Rational Ruijsenaars-Schneider model with cosmological constant

TL;DR

This paper explores a one-parameter deformation of the rational Ruijsenaars-Schneider model by incorporating a cosmological constant through the anti de Sitter algebra, analyzing its feasibility and integrability.

Contribution

It introduces a novel deformation of the rational Ruijsenaars-Schneider model using the anti de Sitter algebra, extending the model's structure with a cosmological constant.

Findings

Feasibility of including a cosmological constant in the rational model.

Hyperbolic and trigonometric variants are incompatible with this deformation.

Complete proof of integrability remains an open challenge.

Abstract

The Ruijsenaars-Schneider models are integrable dynamical realizations of the Poincare group in 1+1 dimensions, which reduce to the Calogero and Sutherland systems in the nonrelativistic limit. In this work, a possibility to construct a one-parameter deformation of the Ruijsenaars-Schneider models by uplifting the Poincare algebra in 1+1 dimensions to the anti de Sitter algebra is studied. It is shown that amendments including a cosmological constant are feasible for the rational variant, while the hyperbolic and trigonometric systems are ruled out by our analysis. The issue of integrability of the deformed rational model is discussed in some detail. A complete proof of integrability remains a challenge.