Numerical Study of Gluon Propagator and Confinement Scenario in Minimal Coulomb Gauge

TL;DR

This study numerically investigates the gluon propagator in SU(2) lattice gauge theory within the minimal Coulomb gauge, revealing insights into confinement mechanisms through the behavior of transverse and Coulomb components.

Contribution

It provides the first detailed numerical analysis of the equal-time gluon propagator components and their implications for confinement in minimal Coulomb gauge.

Findings

Transverse gluon propagator vanishes at zero momentum in infinite volume.

Color-Coulomb potential is strongly enhanced at zero momentum.

Gribov's formula fits the transverse propagator data well.

Abstract

We present numerical results in SU(2) lattice gauge theory for the space-space and time-time components of the gluon propagator at equal time in the minimal Coulomb gauge. It is found that the equal-time would-be physical 3-dimensionally transverse gluon propagator $D^{tr}(\vec{k})$ vanishes at $\vec{k} = 0$ when extrapolated to infinite lattice volume, whereas the instantaneous color-Coulomb potential $D_{44}(\vec{k})$ is strongly enhanced at $\vec{k} = 0$. This has a natural interpretation in a confinement scenario in which the would-be physical gluons leave the physical spectrum while the long-range Coulomb force confines color. Gribov's formula $D^{tr}(\vec{k}) = (|\vec{k}|/2)[(\vec{k}^2)^2 + M^4]^{1/2}$ provides an excellent fit to our data for the 3-dimensionally transverse equal-time gluon propagator $D^{tr}(\vec{k})$ for relevant values of $\vec{k}$.