Obstruction Results in Quantization Theory

Abstract

We define the quantization structures for Poisson algebras necessary to generalise Groenewold and Van Hove's result that there is no consistent quantization for the Poisson algebra of Euclidean phase space. Recently a similar obstruction was obtained for the sphere, though surprising enough there is no obstruction to the quantization of the torus. In this paper we want to analyze the circumstances under which such obstructions appear. In this context we review the known results for the Poisson algebras of Euclidean space, the sphere and the torus.

34 pages, Latex. To appear in J. Nonlinear Science

References in corpus (6)

• Obstructions to Quantization
• Obstruction Results in Quantization Theory
• Questions on quantization
• Geometric Quantization and No Go Theorems
• Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold
• On Quantizing Nilpotent and Solvable Basic Algebras

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