Title:

Classical and quantized solitons

This thesis is concerned with the classical and semiclassical behaviour of solitons in three dimensions. In Chapter 2 we consider the zero mode quantization of the minimal energy Skyrmions for nucleon numbers between four and nine and also the conjectured solution with nucleon number of seventeen. The method relies on determining the contractibility of the loops in the configuration space corresponding to the discrete symmetry of the minimal energy solution. We find that for nucleon numbers four, six and eight the ground states obtained agree with the observed quantum numbers of the ground states of Helium, Lithium and Beryllium. But for nucleon numbers five, seven, nine and seventeen the spins obtained conflict with the observed isodoublet nuclear states. In Chapter 3 we discuss the gradient flow curves for two wellseparated Skyrmions. The form of the equations are quite simple and lead to an unambiguous interpretation of how the solution curves behave. There exists a large number of symmetries which enable us to find the solutions in closed form in the case of massless pions. An algorithm is described that estimates the positions and relative orientation of twoseparated Skyrmions, given the numerically generated Skyrme field. Chapters 4 and 5 are concerned with monopoles in SU(3) gauge theory. In Chapter 4 we consider charge two monopoles in the minimally broken case. A certain class of solutions looks like SU(2) monopoles embedded in SU(3) with a transition region or "cloud" surrounding the monopoles. We solve for the longrange fields in this region, confirming the existence of the cloud. The moduli space metric found by Dancer, is expressed in an explicit form. Chapter 5 discusses the case of maximal symmetry breaking for SU(3) monopoles for magnetic charge (2,1). Some properties of this space are discussed, we also find the axially symmetric geodesic submanifold of the moduli space and study the case of monopole scattering there. We analyse the limit where minimal symmetry breaking occurs, comparing to the results in Chapter 4.
