Zhu, Dan
(2019)
Bifurcation And Transition Phenomena
Of Multiple Charged Monopole Plus
Half-Monopole Of The Su(2)
Yang-Mills-Higgs Theory.
Masters thesis, Universiti Sains Malaysia.
Abstract
Magnetic monopoles and multimonopoles are three-dimensional topological soliton
solutions, which arise when the non-Abelian SU(2) symmetry is spontaneously
broken by the Higgs field. The gauge theory describing their existence is the SU(2)
Yang-Mills-Higgs theory, which is also known as the SU(2) Georgi-Glashow model.
Recently, the existence of half-monopole solutions had been proposed, and a configuration
involving a half-monopole and an ordinary ’t Hooft-Polyakov monopole within
the SU(2) Georgi-Glashow model was also reported. However, since half-monopole
is a relatively new field of research, topics regarding the interactions between onemonopoles
and half-monopoles are rather scarce. In this thesis, the one-monopole
plus half-monopole solution of the SU(2) Yang-Mills-Higgs theory with higher value
of f-winding number, n (2 � n � 4) is studied for a range of the Higgs coupling
constants, l (0 < l � 40), and the resolution of the grids used (110 � 100) in the
numerical method for calculating the solutions is also greater than previous research.
The goal of this dissertation is to gain information about the general behaviors and
properties of the one-plus-half monopole configuration, to probe the interactions between
constituents through phenomena manifested as bifurcations and transitions of
solutions, as well as to obtain a deeper understanding of the structure of gauge theories.
We noticed that for n � 2, the one-monopoles become an n-monopole superimposed
at the same location. At the same time, the half-monopoles at the origin, in
the same manner, becomes a superimposed n-half-monopole. When n = 2, the solutions
behave strangely and diverge after l = 8.00 and when n � 3, in contrary to the
observation in monopole-antimonopole pair (MAP) or monopole-antimonopole chain
(MAC) configurations, the one-monopoles do not merge with the half-monopoles to
form vortex-rings.
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