On the Sutherland's Integrability Condition for Two-Dimensional N-Particle Systems

TL;DR

This paper extends Sutherland's integrability condition from one-dimensional to two-dimensional N-particle systems, proposing it as a potential criterion for integrability based on the absence of genuine three-body forces.

Contribution

It formulates and analyzes a two-dimensional version of Sutherland's integrability condition, highlighting its physical interpretation and potential as a new integrability criterion.

Findings

Formulation of a two-dimensional Sutherland's integrability condition

Interpretation as absence of true 3-body forces

Potential as a new integrability criterion

Abstract

Following Sutherland's work on one-dimensional integrable systems we formulate and study its two-dimensional version. Physically it expresses the absence of true 3-body forces among an assembly of N particles leaving exclusively effective 2-body interactions. This criterion may be a suitable candidate for an integrability condition.