Mathematical Analysis of a Generalized Chiral Quark Soliton Model

TL;DR

This paper introduces a mathematically rigorous generalization of the chiral quark soliton model in nuclear physics, analyzing its spectral properties, symmetry, and supersymmetric structure using operator theory.

Contribution

It presents a new generalized CQSM with an operator-valued mass term and provides rigorous mathematical analysis of its spectral and symmetry properties.

Findings

Supersymmetric structure identified in the model

Spectral properties characterized mathematically

Model shown to be unitarily equivalent to a simplified form

Abstract

A generalized version of the so-called chiral quark soliton model (CQSM) in nuclear physics is introduced. The Hamiltonian of the generalized CQSM is given by a Dirac type operator with a mass term being an operator-valued function. Some mathematically rigorous results on the model are reported. The subjects included are: (i) supersymmetric structure; (ii) spectral properties; (iii) symmetry reduction; (iv) a unitarily equivalent model.