Integrable potentials on Cayley-Klein spaces from quantum groups

TL;DR

This paper extends the class of integrable potentials to all two-dimensional Cayley-Klein spaces using quantum group contractions, revealing how integrable systems are characterized on spaces with degenerate metrics.

Contribution

It introduces a method to derive integrable potentials on Cayley-Klein spaces via contractions of quantum groups, broadening the scope of integrable systems in curved geometries.

Findings

Integrable potentials are extended to all 2D Cayley-Klein spaces.

Systems on degenerate metric spaces are described by two Hamiltonians.

The approach uses contractions of quantum groups to achieve this extension.

Abstract

The family of (super)integrable potentials on spaces with curvature developed by A. Ballesteros et all is extend to all two-dimensional Cayley-Klein spaces with the help of contractions. It is shown that integrable systems on spaces with degenerate metrics are described by two Hamiltonians: one in the base and another in the fiber.