Poisson sigma models and symplectic groupoids - Zurich Open Repository and Archive

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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Item Type: Book Section, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 2001 27 Jan 2010 12:21 05 Apr 2016 13:25 Birkhäuser Progress in Mathematics 198 0743-1643 3-7643-6608-7 The original publication is available at www.springerlink.com http://www.springer.com/birkhauser/mathematics/book/978-3-7643-6608-7 http://www.ams.org/mathscinet-getitem?mr=1938552http://www.ams.org/mathscinet-getitem?mr=1938548