Superintegrable three body systems in one dimension and generalizations

TL;DR

This paper extends the study of superintegrable three-body Hamiltonian systems on a line to systems with more particles and higher-dimensional manifolds, broadening the understanding of integrable models.

Contribution

It introduces methods to generalize superintegrable systems from three particles to multiple particles and higher dimensions, expanding the scope of known integrable models.

Findings

Examples of extended superintegrable systems with more particles

Generalization to higher-dimensional manifolds

Potential new classes of integrable models

Abstract

Superintegrable Hamiltonian systems describing the interactions among three point masses on a line have been described in [2]. Here, we show examples of how the approach of above can be extended to a higher number of particles on a line and on higher dimensional manifolds. This paper is a slightly extended version of a poster presented at the XVI ICMP held in Prague, 3-8 August 2009.