Obstruction Results in Quantization Theory

Details Obstruction Results in Quantization Theory Obstruction Results in Quantization Theory

1996-05-02

arxiv.org/abs/dg-ga/9605001v1

J. Nonlinear Sci. Vol. 6: pps. 469-498 (1996)

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1007/BF02440163

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.

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