Quantum Field Theory, Effective Potentials and Determinants of Elliptic Operators

Abstract

The effective potential augments the classical potential with the quantum effects of virtual particles, and permits the study of spontaneous symmetry breaking. In contrast to the standard approach where the classical potential already leads to electroweak symmetry-breaking, the Coleman-Weinberg mechanism explores quantum corrections as the source of symmetry-breaking. This thesis explores extensions of the Coleman -Weinberg mechanism to the situations with more than one Higgs doublet. These multi-Higgs models have a long history , and occur most naturally in the Minimal Supersymmetric model. Mathematical foundations of the zeta function method will be developed and then applied to regularise the one-loop computation of the effective potentials in a model with two scalar fields.