Neumann-like integrable models

TL;DR

This paper introduces a new class of integrable dynamical systems with four-dimensional phase space, extending the Neumann system, and demonstrates their integrability at both classical and quantum levels.

Contribution

It presents a countable family of integrable models generalizing the Neumann system, with explicit conserved quantities and quantum integrability.

Findings

Existence of a countable class of integrable models

Recovery of the Neumann system for n=1

Models are integrable at the quantum level

Abstract

A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (H\_n,I\_n) are exhibited. For $n=1$ we recover Neumann sytem on T*S^2. All these systems are also integrable at the quantum level.