Slavnov-Taylor Identities in Coulomb Gauge Yang-Mills Theory

TL;DR

This paper explores the color charge conservation and Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory, providing a formal framework that could enable exact solutions for temporal Green's functions and maintain gauge invariance.

Contribution

It demonstrates the existence of a conserved color charge and establishes the closure of Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory, facilitating potential exact solutions.

Findings

Conserved and vanishing total color charge in Coulomb gauge.

Closure of Slavnov-Taylor identities in the second order formalism.

Potential for exact solutions of temporal Green's functions.

Abstract

Two aspects of the color charge in Coulomb gauge continuum Yang-Mills theory are discussed. The first aspect is the existence of a conserved and vanishing total charge exhibited within the first order functional formalism. The second aspect is the closure of the set of Slavnov-Taylor identities in the second order functional formalism, such that the exact solution for temporal Green's functions is in principle possible and thereby preserving the color charge.