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A path integral approach to the Kontsevich quantization formula


Cattaneo, A S; Felder, G (2000). A path integral approach to the Kontsevich quantization formula. Communications in Mathematical Physics, 212(3):591-611.

Abstract

We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory. Its Batalin–Vilkovisky quantization yields a superconformal field theory. The associativity of the star product, and more generally the formality conjecture can then be understood by field theory methods. As an application, we compute the center of the deformed algebra in terms of the center of the Poisson algebra.

Abstract

We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory. Its Batalin–Vilkovisky quantization yields a superconformal field theory. The associativity of the star product, and more generally the formality conjecture can then be understood by field theory methods. As an application, we compute the center of the deformed algebra in terms of the center of the Poisson algebra.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistical and Nonlinear Physics
Physical Sciences > Mathematical Physics
Language:English
Date:2000
Deposited On:27 Jan 2010 12:16
Last Modified:26 Jun 2022 22:37
Publisher:Springer
ISSN:0010-3616
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s002200000229
  • Content: Accepted Version