gap in the literature for applications on curved manifolds.

Findings

Provides a systematic covariant expansion method

Ensures gauge potential expansions are fully covariant

Potential applications in theoretical physics and geometry

Abstract

In this pedagogical note, I present a method for constructing a fully covariant normal coordinate expansion of the gauge potential on a curved space-time manifold. Although the content of this paper is elementary, the results may prove useful in some applications and have not, to the best of my knowledge, been discussed explicitly in the literature.