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

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 Dtr(~k) vanishes at ~k = 0 when extrapolated to infinite lattice volume, whereas the instantaneous color-Coulomb potential D44(~k) is strongly enhanced at ~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 Dtr(~k) = (|~k|/2)[(~k2)2 + M] provides an excellent fit to our data for the 3dimensionally transverse equal-time gluon propagator Dtr(~k) for relevant values of ~k.