Zhu, Dan
(2019)
Bifurcation And Transition Phenomena
Of Multiple Charged Monopole Plus
HalfMonopole Of The Su(2)
YangMillsHiggs Theory.
Masters thesis, Universiti Sains Malaysia.
Abstract
Magnetic monopoles and multimonopoles are threedimensional topological soliton
solutions, which arise when the nonAbelian SU(2) symmetry is spontaneously
broken by the Higgs field. The gauge theory describing their existence is the SU(2)
YangMillsHiggs theory, which is also known as the SU(2) GeorgiGlashow model.
Recently, the existence of halfmonopole solutions had been proposed, and a configuration
involving a halfmonopole and an ordinary ’t HooftPolyakov monopole within
the SU(2) GeorgiGlashow model was also reported. However, since halfmonopole
is a relatively new field of research, topics regarding the interactions between onemonopoles
and halfmonopoles are rather scarce. In this thesis, the onemonopole
plus halfmonopole solution of the SU(2) YangMillsHiggs theory with higher value
of fwinding 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 oneplushalf 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 onemonopoles become an nmonopole superimposed
at the same location. At the same time, the halfmonopoles at the origin, in
the same manner, becomes a superimposed nhalfmonopole. When n = 2, the solutions
behave strangely and diverge after l = 8.00 and when n � 3, in contrary to the
observation in monopoleantimonopole pair (MAP) or monopoleantimonopole chain
(MAC) configurations, the onemonopoles do not merge with the halfmonopoles to
form vortexrings.
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