Ruijsenaars-Schneider three-body models with N=2 supersymmetry

Abstract

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.

v3: 10 pages, imaginary unit missed in Eq. (22) is reinstated

References in corpus (4)

• Supersymmetric Calogero models by gauging
• N=4 mechanics, WDVV equations and roots
• The supersymmetric Ruijsenaars-Schneider model
• Goldfish geodesics and Hamiltonian reduction of matrix dynamics

Cited by in corpus (5)

• $\mathcal{N}$-extended supersymmetric Calogero models
• On $\mathcal{N}=2$ supersymmetric Ruijsenaars-Schneider models
• Remarks on N=1 supersymmetric extension of the Euler top
• N=2 supersymmetric extensions of relativistic Toda lattice
• Relativistic generalization of the rational Calogero model