The rational Ruijsenaars-Schneider model admits a one-parameter deformation realizing the anti-de Sitter algebra, while the hyperbolic and trigonometric variants are incompatible.
On the superintegrability of the rational Ruijsenaars-Schneider model
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abstract
The rational and hyperbolic Ruijsenaars-Schneider models and their non-relativistic limits are maximally superintegrable since they admit action variables with globally well-defined canonical conjugates. In the case of the rational Ruijsenaars-Schneider model we present an alternative proof of the superintegrability by explicitly exhibiting extra conserved quantities relying on a generalization of the construction of Wojciechowski for the rational Calogero model.
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Rational Ruijsenaars-Schneider model with cosmological constant
The rational Ruijsenaars-Schneider model admits a one-parameter deformation realizing the anti-de Sitter algebra, while the hyperbolic and trigonometric variants are incompatible.