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.

19 pages, LateX

Cited by in corpus (12)

• Canonical Quantization of SU(3) Skyrme Model in a General Representation
• Baby Skyrmions stabilized by canonical quantization
• Current conservation, screening and the magnetic moment of the $\Delta$ resonance: 2. Formulation with quark degrees of freedom 3. Magnetic moment of the ${\Delta }^o$ and ${\Delta }^{-}$ resonances
• Nucleon form factors in the canonically quantized Skyrme model
• Quantum SU(3) Skyrme model with noncanonical embedded SO(3) soliton
• The $\alpha$ particle as a canonically quantized multiskyrmion
• The Deuteron as a Canonically Quantized Biskyrmion
• Canonically quantized soliton in the bound state approach to heavy baryons in the Skyrme model
• On quantization of the SU(2) Skyrmions
• The Spectrum of the Baryon Masses in a Self-consistent SU(3) Quantum Skyrme Model
• Current conservation, screening and the magnetic moment of the $\Delta$ resonance. -- 1. Formulation without quark degrees of freedom
• Noncanonicaly Embedded Rational Map Soliton in Quantum SU(3) Skyrme Model