SU(2) Running Coupling Constant and Confinement in Minimal Coulomb and Landau Gauges

We present a numerical study of the space-space and time-time components of the gluon propagator at equal time in the minimal Coulomb gauge, and of the gluon and ghost propagators in the minimal Landau gauge. This work allows a non-perturbative evaluation of the running coupling constant and a numerical check of Gribov's confinement scenarios for these two gauges. Our simulations are done in pure SU(2) lattice gauge theory at $\beta = 2.2$. We consider several lattice volumes in order to control finite-volume effects and extrapolate our results to infinite lattice volume.