Numerical study of the gluon propagator and confinement scenario in the 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 D-tr((k) over right arrow) vanishes at (k) over right arrow =0 when extrapolated to infinite lattice volume, whereas the instantaneous color-Coulomb potential D-44((k) over right arrow) is strongly enhanced at (k) over right arrow =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((k) over right arrow)=(\(k) over right arrow\/2)[((k) over right arrow (2))(2) +M-4](1/2) provides an excellent fit to our data for the 3-dimensionally transverse equal-time gluon propagator D-tr((k) over right arrow) for relevant values of (k) over right arrow.