Dyson-Schwinger Equations and Coulomb Gauge Yang-Mills Theory

TL;DR

This paper explores Coulomb gauge Yang-Mills theory using the first order formalism, demonstrating invariance under specific symmetries and the automatic satisfaction of Ward-Takahashi identities by the equations of motion.

Contribution

It introduces a novel analysis of Coulomb gauge Yang-Mills theory highlighting new symmetry invariances and their implications for the theory's consistency.

Findings

Invariance under standard BRS and additional transformations.

Ward-Takahashi identities are automatically satisfied.

First order formalism provides new insights into gauge invariance.

Abstract

Coulomb gauge Yang-Mills theory is considered within the first order formalism. It is shown that the action is invariant under both the standard BRS transform and an additional component. The Ward-Takahashi identity arising from this non-standard transform is shown to be automatically satisfied by the equations of motion.