Noncompact, Gauge-Invariant Simulations of U(1), SU(2), and SU(3)

We have applied a new noncompact, gauge-invariant, Monte Carlo method to simulate the U(1), SU(2), and SU(3) gauge theories on 8^4 and 12^4 lattices. For U(1) the Creutz ratios of the Wilson loops agree with the exact results for beta > 0.5 after a renormalization of the charge. The SU(2) and SU(3) Creutz ratios robustly display quark confinement at beta = 0.5 and beta = 2, respectively. At much weaker coupling, the SU(2) and SU(3) Creutz ratios agree with perturbation theory after a renormalization of the coupling constant. For SU(3) without quarks, our lattice QCD parameter is Lambda_L = 130 ± 18$ MeV.