Numerical Investigations of U(1) Lattice Gauge Theory

Abstract

U(1) Lattice Gauge Theory in three dimensions is a simple model that exhibits the non-trivial phenomenon of confinement. In this thesis, I numerically study this model using an extended action. This model is mapped to a dual height model defined on the dual lattice. I study the effect of the gamma on the mass gap by performing Monte Carlo simulations of the dual model on a cubic lattice. It will be shown that gamma allows us to probe the continuum behaviour of the system at relatively small beta. An effective coupling beta* will also be computed using the scaling of the mass gap. This model is also studied on a three dimensional `triangular' lattice. In order to validate the simulations, a strong-coupling expansion calculation is performed. I also provide a brief introduction to Lattice Field Theory and give a brief overview of the physics of 3D U(1) Lattice Gauge Theory in terms of monopoles.