The Dn Ruijsenaars-Schneider model

Abstract

The Lax pair of the Ruijsenaars-Schneider model with interaction potential of trigonometric type based on Dn Lie algebra is presented. We give a general form for the Lax pair and prove partial results for small n. Liouville integrability of the corresponding system follows a series of involutive Hamiltonians generated by the characteristic polynomial of the Lax matrix. The rational case appears as a natural degeneration and the nonrelativistic limit exactly leads to the well-known Calogero-Moser system associated with Dn Lie algebra.

LaTeX2e, 14 pages; more remarks are added in the last section

References in corpus (7)

• Quantum Calogero-Moser Models: Integrability for all Root Systems
• Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems
• Integrability of the $C_n$ and $B{C}_n$ Ruijsenaars-Schneider models
• Integrable Many-Body Systems and Gauge Theories
• The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves
• The Lax pair for C_2-type Ruijsenaars-Schneider model
• BC_n Ruijsenaars-Schneider models: R-Matrix structure and hamiltonians

Cited by in corpus (8)

• On factorized Lax pairs for classical many-body integrable systems
• Quantum vs Classical Integrability in Ruijsenaars-Schneider Systems
• Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism
• Scattering theory of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars--Schneider--van Diejen models
• On the scattering theory of the classical hyperbolic C(n) Sutherland model
• Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
• On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• On the Integrability of Classical Ruijsenaars-Schneider Model of $B{C}_2$ Type