On $\mathcal{N}=2$ supersymmetric Ruijsenaars-Schneider models

Abstract

We construct an $\mathcal{N}=2$ supersymmetric extension of $n$-particle Ruijsenaars-Schneider models. The guiding feature is a deformation of the phase space. The supercharges have a "free" form linear in the fermions but produce an interacting four-fermion Hamiltonian. A field-dependent unitary transformation maps to standard fermions obeying conventional Poisson brackets. In this frame, the supercharges and Hamiltonian have long "fermionic tails". We also comment on previous attempts in this direction.

arXiv comment1+5 pages, no figures; v2: eq.(4.6) corrected (Hamiltonian also has fermionic tail), matches published version

References in corpus (15)

• Physics and Mathematics of Calogero particles
• Hidden Algebras of the (super) Calogero and Sutherland models
• Super Lax Pairs and Infinite Symmetries in The $1/r^2$ System
• (Super)conformal many-body quantum mechanics with extended supersymmetry
• Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
• N=4 mechanics, WDVV equations and roots
• Many-particle mechanics with D(2,1;alpha) superconformal symmetry
• The Ruijsenaars-Schneider Model
• Orthogonality of Jack polynomials in superspace
• The supersymmetric Ruijsenaars-Schneider model
• Jack polynomials in superspace
• $\mathcal{N}$-extended supersymmetric Calogero models
• Evaluation and normalization of Jack superpolynomials
• Extended supersymmetric Calogero model
• Ruijsenaars-Schneider three-body models with N=2 supersymmetry

Cited by in corpus (3)

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• Relativistic generalization of the rational Calogero model