Noncompact, Gauge-Invariant Simulations of U(1), SU(2), and SU(3)
Kevin Cahill, Gary Herling
Abstract
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 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 LambdaL = 130 +- 18$ MeV.
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