Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body system

TL;DR

This paper constructs an N=1 supersymmetric extension of the Ruijsenaars-Schneider three-body model, proving its integrability and introducing a new isospin extension with Grassmann-odd constants of motion.

Contribution

It presents the first supersymmetric extension of the three-body Ruijsenaars-Schneider model and demonstrates its integrability with new algebraic structures.

Findings

Established integrability of the supersymmetric model

Identified three Grassmann-odd constants of motion

Developed a novel isospin extension of the system

Abstract

An N=1 supersymmetric extension of the Ruijsenaars-Schneider three-body model is constructed and its integrability is established. In particular, three functionally independent Grassmann-odd constants of the motion are given and their algebraic resolvability is proven. The supersymmetric generalization is used to build a novel integrable isospin extension of the Ruijsenaars-Schneider three-body system.