A study of U(1) lattice gauge theory in four dimensions

Abstract

We examine some aspects of four dimensional U(1) lattice gauge theory. Throughout this report we use a pure gauge action without fermions. In the introductory Chapter I we briefly review the general formalism of lattice gauge theory and the current state of knowledge in U(1) lattice gauge theory. We also give a brief account of Monte-Carlo methods and describe some of the numerical techniques to be used in later chapters. In Chapter II we present results from an analysis of a U(1) model on a simplicial lattice. We comment on the need to consider alternative lattices, briefly describe the simplicial lattice geometry, show that it has the correct naive continuum limit and report on measurements of Wilson loops, string tension and specific heat. We compare our results to those obtained with the more commonly used hypercubic lattice and find good agreement with improved simulation time. In Chapter III we apply the techniques of the Monte-Carlo Renormalization group to U(1) lattice gauge theory. After a brief introduction to the Real Space Renormalization Group formalism we describe some special numerical techniques which are appropriate to this work. We report on measurements of the model's critical exponents and calculate the renormalized parameters using the Swendsen Method. We discuss the relevance of our results to the understanding of the U(1) phase diagram in a multi-parameter space.