Communications in Mathematical Physics

, Volume 212, Issue 3, pp 591–611 | Cite as

A Path Integral Approach¶to the Kontsevich Quantization Formula

  • Alberto S. Cattaneo
  • Giovanni Felder


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.


Manifold Field Theory String Theory Open String Perturbative Expansion 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Alberto S. Cattaneo
    • 1
  • Giovanni Felder
    • 2
  1. 1.Institut für Mathematik, Universität Zürich, 8057 Zürich, Switzerland. E-mail: asc@math.unizh.chCH
  2. 2.Departement Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland. E-mail: felder@math.ethz.chCH

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