Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory

TL;DR

This paper derives Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory from the functional formalism, enabling the potential exact determination of Green's functions involving the temporal gauge field component.

Contribution

It presents a derivation of Slavnov-Taylor identities specific to Coulomb gauge Yang-Mills theory, establishing a framework for exact Green's function calculations.

Findings

Identified closed sets of identities for Green's functions.

Showed potential for exact solutions without approximation.

Provided a formal basis for future non-perturbative analyses.

Abstract

The Slavnov-Taylor identities of Coulomb gauge Yang-Mills theory are derived from the (standard, second order) functional formalism. It is shown how these identities form closed sets from which one can in principle fully determine the Green's functions involving the temporal component of the gauge field without approximation, given appropriate input.