Quantization of the Skyrmion

The Skyrmion is a localized, persistent excitation of the Skyrme model, a field theory of three independent meson fields in three spatial dimensions that has proven to be useful for modeling the baryons (e.g. neutron, proton, delta, ...). The standard approach to predicting values for physical observables within the Skyrme model consists of solving the classical field equations, quantizing the zero modes (such as rotation and translation) and fluctuations about the classical configuration, and projecting out states having the correct symmetries. With only three input parameters, this method has led to predictions for roughly three dozen quantities which differ from their corresponding experimental measurements by approximately 30%. In this thesis, the Herman-Klein method of quantization, an approach based on Heisenberg matrix mechanics, is applied to the Skyrme model. In this intrinsically quantum mechanical approach, the operator equations of motion are evaluated within an appropriately chosen Hilbert space, and the resulting set of c-number equations are solved to determine the values of matrix elements of the field operators. These values permit predictions for physical observables. In contrast with the usual approach of projecting symmetry-preserving states from configurations built around a symmetry-breaking mean-field solution, the Herman-Klein method allows symmetries to be maintained throughout the computation, a property shared with methods based on variation after projection techniques. This research focuses on quantization of the translational and rotational zero modes of a Skyrmion. The results indicate that (i) a symmetry-preserving treatment of the translational modes leads to a larger value for the mass of the hedgehog Skyrmion compared to that found in the previous treatments, and that (ii) the rotational modes cause a swelling of the delta states with respect to the nucleon states, and modify the predictions for physical observables.