Confinement made simple in the Coulomb gauge

TL;DR

This paper provides exact analytical results on the behavior of gluon propagators in Coulomb gauge, supporting the confinement mechanism via the color-Coulomb potential and analyzing the running coupling constant.

Contribution

It offers the first exact analytic expressions for key gluon propagators in Coulomb gauge, confirming confinement features and linking to the running coupling constant.

Findings

D^{tr}(k) vanishes at k=0, indicating gluon confinement.

Exact analytic forms for D_{44} and D^{tr} are derived.

The running coupling constant is determined from the gluon propagator.

Abstract

In Gribov's scenario in Coulomb gauge, confinement of color charge is due to a long-range instantaneous color-Coulomb potential V(R). This may be determined numerically from the instantaneous part of the gluon propagator D_{44, inst} = V(R) \delta(t). Confinement of gluons is reflected in the vanishing at k = 0 of the equal-time three-dimensionally transverse would-be physical gluon propagator D^{tr}(k). We present exact analytic results on D_{44} and D^{tr} (which have also been investigated numerically, A. Cucchieri, T. Mendes, and D. Zwanziger, this conference), in particular the vanishing of D^{tr}(k) at k = 0, and the determination of the running coupling constant from x_0 g^2(k) = k^2 D_{44, inst}, where x_0 = 12N/(11N-2N_f).