Quantization of T_d- and O_h-symmetric Skyrmions

Abstract

The geometrical construction of rational maps using a cubic grid has led to many new Skyrmion solutions, with baryon numbers up to 108. Energy spectra of some of the new Skyrmions are calculated here by semi-classical quantization. Quantization of the B=20 T_d-symmetric Skyrmion, which is one of the newly found Skyrmions, is considered, and this leads to the development of a new approach to solving Finkelstein-Rubinstein (F-R) constraints. Matrix equations are simplified by introducing a Cartesian version of angular momentum basis states, and the computations are easier. The quantum states of all T_d-symmetric Skyrmions, constructed from the cubic grid, are classified into three classes, depending on the contribution of vertex points of the cubic grid to the rational maps. The analysis is extended to the larger symmetry group O_h. Quantum states of O_h-symmetric Skyrmions, constructed from the cubic grid, form a subset of the T_d-symmetric quantum states.