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

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 $\vec{k}$.