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 84 and 124 lattices. For U(1) the Creutz ratios of the Wilson loops agree with the exact results for β ≥ 0.5 after a renormalization of the charge. The SU(2) and SU(3) Creutz ratios robustly display quark confinement at β = 0.5 and β = 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 ΛL = 130 ± 18 MeV. Research supported by the U. S. Department of Energy under contracts DE-FG0484ER40166 and DE-FG03-92ER40732/A004 (task B). Permanent address, e-mail: [email protected] Unité de Recherche des Universités Paris XI et Paris VI associée au CNRS E-mail: herling @ unm.edu