In this work, we study various Monte Carlo methods for lattice gauge theories. The mass of the 0+ glueball for SU(2) gauge theory in 4 dimensions is calculated. This computation was done on a prototype parallel processor and the implementation of gauge theories on this system is described in detail. Using an action of the purely Wilson form (trace of plaquette in the fundamental representation), we obtain results with high statistics . We conclude that these results are not consistent with scaling according to the continuum renormalization group. Using actions containing higher representations of the group, we search for one which is closer to the continuum limit. Our choice is based upon the phase structure of these extended theories and also upon the Migdal-Kadanoff approximation to the renormalization group on the lattice . We obtain the mass of the 0+ glueball for this improved action and find that the mass divided by the square root of the string tension is a constant as the lattice spacing is varied. We conclude that scaling has set in and that this lattice theory is closer to the continuum limit than the simple Wilson version.
The other topic studied is the inclusion of dynamical fermions into Monte Carlo calculations via the pseudo fermion technique. Monte Carlo results obtained with this method are compared with those from an exact algorithm based on Gauss-Seidel inversion. We first apply the methods to the Schwinger model (QED in 1 + 1 dimensions) and show, in a coupling regime where the dynamical fermions have a nontrivial effect, that the mass gap is obtained with the correct value . After giving simple arguments explaining why the method works better than expected, we turn to a study of SU(3) in 4 dimensions (although on small lattices). Comparing with the exact algorithm, we again find encouraging agreement with the pseudo fermion technique. Evidence is given which shows that any systematic bias, associated with the breaking of the Markov process which generates the field configurations, is small.
