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

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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 + M⁴]¹/² provides an excellent fit to our data for the 3-dimensionally transverse equal-time gluon propagator Dtr(k) for relevant values of k.