Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space

TL;DR

This paper classifies orthogonal coordinate systems in Euclidean space using Klein's Erlangen Program and applies these results to analyze the integrability of the Calogero-Moser model.

Contribution

It provides a comprehensive invariant classification of orthogonal coordinate webs in Euclidean space, linking geometric structures to integrability of specific Hamiltonian systems.

Findings

Complete classification of orthogonal coordinate webs in Euclidean space.

Application of classification results to Calogero-Moser model.

Insights into the geometric structure underlying integrable systems.

Abstract

The problem of the invariant classification of the orthogonal coordinate webs defined in Euclidean space is solved within the framework of Felix Klein's Erlangen Program. The results are applied to the problem of integrability of the Calogero-Moser model.