Deformation Quantization of the Isotropic Rotator

TL;DR

This paper applies deformation quantization to the classical isotropic rigid rotator, resulting in a quantum system with a modified quantum group symmetry rather than the classical symmetry.

Contribution

It introduces a deformation quantization approach to the isotropic rotator, revealing a quantum symmetry structure different from the classical case.

Findings

Quantum system exhibits $SU_{q^{-1}}(2) imes SU_q(2)$ symmetry.

Deformation quantization alters classical symmetry properties.

Provides a new perspective on quantizing rotational systems.

Abstract

We perform a deformation quantization of the classical isotropic rigid rotator. The resulting quantum system is not invariant under the usual $SU(2)\times SU(2)$ chiral symmetry, but instead $SU_{q^{-1}}(2) \times SU_q(2)$.