Algorithms for fully interacting lattice gauge theory

The numerical simulation of fully interacting lattice gauge theory is one of the most computationally demanding problems in physics due to the anti-commuting nature of fermion fields. One approach to the problem uses stochastic matrix inversion. Several substantial new improvements to this technique have been discovered. One of the improvements is obtained by solving an intricate counting problem. The method is tested on a two dimensional version of QED known as the massive Schwinger model. The results indicate that the algorithm is effective in computing the properties of fully interacting fermions. The mass extraction technique allowed by the algorithm permits the computation of particle masses in the light mass regime inaccessible by conventional techniques. One result obtained is that the quenched approximation is nearly exact in two dimensional QED, contrary to some theoretical predictions. The stochastic algorithm avoids many of the systematic errors associated with fermion methods currently in use for QCD. With the advent of large scale multi-processing computers, it can become competitive, if not superior, in terms of speed as well. The successes of the techniques presented in this thesis offer a reasonable prospect of non-perturbative solutions of fully interacting field theories