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Ruijsenaars-Schneider three-body models with N=2 supersymmetry
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The Ruijsenaars-Schneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. Surprisingly enough, their supersymmetric generalizations escaped attention. In this work, N=2 supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider three-body models are constructed within the framework of the Hamiltonian formalism. It is also known that the rational model can be described by the geodesic equations associated with a metric connection. We demonstrate that the hyperbolic systems are linked to non-metric connections.
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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.
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