On the Groenewold–Van Hove problem for R2n

DOI10.1063/1.532854zbMath0977.53081arXivmath-ph/9809015OpenAlexW3100701428MaRDI QIDQ4701841

Mark J. Gotay

Publication date: 21 November 1999

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

Full work available at URL: https://arxiv.org/abs/math-ph/9809015

zbMATH Keywords

Lie subalgebrasPoisson algebraquantizations

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Geometry and quantization, symplectic methods (81S10) Poisson algebras (17B63) Geometric quantization (53D50)

Related Items (14)

Shouldn’t there be an antithesis to quantization? ⋮ Conformal fluid dynamics ⋮ Deformation quantization as an appropriate guide to ontic structure ⋮ Quantization via deformation of prequantization ⋮ Born-Jordan pseudodifferential operators and the Dirac correspondence: beyond the Groenewold-van Hove theorem ⋮ Problem of time in quantum gravity ⋮ From Weyl to Born-Jordan quantization: the Schrödinger representation revisited ⋮ Bouncing and cyclic quantum primordial universes and the ordering problem ⋮ Generalized Weyl transform for operator ordering: Polynomial functions in phase space ⋮ On a special picture of dynamical evolution of nonlinear quantum systems in the phase-space representation ⋮ Bypassing the Groenewold–van Hove obstruction on ${{\mathbb{R}}}^{2n}$: a new argument in favor of Born–Jordan quantization ⋮ Geometric Aspects of the Quantization of a Rigid Body ⋮ THEORY OF QUANTUM FIRST TIME OF ARRIVAL VIA SPATIAL CONFINEMENT I: CONFINED TIME OF ARRIVAL OPERATORS FOR CONTINUOUS POTENTIALS ⋮ Lie groupoids and Lie algebroids in physics and noncommutative geometry

Cites Work

• Functorial geometric quantization and Van Hove's theorem
• On quantizing \(T^*S^1\)
• Derivations of Lie brackets and canonical quantisation
• Separate and joint analyticity in Lie groups representations
• Obstruction results in quantization theory
• On Quantizing Nilpotent and Solvable Basic Algebras
• A Groenewold-Van Hove Theorem for $S^2$
• On the principles of elementary quantum mechanics

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