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2009-01-01 - Article/Dans un journal avec peer-review - Anglais - 31 page(s)

Bieliavsky P., Detournay S., Spindel Philippe , "The deformation quantizations of the hyperbolic plane" in Communications in Mathematical Physics, 289, 2, 529–559.

  • Edition : Springer Science & Business Media B.V.
  • Codes CREF : Mécanique quantique classique et relativiste (DI1211), Théorie quantique des champs (DI1215)
  • Unités de recherche UMONS : Mécanique et gravitation (S884)
Texte intégral :

Abstract(s) :

(Anglais) We describe the space of (all) invariant deformation quantizations on the hyperbolic plane D as solutions of the evolution of a second order hyperbolic di erential operator. The construction is entirely explicit and relies on non-commutative harmonic analytical techniques on symplectic symmetric spaces. The present work presents a uni ed method producing every quantization of D, and provides, in the 2-dimensional context, an exact solution to Weinstein's WKB quantization program within geometric terms. The construction reveals the existence of a metric of Lorentz signature canonically attached (or `dual') to the geometry of the hyperbolic plane through the quantization process.

Notes :
  • (Anglais) e-Print : arXiv: 0806.4741 [math-ph],ISNN 1432-0916 (Online),Bibliographic Code:2009CMaPh.289..529B
Identifiants :
  • DOI : 10.1007/s00220-008-0697-9
  • ISSN : 0010-3616