Riemann surfaces, separation of variables and classical and quantum integrability

DOI10.1016/S0375-9601(03)00611-XzbMath1071.37510arXivhep-th/0209071MaRDI QIDQ1566205

O. Babelon, Michel Talon

Publication date: 1 June 2003

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

Full work available at URL: https://arxiv.org/abs/hep-th/0209071

zbMATH Keywords

Baxter equationsclassical Poisson-commuting Hamiltoniansquantum commuting Hamiltonians

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Groups and algebras in quantum theory and relations with integrable systems (81R12)

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Algebraic properties of Manin matrices. I, Harmonics on hyperspheres, separation of variables and the Bethe ansatz, Geodesics on Ellipsoids, Continuum limit of the Volterra model, separation of variables and non-standard realizations of the Virasoro Poisson bracket, Classical Bethe ansatz and normal forms in an integrable version of the Dicke model, Spectral curves of the hyperelliptic Hitchin systems, Hitchin systems on hyperelliptic curves, Canonical structure and symmetries of the Schlesinger equations, Spectrum of the quantum Neumann model, Quantum geometry of refined topological strings, Integrable systems of algebraic origin and separation of variables, On the Bethe ansatz for the Jaynes–Cummings–Gaudin model

Cites Work

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• On the integrable geometry of soliton equations and \(N=2\) supersymmetric gauge theories
• The symplectic structure of rational Lax pair systems
• Introduction to Classical Integrable Systems