Monopoles in gauge field theory

Abstract

In this thesis, I explore the possible existence of finite-energy monopoles and dyons in the electroweak theory of Weinberg and Salam which is characterized by the symmetry breaking pattern SU(2) x U(1)Y → U(1)em. It has been asserted that there exists no topological monopoles in the electroweak theory as the consequence of trivial second homotopy of the quotient group SU(2) x U(1)Y/U(1)em after the spontaneous symmetry breaking. This thesis examines the Standard Model as a gauged CP1 model that would bypass the previous trivial group topology argument by decomposing the Higgs doublet. Further analysis on the energy functional corresponding to the electroweak bosonic sector within the framework of CP1 model results in a set of requirements that define the structure of the Higgs vacuum, particularly the condition in which the Higgs unit doublet ξ should satisfy Dµξ/2 =0 at asymptotic infinity.