A new integrable system on the sphere and conformally equivariant quantization

TL;DR

This paper introduces a new integrable system on the sphere called the dual Moser system, derived from projectively equivalent metrics, and demonstrates its quantum integrability via conformally equivariant quantization.

Contribution

It presents the dual Moser system on the sphere and proves its quantum integrability using conformally equivariant quantization, expanding the class of known integrable systems.

Findings

Introduction of the dual Moser system on the sphere.

Quantum integrability established for dual Moser and Neumann-Uhlenbeck systems.

Connection of the system to Stäckel systems and projectively equivalent metrics.

Abstract

Taking full advantage of two independent projectively equivalent metrics on the ellipsoid leading to Liouville integrability of the geodesic flow via the well-known Jacobi-Moser system, we disclose a novel integrable system on the sphere $S^n$, namely the "dual Moser" system. The latter falls, along with the Jacobi-Moser and Neumann-Uhlenbeck systems, into the category of (locally) St\"ackel systems. Moreover, it is proved that quantum integrability of both Neumann-Uhlenbeck and dual Moser systems is insured by means of the conformally equivariant quantization procedure.