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