Integrable perturbations of the N-dimensional isotropic oscillator

TL;DR

This paper introduces two new families of integrable perturbations for the N-dimensional isotropic harmonic oscillator, utilizing h_6-coalgebra symmetry, and explores their properties and special cases.

Contribution

It presents novel integrable perturbations depending on arbitrary functions and parameters, with explicit integrals of motion, expanding the class of known integrable systems.

Findings

Explicit construction of integrals of motion for new perturbations

Recovery of known low-dimensional integrable Hamiltonians as special cases

Canonical transformation approach enabling addition of Rosochatius terms

Abstract

Two new families of completely integrable perturbations of the N-dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are explicitly constructed by making use of an underlying h_6-coalgebra symmetry. Several known integrable Hamiltonians in low dimensions are obtained as particular specializations of the general results here presented. An alternative route for the integrability of all these systems is provided by a suitable canonical transformation which, in turn, opens the possibility of adding (N-1) `Rosochatius' terms that preserve the complete integrability of all these models.