The traditional approach to fixing the parameters of the Skyrme model requires the energy of a spinning Skyrmion to reproduce the nucleon and delta masses. The standard Skyrme parameters, which are used almost exclusively, fix the pion mass to its experimental value and fit the two remaining Skyrme parameters by approximating the spinning Skyrmion as a rigid body. In this paper we remove the rigid body approximation and perform numerical calculations which allow the spinning Skyrmion to deform and break spherical symmetry. The results show that if the pion mass is set to its experimental value then the nucleon and delta masses can not be reproduced for any values of the Skyrme parameters; the commonly used Skyrme parameters are simply an artifact of the rigid body approximation. However, if the pion mass is taken to be substantially larger than its experimental value then the nucleon and delta masses can be reproduced. This result has a significant effect on the structure of multi-Skyrmions.

Numerical methods are used to compute sphaleron solutions of the Skyrme model. These solutions have topological charge zero and are axially symmetric, consisting of an axial charge n Skyrmion and an axial charge −n antiSkyrmion (with n > 1), balanced in unstable equilibrium. The energy is slightly less than twice the energy of the axially symmetric charge n Skyrmion. A similar configuration with n = 1 does not produce a sphaleron solution, and this difference is explained by considering the interaction of asymptotic pion dipole fields. For sphaleron solutions with n > 4 the positions of the Skyrmion and antiSkyrmion merge to form a circle, rather than isolated points, and there are some features in common with Hopf solitons of the Skyrme-Faddeev model.

The Skyrme model is a classical field theory which models the strong interaction between atomic nuclei. It has to be quantized in order to compare it to nuclear physics. When the Skyrme model is semi-classically quantized it is important to take the Finkelstein-Rubinstein constraints into account. The aim of this paper is to show how to calculate these FR constraints directly from the rational map ansatz using basic homotopy theory. We then apply this construction in order to quantize the Skyrme model in the simplest approximation, the zero mode quantization. This is carried out for up to 22 nucleons, and the results are compared to experiment.

We investigate the dynamics of BPS vortices in the presence of magnetic impurities taking the form of axially-symmetric localised lumps and delta-functions. We present numerical results for vortices on flat space, as well as exact results for vortices on hyperbolic space in the presence of delta-function impurities. In fact, delta-function impurities of appropriate strength can be captured within the moduli space approximation by keeping one or more of the vortices fixed. We also show that previous work on vortices on the 2-sphere extends naturally to the inclusion of delta-function impurities.

In this paper we show how to quantize Hopf solitons using the Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if their Hopf charge is odd. Symmetries of classical minimal energy configurations induce loops in configuration space which give rise to constraints on the wave function. These constraints depend on whether the given loop is contractible. Our method is to exploit the relationship between the configuration spaces of the Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then use recent results in the Skyrme model to determine whether loops are contractible. We discuss possible quantum ground states up to Hopf charge Q = 7. *