The deformation quantizations of the hyperbolic plane
type: Item
instance of: scholarly article
title: The deformation quantizations of the hyperbolic plane
zbMATH Open document ID: 1170.53074
author: J. Blot
published in: Communications in Mathematical Physics
publication date: 2009-07-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/0806.4741
review text: The paper gives an explicit description of all invariant deformation quantizations of the hyperbolic plane. The formal deformation quantization program, inaugurated by Bayen, Flato, Fronsdal, Lichnerowicz and Sternheimer, proposes a generalization of the non formal Weyl product to an arbitrary Poisson manifold. In this work, the authors concentrate on the hyperbolic plane. Observing that the hyperbolic plane admits a unique contraction into a generic co-adjoint orbit of the Poincaré group, they give a detailed description of the space of all invariant, both formal and non formal, deformation quantizations of the hyperbolic plane. The method used gives in the 2-dimensional context an exact solution to Weinstein's WKB quantization program within geometric terms.
reviewed by: Angela Gammella-Mathieu
Mathematics Subject Classification ID: 53D55
Mathematics Subject Classification ID: 53D10
Mathematics Subject Classification ID: 53D15
zbMATH DE Number: 5575968
zbMATH Keywords: deformation quantization
zbMATH Keywords: Weyl product
zbMATH Keywords: hyperbolic plane
zbMATH Keywords: symplectic symmetric spaces
MaRDI profile type: Publication
OpenAlex ID: W2053621654
arXiv ID: 0806.4741
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DOI: 10.1007/S00220-008-0697-9
description: scientific article