Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-10-26
Annals Phys. 235 (1994) 1-34
Physics
High Energy Physics
High Energy Physics - Theory
37 pgs+3 figures (not included), PlainTeX, Preprint CRM-1838
Scientific paper
10.1006/aphy.1994.1089
In this work we propose an alternative description of the quantum mechanics of a massive and spinning free particle in anti-de~Sitter spacetime, using a phase space rather than a spacetime representation. The regularizing character of the curvature appears clearly in connection with a notion of localization in phase space which is shown to disappear in the zero curvature limit. We show in particular how the anti-de~Sitter optimally localized (coherent) states contract to plane waves as the curvature goes to zero. In the first part we give a detailed description of the classical theory {\it \a la Souriau\/}. This serves as a basis for the quantum theory which is constructed in the second part using methods of geometric quantization. The invariant positive K\"ahler polarization that selects the anti-de~Sitter quantum elementary system is shown to have as zero curvature limit the Poincar\'e polarization which is no longer K\"ahler. This phenomenon is then related to the disappearance of the notion of localization in the zero curvature limit.
Bievre Stephan de
El Gradechi Amine M.
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