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Deformation quantization from functional integrals


Cattaneo, A S (2005). Deformation quantization from functional integrals. In: Cattaneo, A S; Keller, B; Torossian, C; Bruguières, A. Déformation, quantification, théorie de Lie. Paris: Société Mathématique de France, 123-164.

Abstract

The aim of this Chapter is to explain how to obtain Kontsevich’s formula [7] from the perturbative computation of the functional integral of a topological field theory
known as the Poisson sigma model. We start with an introduction to the perturbative evaluation of functional integrals. We describe next how to do it in the presence of
symmetries generated by the free action of a Lie algebra. This allows the full treatment of the Poisson sigma model for an affine Poisson structure. For the general case, we
refer to [5].

Abstract

The aim of this Chapter is to explain how to obtain Kontsevich’s formula [7] from the perturbative computation of the functional integral of a topological field theory
known as the Poisson sigma model. We start with an introduction to the perturbative evaluation of functional integrals. We describe next how to do it in the presence of
symmetries generated by the free action of a Lie algebra. This allows the full treatment of the Poisson sigma model for an affine Poisson structure. For the general case, we
refer to [5].

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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:2005
Deposited On:08 Feb 2010 15:17
Last Modified:05 Apr 2016 13:24
Publisher:Société Mathématique de France
Series Name:Panoramas et Synthèses
Number:20
ISSN:1272-3835
ISBN:978-2-85629-183-2
Official URL:http://smf4.emath.fr/Publications/PanoramasSyntheses/2005/20/html/smf_pano-synth_20.html
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2274226

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