The Study Of The Soliton Solutions In (2+1) Yang-Mills-Higgs Field Theory
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Date
2012-03
Authors
Koh, Poh Wai
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
The purpose of this thesis is to study the solitonic solutions in (2+1) dimensions
of the Yang-Mills-Higgs eld theories. Soliton is de ned as solitary, traveling
wave pulse solution of nonlinear ordinary di erential equations (ODEs) or partial
di erential equations (PDEs). In order to nd the soliton, we must solve the
di erential equations either analytically or numerically.
In this thesis, the soliton solutions such as vortex, monopole-instanton are
studied in the context of U(1) Abelian gauge theory and the non-Abelian SU(2)
Yang-Mills-Higgs eld theory which is also known as the SU(2) Georgi-Glashow
model. The aim is to gain information on the existence and properties of these
topological solitons, their structure and behaviour by studying the classical eld
equations.
The theory of Cho's Abelian decomposition is introduced to study and nd
the exact solution of the monopoles. We are able to obtain the monopole solutions
by switching on the restricted part of the decomposition, when the valence part is
switched o . The monopole solutions possess free parameters that can represent
di erent types of monopole solutions, such as, Wu-Yang monopole, t' Hooft-
Polyakov monopole and half monopole solutions.
We also investigate the properties of the non-Abelian vortex solutions with the
Chern-Simon term. We generate the numerical solutions from a set of nonlinear
di erential equations which is also known as the equations of motion of the vortex.
Finally, we study the monopole-instanton solution in topologically massive
gauge theory in (2 + 1) dimensions with a Chern-Simons mass term that have
been studied by Pisarski many years ago. We obtained numerical regular solutions
that smoothly interpolates between the behavior at small and large distances for
various values of the Chern-Simons term strength and also Higgs eld strength.
Description
Keywords
The solitonic solutions in (2+1) dimensions , of the Yang-Mills-Higgs eld theories