Bifurcation And Transition Phenomena Of Multiple Charged Monopole Plus Half-Monopole Of The Su(2) Yang-Mills-Higgs Theory - Zhu, Dan (2019)
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.