Coulomb-gauge in QCD: renormalization and confinement

TL;DR

This paper reviews the Coulomb gauge in QCD, discussing its renormalization, the structure of the fundamental modular region, and the potential role of Coulomb interaction in confinement, proposing that the Coulomb string tension may serve as an order parameter.

Contribution

It introduces a detailed analysis of Coulomb gauge in QCD, including the renormalization properties and the conjecture that Coulomb potential relates to confinement.

Findings

The Coulomb potential $V(R)$ is renormalization-group invariant.

$V(R)$ contributes exponentially to the Wilson loop.

Conjecture that $V(R)$ becomes linear at large distances, indicating confinement.

Abstract

We review the Coulomb gauge in QCD and report some recent results. The minimal Coulomb gauge is defined and the fundamental modular region, a region without Gribov copies, is described. The Coulomb gauge action is expressed in terms of the dynamical degrees of freedom with an instantaneous Coulomb interaction, and its physical meaning is discussed. The local Coulomb gauge action with phase-space and ghost variables is derived, and its BRS-invariance and renormalizability are reviewed. It is shown that the instantanteous part $V(R)$ of $g^2 D_{00}(R, t)$, the time-time component of the gluon propagator, is a renormalization-group invariant $V(R) = f(R\Lambda_{QCD})/R$, and that the contribution of $V(R)$ to the Wilson loop exponentiates. It is conjectured that $V(R) \sim \kappa_{coul}R$ at large $R$, and that $\kappa_{coul}$ provides an order parameter for confinement of color even in the presence of dynamical quarks.