Numerical Studies of Large N Lattice Gauge Theories.

This thesis describes the use of the coherent state variational algorithm for solving large N lattice gauge theories numerically. The algorithm is capable of studying hamiltonian or euclidean formulations of lattice gauge theories, in any dimension. Matter fields, such as bose or fermi fields may be included. The first half of the thesis discusses the implementation and the testing of this algorithm for exactly soluble model theories. Bosonic and fermion theories have been tested in detail. In the bosonic case physical quantities from the scalar phi^4 model have been computed with the algorithm and compared with exact results. For fermions the Gross-Neveu model has been studied in a similiar manner. We have found that only a small number of variational parameters yield accurate results in most cases. This includes computations where the theories contained asymptotic freedom and phase transitions. The second half of the thesis discusses computations of non-Abelian gauge theories. First the pure gauge sector is explored and ratios of glueball masses in 2 + 1 and 3 + 1 dimensions are calculated. Next the fermion sector, i.e., lattice QCD, is considered. Ratios of various non -strange meson masses in 3 + 1 dimensions are obtained. The ratios of the f and omega mesons to the S meson is found to be within a few percent of measured values. Other meson mass ratios are within 15-25% of experimentally measured ratios. Mass ratios of glueballs to mesons are also obtained and estimates of the 0^{++ }, 1^{+-} and 2^{++} glueballs are given.