Completing Continuum Coulomb Gauge in the Functional Formalism

TL;DR

This paper argues that in the continuum functional formalism for Yang-Mills theory, the Coulomb gauge is inherently complete without additional constraints, but attempts to complete it naturally conflict with the theory's renormalizability.

Contribution

It demonstrates that the Coulomb gauge in the continuum formalism does not require extra constraints and shows that natural completions lead to contradictions with renormalizability.

Findings

No need for additional gauge constraints in Coulomb gauge

Natural completions conflict with perturbative renormalizability

Clarifies gauge fixing in continuum Yang-Mills theory

Abstract

It is argued that within the continuum functional formalism, there is no need to supply a further (spatially independent) gauge constraint to complete the Coulomb gauge of Yang-Mills theory. It is shown explicitly that a natural completion of the gauge-fixing leads to a contradiction with the perturbative renormalizability of the theory.