## Phase transitions in induced lattice gauge models.

##### Abstract

The present research is based on the study of the phase structure of lattice models incorporating selfinteracting scalars and gauge background fields otherwise known as induced gauge models. Emphasis is placed on the effect the choice of the integration measure over the radial modes of the scalar fields have on the phase structure of these models. Both numerical simulations and analytical results based on the mean field approximations are presented.
In Chapter 1 an introduction to quantum field theory is given leading to the formulation of Euclidean quantum field theory.
In Chapter 2 global and local gauge invariance together with the mechanism of spontaneous symmetry breaking are discussed.
In Chapter 3 the formulation of quantum field theory on the lattice is introduced. The lattice regularization entails discretizing space and time and presents an elegant approach to studying certain phenomena of the continuum theory which are beyond the reach of standard perturbative analysis.
In Chapter 4 the Monte Carlo methods for evaluating the Euclidean Feynman path integral as applied to lattice gauge theory are discussed.
In Chapter 5 numerical studies of some lattice gauge models are presented. Both pure lattice gauge models and gauge-Higgs models are examined.
In Chapter 6 the Kazakov-Migdal model which presents an interesting approach to inducing QCD is discussed.
In Chapter 7 the mixed fundamental-adjoint induced model is introduced. This model succeeds in breaking the local ZN symmetry of the Kazakov-Migdal model by adding to it scalar fields in the fundamental representation of the gauge group. The effect of the choice of the radial integration measure on the phase structure of a class of Abelian induced models is studied.