The symplectic structure of the spin Calogero model

DOI10.1016/S0375-9601(97)00846-3zbMath0969.37525arXivq-alg/9707011OpenAlexW3100333466WikidataQ127933826 ScholiaQ127933826MaRDI QIDQ1966489

O. Babelon, Michel Talon

Publication date: 7 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9707011

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Applications of global analysis to the sciences (58Z05) Many-body theory; quantum Hall effect (81V70)

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On a second Lax structure for the Calogero-Moser system: time-dependent constants and superintegrability, A technique to identify solvable dynamical systems, and a solvable generalization of the goldfish many-body problem, The symplectic structure of rational Lax pair systems, A technique to identify solvable dynamical systems, and another solvable extension of the goldfish many-body problem, Superintegrability of the Calogero–Moser system: Constants of motion, master symmetries, and time-dependent symmetries, Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - an analytic approach, Generalized Calogero-Moser-Sutherland models from geodesic motion on \(\text{GL}^+(n,\mathbb{R})\) group manifold

Cites Work

• On the integrable geometry of soliton equations and \(N=2\) supersymmetric gauge theories
• On the deformation of Abelian integrals
• Exact Yangian symmetry in the classical Euler-Calogero-Moser model
• Canonically Conjugate Variables for the Korteweg-de Vries Equation and the Toda Lattice with Periodic Boundary Conditions