The RP(^2) sigma and easy plane baby skyrme models

Abstract

This thesis examines the behaviour of two new models exhibiting topological solitons. This analysis is predominantly numerical, but a limited collective coordinate approach is attempted where appropriate. In chapter 1 we review the field of solitons. In particular the nature of topological solitons and their associated mathematical formalism are explained. A number of models admitting solitons are defined. In chapter 2 we look at the numerical methods necessary to solve the time evolution of topological solitons in the S(^2) sigma model and the baby Skyrme model. We also examine methods for finding static solutions of the equations of motion of such models. In chapter 3 we define the RP(^2) sigma and baby Skyrme models. We examine the behaviour of these models and find them to be identical to their (S^2) counterparts for most field configurations. The topological reason for this is explained. The existence of a topological object called a defect is noted and the behaviour of solitons in the presence of a defect is examined. A collective coordinate approach is used to examine the behaviour of solitons in the presence of a defect. In chapter 4 the easy plane baby Skyrme model is defined. An ansatz for the static skyrmions is proposed and its energy found to be accurate to 1.2% for the 1-skyrmion and about 0.5% for 2 to 4-skyrmions. These skyrmions are composed of two quasi- independent soliton like objects which we name "half lumps". These objects may not exist alone. The scattering properties of these objects are examined numerically. The behaviour of these scattering processes are explained in terms of the fields and potential energy of their intermediate states in the simulation. In chapter 5 we summarise our work and propose future work in this field.