Renormalization in a Landau to Coulomb interpolating gauge in Yang-Mills theory

TL;DR

This paper investigates the renormalization properties of an interpolating gauge between Landau and Coulomb gauges in Yang-Mills theory, aiming to clarify the gauge's mathematical consistency and special features across the interpolation.

Contribution

It provides a detailed analysis of the renormalization of the theta-gauge, a gauge interpolating between Landau and Coulomb gauges, for all values of the interpolation parameter.

Findings

Renormalization behavior varies with the interpolation parameter.

Identification of special features at specific gauge limits.

Clarification of the gauge's mathematical consistency.

Abstract

The Coulomb gauge in QCD is the only explicitly unitary gauge. But it suffers from energy-divergences which means that it is not rigorously well-defined. One way to define it unambiguously is as the limit of a gauge interpolating between the Landau gauge and the Coulomb gauge. This interpolating gauge is characterised by a parameter theta and the Coulomb gauge is obtained in the limit theta tends to zero. We study the renormalization of this theta-gauge for all values of theta, and note some special features of it.