The Coherent State Variational Algorithm
and the QCD Deconfinement Phase Transition

Abstract

"Research," explained Dorcas,
"is the concentrated examination and correlation
of the multitudinous phenomena co-existent in some specific field of activity."
- Dr. Seuss, The Seven Lady Godivas

This thesis describes the coherent state variational algorithm, its implementation in a recently completed set of computer programs, and its application to the study of the QCD deconfinement phase transition. The coherent state variational algorithm is a computational method for studying the large-N limit of non-abelian gauge theories by direct exploitation of the classical nature of the limit. Unlike Monte Carlo methods, this technique is applicable to both euclidian and hamiltonian formulations of lattice gauge theories and is deterministic, rather than statistical, in nature. The first part of this thesis presents the theoretical basis of the coherent state algorithm and describes the application of the algorithm to non-abelian lattice gauge theories. The second part describes the symbolic methods involved in the computer implementation of the coherent state algorithm and gives an overview of the programs which form the full coherent state implementation. The final part of this thesis discusses the applications of the coherent state algorithm to the study of the QCD deconfinement phase transition at large N. The results obtained are indicative of a second-order transition for lattices of temporal extent N_tau=1 and N_tau=2 in both three and four space-time dimensions.