Inequivalent Quantization in the Skyrme Model

TL;DR

This paper explores how the non-uniqueness of quantization on manifolds, specifically in the Skyrme model with a configuration space of S^3, affects physical predictions due to different induced gauge structures.

Contribution

It analyzes the impact of inequivalent quantizations on the Skyrme model's physical observables, highlighting the role of gauge structures and spin.

Findings

Quantization on S^3 is not unique, leading to different physical predictions.

Induced gauge structures influence the quantization outcomes.

Multiple inequivalent quantizations can be characterized by spin and gauge structures.

Abstract

Quantum mechanics on manifolds is not unique and in general infinite number of inequivalent quantizations can be considered. They are specified by the induced spin and the induced gauge structures on the manifold. The configuration space of collective mode in the Skyrme model can be identified with $S^{3}$ and thus the quantization is not unique. This leads to the different predictions for the physical observables.