Yang-Mills as a Constrained Gaussian

TL;DR

This paper presents a reformulation of Yang-Mills theory using the logarithmic derivative of holonomies, expressing the path integral as a constrained Gaussian, which offers new perspectives on its classical and quantum structure.

Contribution

It introduces a novel representation of Yang-Mills theory as a constrained Gaussian, connecting classical equations of motion with a new path integral formulation.

Findings

Classical equations of motion are recovered in the new formulation.

Path integral is expressed as a constrained Gaussian.

Provides a new mathematical framework for Yang-Mills theory.

Abstract

Yang-Mills is reformulated in terms of the logarithmic derivative of the holonomies. The classical equations of motion are recovered, and the path integral is rewritten in two ways, both of which are of the form of a Gaussian satisfying a quadratic constraint.