Geometric quantization of Neumann-type completely integrable Hamiltonian systems

DOI10.1063/1.530605zbMath0801.58018OpenAlexW2089251282MaRDI QIDQ4298619

Anatoliy K. Prykarpatsky, I. V. Mykytiuk, Roman I. Andrushkiw, Valeriy H. Samoylenko

Publication date: 9 August 1994

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

Full work available at URL: https://doi.org/10.1063/1.530605

zbMATH Keywords

spheregeometric quantizationcompletely integrable dynamical systemsNeumann's nonharmonic oscillatory system

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) Geometry and quantization, symplectic methods (81S10) Geometric quantization (53D50)

Related Items (3)

Quantization of noncommutative completely integrable Hamiltonian systems ⋮ Flat minimal quantizations of Stäckel systems and quantum separability ⋮ Geometric quantization of completely integrable Hamiltonian systems in the action-angle variables

Cites Work

• Abelian integrals, integrable dynamic systems of the Neumann-Rosochatius type, and the Lax representation
• Generalized classical BRST cohomology and reduction of Poisson manifolds
• Reduction of symplectic manifolds with symmetry
• Dual moment maps into loop algebras
• Algebraic structure of the gradient-holonomic algorithm for Lax integrable nonlinear dynamical systems. I
• Quantization and unitary representations

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