Gauge-Invariant Noncompact Lattice Simulations

Three techniques for performing gauge-invariant, noncompact lattice simulations of nonabelian gauge theories are discussed. In the first method, the action is not itself gauge invariant, but a kind of lattice gauge invariance is restored by random compact gauge transformations during the successive sweeps of the simulation. This method has been applied to pure $SU(2)$ gauge theory on a $12^4$ lattice, and Wilson loops have been measured at strong coupling, $\beta=0.5$. These Wilson loops display a confinement signal not seen in simulations performed earlier with the same action but without the random gauge transformations. In the second method, the action is gauge symmetrized by integrations over the group manifold. The third method is based upon a new, noncompact form of the action that is exactly invariant under lattice gauge transformations. The action is a natural discretization of the classical Yang-Mills action.