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29 March 2024
 
  » arxiv » math.QA/9902090

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A path integral approach to the Kontsevich quantization formula
Alberto S. Cattaneo ; Giovanni Felder ;
Date 15 Feb 1999
Journal Commun.Math.Phys. 212 (2000) 591-611
Subject Quantum Algebra; Mathematical Physics | math.QA hep-th math-ph math.MP
AbstractWe 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.
Source arXiv, math.QA/9902090
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