\(R\)-matrices for elliptic Calogero-Moser models

DOI10.1007/BF00939702zbMath0790.35090arXivhep-th/9309033OpenAlexW2019051977MaRDI QIDQ1317888

Takashi Suzuki, Harry W. Braden

Publication date: 22 March 1994

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9309033

zbMATH Keywords

Lie algebraWeierstrass elliptic functionLax pair formulationmomentum independence

Mathematics Subject Classification ID

(n)-body potential quantum scattering theory (81U10) PDEs in connection with quantum mechanics (35Q40) Elliptic curves (14H52)

Related Items (17)

Structures in BCN Ruijsenaars–Schneider models ⋮ Spin Calogero models obtained from dynamical \(r\)-matrices and geodesic motion ⋮ On additional symmetry: The many-body problem related to the KP hierarchy ⋮ The Euler-Calogero-Moser model in an external potential---Yangian and loop algebra ⋮ \(R\)-matrices for the \(n=2,3\) elliptic Calogero-Moser models ⋮ The classical \(r\)-matrix for the relativistic Ruijsenaars-Schneider system. ⋮ Generating equation for \(r\)-matrices related to dynamical systems of Calogero type. ⋮ Why is the Ruijsenaars-Schneider hierarchy governed by the same \(R\)-operator as the Calogero-Moser one? ⋮ Characteristic classes and Hitchin systems. General construction ⋮ \(R\)-matrix quantization of the elliptic Ruijsenaars-Schneider model ⋮ Dynamical R-matrices for Calogero models ⋮ On the classical \(r\)-matrix structure of the rational \(BC_n\) Ruijsenaars-Schneider-van Diejen system ⋮ Direct proof of integrability of Calogero–Moser model ⋮ On integrable systems and supersymmetric gauge theories ⋮ Poisson reduction of twisted Heisenberg double and finite-dimensional integrable systems ⋮ Liouville integrability of classical Calogero-Moser models ⋮ On the r-matrix structure of the hyperbolic BC n Sutherland model

Cites Work

• Unnamed Item
• Unnamed Item
• What is a classical r-matrix?
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• Classical integrability and higher symmetries of collective string field theory.
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles
• Three integrable Hamiltonian systems connected with isospectral deformations
• Completely integrable Hamiltonian systems connected with semisimple Lie algebras
• General Analytic Solution of Certain Functional Equations of Addition Type
• Hamiltonian group actions and dynamical systems of calogero type

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