Spin-isospin rotation dynamics

TL;DR

This paper derives equations for arbitrarily rotating solitons in spin-isospin space, analyzes their quantum wave functions, and shows how spin-isospin rotation stabilizes soliton states in the SU(2) sigma-model.

Contribution

It introduces a variational approach to describe spin-isospin rotation dynamics and establishes equations for degenerate moments of inertia configurations.

Findings

Degenerate moments of inertia matrix for O(2)-invariant configurations

Spin-isospin rotation prevents soliton collapse in the SU(2) sigma-model

Quantum wave functions for dynamic states are derived

Abstract

The equations for the solitons arbitrarily rotating in the ordinary and isotopic space are obtained. The wave functions of the corresponding dynamic states in the quantum case are found. The generalized matrix of the moments of inertia is degenerate for the O(2)-invariant configurations characteristic for the nucleon and delta-isobar. The equation for such configurations is established. It is shown that the spin-isospin rotation prevents the collapse of the soliton states in the SU(2) sigma-model. The entire consideration is based on the variational approach to the method of collective variables.