Comments on a Full Quantization of the Torus

Details Comments on a Full Quantization of the Torus Comments on a Full Quantization of the Torus

1997-04-09

arxiv.org/abs/hep-th/9704071v3

Int.J.Mod.Phys. A13 (1998) 3905-3914

Physics

High Energy Physics

High Energy Physics - Theory

10 pages. New "Discussion" section. References added. To appear in IJMPA

Scientific paper

10.1142/S0217751X98001827

Gotay showed that a representation of the whole Poisson algebra of the torus given by geometric quantization is irreducible with respect to the most natural overcomplete set of observables. We study this representation and argue that it cannot be considered as physically acceptable. In particular, classically bounded observables are quantized by operators with unbounded spectrum. Effectively, the latter amounts to lifting the constraints that compactify both directions in the torus.

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