The rational Ruijsenaars-Schneider model admits a one-parameter deformation realizing the anti-de Sitter algebra, while the hyperbolic and trigonometric variants are incompatible.
Remarks on integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models
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abstract
Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models based upon the potentials W(x)=2/x, W(x)=2/sin(x), and W(x)=2/sinh(x) is proven. The problem of constructing an algebraically resolvable set of Grassmann-odd constants of motion is reduced to finding a triplet of vectors such that all their scalar products can be expressed in terms of the original bosonic first integrals. The supersymmetric generalizations are used to build novel integrable (iso)spin extensions of the respective Ruijsenaars-Schneider three-body systems.
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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.