Integrable many-body systems in the field theories

DOI10.1007/BF02065867zbMath0855.35106arXivhep-th/9410228OpenAlexW1736350091MaRDI QIDQ1920642

Alexander Gorsky

Publication date: 16 February 1997

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9410228

zbMATH Keywords

quantum field theoryintegrable many-body problemsdynamics of the topological degrees of freedom

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) PDEs in connection with quantum mechanics (35Q40) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Many-body theory; quantum Hall effect (81V70)

Related Items (12)

Bootstrapping the superconformal index with surface defects ⋮ Duality between the trigonometricBC_nSutherland system and a completed rational Ruijsenaars–Schneider–van Diejen system ⋮ Gauge theories and Macdonald polynomials ⋮ Global description of action-angle duality for a Poisson-Lie deformation of the trigonometric \(\mathrm {BC}_n\) Sutherland system ⋮ Hilbert space theory for reflectionless relativistic potentials ⋮ Integrable many-body systems and gauge theories ⋮ Raising operators for the Whittaker wave functions of the Toda chain and intertwining operators ⋮ The Superconformal Index of Theories of Class $$\mathcal {S}$$ ⋮ A note on the action-angle variables for the rational Calogero-Moser system ⋮ Poisson reduction of twisted Heisenberg double and finite-dimensional integrable systems ⋮ Trigonometric Sutherland systems and their Ruijsenaars duals from symplectic reduction ⋮ A new model in the Calogero-Ruijsenaars family

Cites Work

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• Stable bundles and integrable systems
• Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras
• Another algebraic proof of Weil's reciprocity
• Representations of affine Lie algebras, parabolic differential equations, and Lamé functions
• Derivation of the Verlinde formula from Chern-Simons theory and the \(G/G\) model.
• An elementary approach to the hypergeometric shift operators of Opdam
• Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem
• Hamiltonian group actions and dynamical systems of calogero type

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