Numerical study of the gluon propagator and confinement scenario in the minimal Coulomb gauge

We present numerical results in $\mathrm{SU}\left(2\right)\mathrm{}$ 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 $D^{\mathrm{tr}}\left(\overrightarrow{k}\right)$ vanishes at $\overrightarrow{k}=0\mathrm{}$ when extrapolated to infinite lattice volume, whereas the instantaneous color-Coulomb potential $D_{44}\left(\overrightarrow{k}\right)$ is strongly enhanced at $\overrightarrow{k}=0.\mathrm{}$ 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 $D^{\mathrm{tr}}\left(\overrightarrow{k}\right)=(|\overrightarrow{k}|/2)\left[\right(k^2{)}^2{+M}^4{]}^{1/2}$ provides an excellent fit to our data for the 3-dimensionally transverse equal-time gluon propagator $D^{\mathrm{tr}}\left(\overrightarrow{k}\right)$ for relevant values of $\overrightarrow{k}.$