On the possibility of spinorial quantization in the Skyrme model

TL;DR

This paper investigates the topological properties of the Skyrme model's configuration space, demonstrating how spatial rotations relate to contractibility depending on the winding number sector.

Contribution

It provides a straightforward proof of the contractibility of rotation loops in the Skyrme model's configuration space, clarifying topological distinctions between sectors.

Findings

Loops from full spatial rotations are contractible in even-winding sectors.

Loops are non-contractible in odd-winding sectors.

Topological structure depends on winding number.

Abstract

We consider the configuration space of the Skyrme model and give a simple proof that loops generated by full spatial rotations are contractible in the even-, and non-contractible in the odd-winding-number sectors.