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Poisson sigma models and deformation quantization


Cattaneo, A S; Felder, G (2001). Poisson sigma models and deformation quantization. Modern Physics Letters A, 16(4-6):179-189.

Abstract

This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we describe the reduced phase space and its structures (symplectic groupoid), explaining in particular the classical origin of the non-commutativity of the string end-point coordinates. We also review the perturbative Lagrangian approach and its connection with Kontsevich's star product. Finally we comment on the relation between the two approaches.

This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we describe the reduced phase space and its structures (symplectic groupoid), explaining in particular the classical origin of the non-commutativity of the string end-point coordinates. We also review the perturbative Lagrangian approach and its connection with Kontsevich's star product. Finally we comment on the relation between the two approaches.

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39 citations in Web of Science®
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Additional indexing

Other titles:Euroconference on Brane New World and Noncommutative Geometry (Torino, 2000)
Item Type:Journal Article, 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 12:19
Last Modified:05 Apr 2016 13:25
Publisher:World Scientific Publishing
ISSN:0217-7323
Additional Information:Electronic version of an article published as [Modern Phys. Lett. A; vol. 16 (2001), no. 4-6, p. 179-189]© 2001 copyright World Scientific Publishing Company http://www.worldscinet.com/mpla/mpla.shtml
Publisher DOI:10.1142/S0217732301003255
Related URLs:http://www.forschungsportal.ch/unizh/p3845.htm
Permanent URL: http://doi.org/10.5167/uzh-22009

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