Charged solution excitations and the vaccum state of.. field theories

Abstract

This thesis describes some theoretical investigations on ?? field theories (i.e., theories governed by Lagrangians which are sixth-degree polynomials in ?) where ? is either a real or a complex scalar field. We work in one space and one time dimension, since such theories are renormalizable only then. The ?? field theories are the simplest model systems (i) which can support charged soliton solutions when the field ? is complex. These solutions have been obtained in the literature. We study the long-range interactions between them as a function of their charge and separation. Furthermore, given these solutions, one would expect on physical grounds that they would contribute as 'elementary' excitations in the statistical mechanics of the complex ? field. We show this to be true by deriving these charged excitations systematically from the functional integral for the classical partition function. (ii) for which there exists the possibility of symmetry restoration by quantum or statistical fluctuations. This is studied using the method of the loop expansion of the effective potential. To achieve the double goal of having a significant one-loop contribution without spoiling the convergence of the loop expansion, a theory with at least two coupling constants is required. The ?? field theory does have two coupling constants.