Fermionic quantization of Hopf solitons

TL;DR

This paper develops a method to quantize Hopf solitons as fermions based on their topological properties, utilizing the Finkelstein-Rubinstein approach and the relationship with Skyrme model configuration spaces.

Contribution

It introduces a novel quantization scheme for Hopf solitons that accounts for their fermionic nature depending on Hopf charge, leveraging the Hopf fibration and recent Skyrme model results.

Findings

Hopf solitons with odd Hopf charge can be quantized as fermions.

The method relates configuration space loops to their contractibility to determine wave function constraints.

Discussion of quantum ground states for Hopf charge up to 7.

Abstract

In this paper we show how to quantize Hopf solitons using the Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if their Hopf charge is odd. Symmetries of classical minimal energy configurations induce loops in configuration space which give rise to constraints on the wave function. These constraints depend on whether the given loop is contractible. Our method is to exploit the relationship between the configuration spaces of the Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then use recent results in the Skyrme model to determine whether loops are contractible. We discuss possible quantum ground states up to Hopf charge Q=7.