Semiclassical Quantization of Hopf Solitons

TL;DR

This paper investigates the quantum properties of Hopf solitons in the Faddeev-Skyrme model using a gauge equivalent formulation, revealing their rotational excitations resemble a symmetric top in SU(2).

Contribution

It introduces a quantum analysis of Hopf solitons via collective coordinates, connecting their excitations to a symmetric top Hamiltonian in SU(2).

Findings

Quantum Hamiltonian matches that of a symmetric top in SU(2).

Rotational excitations are characterized by irreducible representations.

The gauge equivalent formulation facilitates quantum analysis.

Abstract

The gauge equivalent formulation of the Faddeev-Skyrme model is used for the study of the quantum theory. The rotational quantum excitations around the soliton solution of Hopf number unity are investigated by the method of collective coordinates. The quantum Hamiltonian of the system is found to coincide with the Hamiltonian of a symmetrical top rotating in SU(2). Thus, the irreducible representations of physical observables can be constructed.