Soliton dynamics and symmetry in CP(^2) Sigma Models

Abstract

The primary purpose of the work undertaken in this thesis is to investigate soliton scattering in the non linear CP(^2) sigma model. This has two spatial and one temporal dimension. The vector fields used to represent the model have three components and hence there exists a global SU(3) symmetry. The effects of adding an Hopflike term to the basic lagrangian is considered. A review of the model is given in chapter I. The second chapter discusses Noether's theorem which states that each symmetry of the lagrangian has associated with it a conserved charge. In the third chapter, the eight charges relating to the internal symmetry are calculated. Explanations are provided for the results calculated during the numerical simulations. The results for the CP(^1) model are also discussed. In the fourth chapter, these charges are used to predict the qualitative behaviour of the solitons. It will provide an explanation for the effect of the coefficient of the hopflike term on the scattering. The single soliton ansatz is also investigated. In the penultimate chapter, an alternative approach is used. This involves looking for the closest static approximation to the evolved solution. It is able to predict the trajectory for pure CP(^2) and some confirmation is provided for the ansatz used in the full lagrangian. The last chapter summarises the results. It also provides some suggestions for further work.