Functorial geometric quantization and Van Hove's theorem

DOI10.1007/BF00669766zbMath0447.58020OpenAlexW2075828439MaRDI QIDQ1146432

Mark J. Gotay

Publication date: 1980

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00669766

zbMATH Keywords

polarizationsprequantizationSchrödinger quantizationcategory of Lagrangian submanifoldsgeometric quantization as a functorglobal analogon of Van Hove's theoremKostant-Souriau quantization

Mathematics Subject Classification ID

Geometric quantization (53D50) Categories in geometry and topology (18F99)

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Central extensions and physics ⋮ Unfinished history and paradoxes of quantum potential. I: Non-relativistic origin, history and paradoxes ⋮ Unfinished history and paradoxes of quantum potential. II: Relativistic point of view ⋮ Remarks on the connection between the additive separation of the Hamilton–Jacobi equation and the multiplicative separation of the Schrödinger equation. II. First integrals and symmetry operators ⋮ Degenerating Kähler structures and geometric quantization ⋮ Quantum Liouville equation ⋮ Geometric Quantization and Epistemically Restricted Theories: The Continuous Case ⋮ Deformation quantization as an appropriate guide to ontic structure ⋮ The operator formulation of classical mechanics and semiclassical limit ⋮ A global version of Günther's polysymplectic formalism using vertical projections ⋮ A Groenewold-Van Hove Theorem for $S^2$ ⋮ A representation space for minimal coupling ⋮ On the Groenewold–Van Hove problem for R2n ⋮ Obstruction results in quantization theory ⋮ Lie groupoids and Lie algebroids in physics and noncommutative geometry

Cites Work

• Geometric quantization and quantum mechanics
• Lectures on geometric quantization
• Canonical quantization
• Polarization and unitary representations of solvable Lie groups. Appendix by Calvin C. Moore
• Quantization and unitary representations
• On the principles of elementary quantum mechanics
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