Noncompact Gauge-Invariant Lattice Simulations

Abstract

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 Creutz ratios of the Wilson loops agree with the exact results for $U(1)$ for $β\ge 1$ apart from a renormalization of the charge. The $SU(2)$ and $SU(3)$ Creutz ratios robustly display quark confinement at $β= 0.5$ and $β= 1.5$, respectively. At much weaker coupling, the $SU(2)$ and $SU(3)$ Creutz ratios agree with perturbation theory after a renormalization of the coupling constant.