Quantum integrability of quadratic Killing tensors

Abstract

Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a "minimal" quantization scheme, quantum integrability is insured for a large class of classic examples.

LaTeX 2e, no figure, 35 p., references added, minor modifications. To appear in the J. Math. Phys

References in corpus (7)

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• Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions
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• Separability of the Hamilton-Jacobi and Klein-Gordon Equations in Kerr-de Sitter Metrics
• Integrability and the Kerr-(A)dS black hole in five dimensions
• Properties of some five dimensional Einstein metrics
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• Second Order Symmetries of the Conformal Laplacian
• First Integrals from Conformal Symmetries: Darboux-Koenigs Metrics and Beyond
• Canonical quantization of classical mechanics in curvilinear coordinates. Invariant quantization procedure
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• Hidden symmetries from distortions of the conformal structure
• Invariant prolongation of the Killing tensor equation
• Integrable quantum Stäckel systems
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• Hidden symmetries in a gauge covariant approach, Hamiltonian reduction and oxidation
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• Neumann-like integrable models
• Covariant quantizations in plane and curved spaces
• Integrable and Superintegrable Extensions of the Rational Calogero-Moser Model in 3 Dimensions
• Flat minimal quantizations of Stackel systems and quantum separability
• Conformally equivariant quantization for spinning particles
• Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator
• Further results on non-diagonal Bianchi type III vacuum metrics