The Classical $r$-Matrix for the Relativistic Ruijsenaars-Schneider System

Abstract

We compute the classical $r$-matrix for the relativistic generalization of the Calogero-Moser model, or Ruijsenaars-Schneider model, at all values of the speed-of-light parameter $\lambda$. We connect it with the non-relativistic Calogero-Moser $r$-matrix $(\lambda \to -1)$ and the $\lambda =1$ sine-Gordon soliton limit.

LaTeX file, no figures, 8 pages

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Cited by in corpus (10)

• Relativistic Classical Integrable Tops and Quantum R-matrices
• Dynamical r-matrix for the elliptic Ruijsenaars-Schneider system
• Why are the rational and hyperbolic Ruijsenaars-Schneider hierarchies governed by the same R-operators as the Calogero-Moser ones?
• Elliptic Ruijsenaars-Schneider and Calogero-Moser hierarchies are governed by the same r-matrix
• On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
• R-matrix Quantization of the Elliptic Ruijsenaars--Schneider model
• Integrable discretizations of the spin Ruijsenaars-Schneider models
• The non-dynamical r-matrices of the degenerate Calogero-Moser models
• Quantum Trace Formulae for the Integrals of the Hyperbolic Ruijsenaars-Schneider model
• Structures in BC_N Ruijsenaars-Schneider models