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

Abstract

We have applied a new gauge-invariant, noncompact, Monte Carlo method to simulate the $U(1)$, $SU(2)$, and $SU(3)$ gauge theories on $8^4$ and $12^4$ lattices. The Creutz ratios of the Wilson loops agree with the exact results for $U(1)$ for $β\ge 0.5$ apart from 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 $SU(3)$ the scaling window is near $ β= 2 $, and the relation between the string tension $σ$ and our lattice QCD parameter $ Λ_L $ is $\sqrtσ \approx 5 Λ_L$.