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Poisson sigma models and symplectic groupoids


Cattaneo, A S; Felder, G (2001). Poisson sigma models and symplectic groupoids. In: Landsmann, N P; Pflaum, M; Schlichenmaier, M. Quantization of singular symplectic quotients. Basel: Birkhäuser, 61-93.

Abstract

We consider the Poisson sigma model associated to a Poisson manifold. The perturbative quantization of this model yields the Kontsevich star product formula. We study here the classical model in the Hamiltonian formalism. The phase space is the space of leaves of a Hamiltonian foliation and has a natural groupoid structure. If it is a manifold then it is a symplectic groupoid for the given Poisson manifold. We study various families of examples. In particular, a global symplectic groupoid for a general class of two-dimensional Poisson domains is constructed.

Abstract

We consider the Poisson sigma model associated to a Poisson manifold. The perturbative quantization of this model yields the Kontsevich star product formula. We study here the classical model in the Hamiltonian formalism. The phase space is the space of leaves of a Hamiltonian foliation and has a natural groupoid structure. If it is a manifold then it is a symplectic groupoid for the given Poisson manifold. We study various families of examples. In particular, a global symplectic groupoid for a general class of two-dimensional Poisson domains is constructed.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2001
Deposited On:27 Jan 2010 12:21
Last Modified:06 Dec 2017 20:52
Publisher:Birkhäuser
Series Name:Progress in Mathematics
Number:198
ISSN:0743-1643
ISBN:3-7643-6608-7
Additional Information:The original publication is available at www.springerlink.com
Official URL:http://www.springer.com/birkhauser/mathematics/book/978-3-7643-6608-7
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1938552
http://www.ams.org/mathscinet-getitem?mr=1938548

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