BIFURCATION AND TRANSITION FOR ELECTRICALLY CHARGED MULTIMONOPOLE CHAINS IN SU(2) YANG-MILLS-HIGGS THEORY

MAP and MAC solutions as axially symmetric multimonopole solutions with finite energy in SU(2) Yang-Mills-Higgs (YMH) theory, recently have caused a great amount of attention. In this thesis, the dependence of physical and geometrical properties of electrically charged MAP and MAC solutions in the Higgs self-coupling constant l, is investigated. For MAC systems, the cases with three and four poles are considered here. The study includes f-winding numbers of n = 2;3 and 4 for MAP and four-pole MAC systems. For the case of three-pole MAC systems, we extended the study to the f-winding number of n = 5 as well. For the case of MAP systems, for each value of n = 2;3 and 4, we found a bifurcation with higher energy in comparison with the fundamental solution. For the cases with n = 3 and 4, the Higher Energy Branch (HEB) solution undergoes a transition from MAP configuration to vortex-ring configuration. For the case of n = 2 a new bifurcation is introduced in this thesis. The two new branches are the only known bifurcating purely vortex-ring solutions so far. For the three-pole MAC systems, there is only one bifurcation for each one of the cases with n=3 and 4. However for the case of n=5, there are two bifurcations and therefore five co-existing branches for large values of l. For these systems transitions are detected along fundamental solutions as well as HEB solutions. There is also a joining point for which the fundamental solution of the case of n = 3 joins to the Lower Energy Branch (LEB) solution for the case of n = 3 and both branches stop at this point and do not survive for larger values of l. Also, for the first time we have detected a transition between a monopole and antimonopole for the pole which is located at the centre. For four-pole systems, a multi-branch structure is found for the cases of n = 3 and 4. For the case of n = 4 there are four bifurcations along with the fundamental solution. Also there is a joining point for which two HEB solutions of two different bifurcations join to each other. Here for the first time, a transition along the one LEB solution is detected. As another important result, a new bifurcation is introduced for the case of n = 3 which was not detected with the previous studies.