Group-quantization of non-linear sigma models: particle on S^2 revisited

TL;DR

This paper develops a symmetry-based quantum mechanics approach for non-linear sigma models, exemplified by a particle on S^2, avoiding explicit constraints and ordering ambiguities, and accurately reproducing the energy spectrum.

Contribution

It introduces a novel symmetry-based method for quantizing non-linear sigma models, specifically applied to a particle on S^2, eliminating the need for explicit constraints.

Findings

No explicit constraint treatment needed

No ordering ambiguities encountered

Energy spectrum matches expected results

Abstract

We present the quantum mechanics of "partial-trace" non-linear sigma models, on the grounds of a fully symmetry-based procedure. After the general scheme is sketched, the particular example of a particle on the two-sphere is explicitly developed. As a remarkable feature, no explicit constraint treatment is required nor ordering ambiguities do appear. Moreover, the energy spectrum is recovered without extra terms in the curvature of the sphere.