Monte Carlo computations for lattice gauge theories with finite gauge groups

The lattice formulation of quantum gauge field theories provides a regularization of the ultraviolet divergences and allows computational techniques, such as strong coupling expansions, which cannot be applied to the continuum theory. After a Wick rotation of time to imaginary time, the weighted sum over all configurations used to define quantum expectation values becomes formally identical to a statistical sum for a four-dimensional system. This has suggested the recourse to Monte Carlo simulations for obtaining numerical information about lattice gauge field theories. Monte Carlo computations have indeed constituted for a while, basically since the advent of modern high-speed computers, a very powerful tool to study statistical systems. The author describes results obtained in a variety of Monte Carlo investigations in which he has been involved. (11 refs).