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 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.