Monopole-Antimonopole Pair, Vortex Dyons Of The SU(2) Yang-Mills-Higgs Field Theory
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Date
2011-01
Authors
Lim, Kok Geng
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Magnetic monopoles and dyons are topological soliton solutions in three space
dimensions, which arise in Yang-Mills-Higgs gauge theory where the non-Abelian
gauge group SU(2) is spontaneously broken by the Higgs eld to a residual symmetry
group U(1). While the magnetic charge is quantized due to topological
arguments, the electric charge is not.
In this thesis, the magnetic monopoles and dyons are studied in the context of
the 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.
Generically, an appropriate ansatz is pivotal in solving the second order equations
of motion which are a set of nonlinear partial di erential equations. Then
the next step is either solving them analytically or numerically. The early literature
review on magnetic monopoles and dyons are described in this thesis.
By applying a proper gauge transformation, we found that the magnetic
charge of the monopole can be transferred from the Higgs eld to the gauge eld
and vice versa. The results show that the string singularity from the Abelian
gauge can be removed by varying the parameter from the regulated polar angle
(Boulware et al., 1976) after gauge transformation.
We also study the one half topological charge monopole solutions. These
solutions do not necessarily satisfy the rst order Bogomol'nyi equations and
they possess in nite energy density at the origin. Our results show that these
half-monopoles are actually a half Wu-Yang type monopole and they can possess
electric charge and become half-dyons.
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Keywords
The magnetic monopoles and dyons , the SU(2) Yang-Mills-Higgs eld theory