Quantum integrability of quadratic Killing tensors

TL;DR

This paper investigates the quantum integrability of classical systems characterized by quadratic Killing tensors on curved spaces, demonstrating that a minimal quantization approach preserves integrability in many cases.

Contribution

It proves that a minimal quantization scheme ensures quantum integrability for a broad class of classical systems with quadratic Killing tensors.

Findings

Quantum integrability is preserved under minimal quantization for many classical systems.

The study bridges classical and quantum integrability on curved configuration spaces.

Key examples confirm the effectiveness of the proposed quantization scheme.

Abstract

Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a "minimal" quantization scheme, quantum integrability is insured for a large class of classic examples.