A path integral approach to the Kontsevich quantization formula

Details A path integral approach to the Kontsevich quantization formula A path integral approach to the Kontsevich quantization formula

1999-02-15

arxiv.org/abs/math/9902090v3

Commun.Math.Phys. 212 (2000) 591-611

Mathematics

Quantum Algebra

22 pages, 2 figures, references added. Conjecture on the center made more precise

Scientific paper

10.1007/s002200000229

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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