NONCOMPACT GAUGE-INVARIANT SIMULATIONS OF U(1), SU(2), AND SU(3)

We have applied a new gauge-invariant, noncompact, Monte Carlo method to simulate U(1), SU(2), and SU(3) gauge theories on 8(4) and 12(4) lattices. The Crentz ratios of the Wilson loops agree with the exact results for U(1) for beta greater than or equal to 1 apart from a renormalization of the charge. The SU(2) and SU(3) Crentz ratios robustly display quark confinement at beta = 0.5 and beta = 2, respectively. At much weaker coupling, the SU(2) and SU(3) Crentz ratios agree with perturbation theory after a renormalization of the coupling constant. For SU(3) the scaling window is near beta = 2, and the relation between the string tension LT and our lattice QCD parameter Delta(L) is root sigma approximate to Delta(L).