Elliptic Ruijsenaars–Schneider model from the cotangent bundle over the two-dimensional current group

DOI10.1063/1.532160zbMath0892.58039arXivhep-th/9608013OpenAlexW3101727903MaRDI QIDQ4378314

P. B. Medvedev, Sergeĭ Anatol'evich Frolov, Gleb E. Arutyunov

Publication date: 27 July 1998

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

Full work available at URL: https://arxiv.org/abs/hep-th/9608013

zbMATH Keywords

cotangent bundleelliptic Ruijsenaars-Schneider modelHamiltonian reduction proceduretwo-dimensional current group

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) (S)-matrix theory, etc. in quantum theory (81U20)

Related Items (15)

Integrable multi-Hamiltonian systems from reduction of an extended quasi-Poisson double of \({\mathrm{U}}(n)\) ⋮ Hyperbolic spin Ruijsenaars-Schneider model from Poisson reduction ⋮ Interfaces and quantum algebras. I: Stable envelopes ⋮ Why is the Ruijsenaars-Schneider hierarchy governed by the same \(R\)-operator as the Calogero-Moser one? ⋮ BPS/CFT correspondence. IV: Sigma models and defects in gauge theory ⋮ Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an Appendix by S. Ruijsenaars) ⋮ Hilbert space theory for reflectionless relativistic potentials ⋮ \(R\)-matrix quantization of the elliptic Ruijsenaars-Schneider model ⋮ The Lax pairs for elliptic Cn and BCn Ruijsenaars–Schneider models and their spectral curves ⋮ Integrable many-body systems and gauge theories ⋮ Poisson-Lie generalization of the Kazhdan-Kostant-Sternberg reduction ⋮ Quantum trace formulae for the integrals of the hyperbolic Ruijsenaars-Schneider model ⋮ Five-dimensional gauge theories and relativistic integrable systems ⋮ Multiplicative Hitchin systems and supersymmetric gauge theory ⋮ A new model in the Calogero-Ruijsenaars family

Cites Work

• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Completely integrable Hamiltonian systems connected with semisimple Lie algebras
• Generating equation for \(r\)-matrices related to dynamical systems of Calogero type.
• Hamiltonian group actions and dynamical systems of calogero type

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