Stability and Representation Dependence of the Quantum Skyrmion

Abstract

A constructive realization of Skyrme's conjecture that an effective pion mass ``may arise as a self consistent quantal effect'' based on an ab initio quantum treatment of the Skyrme model is presented. In this quantum mechanical Skyrme model the spectrum of states with $I=J$, which appears in the collective quantization, terminates without any infinite tower of unphysical states. The termination point depends on the model parameters and the dimension of the SU(2) representation. Representations, in which the nucleon and $\Delta_{33}$ resonance are the only stable states, exist. The model is developed for both irreducible and reducible representations of general dimension. States with spin larger than 1/2 are shown to be deformed. The representation dependence of the baryon observables is illustrated numerically.