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Zbl 1058.53065
Kontsevich, Maxim
Deformation quantization of Poisson manifolds. (English)
[J] Lett. Math. Phys. 66, No. 3, 157-216 (2003). ISSN 0377-9017; ISSN 1573-0530/e

The author proves that any finite-dimensional Poisson manifold can be canonically quantized in the sense of deformation quantization. The solution presented here uses in an essential way some ideas of string theory. The author's formulas can be viewed as a perturbation series for a topological 2-dimensional quantum field theory coupled with gravity. \par This important article circulated since 1997 as a frequently cited preprint (q-alg/9709040).
[Mircea Puta (Timişoara)]

MSC 2000:: *53D55 Deformation quantization, star products
16E40 Homology and cohomology theories for assoc. rings
18G55 Nonabelian homotopical algebra
53D17 Poisson manifolds
81S10 Geometric quantization, symplectic methods

Keywords: deformation quantization; homotopy Lie algebra

Cited in: Zbl 1250.53081 Zbl 1175.19003 Zbl 1225.17023 Zbl 1152.81433 Zbl 1143.14002 Zbl 1119.53061 Zbl 1156.53321 Zbl 1093.53095 Zbl 1085.53081 Zbl 1084.18007 Zbl 1081.53079 Zbl 1077.53074 Zbl 1072.58008 Zbl 1066.53143 Zbl 1059.22008 Zbl 1056.53060 Zbl 1134.53304 Zbl 1042.81035 Zbl 1058.53511 Zbl 0957.53047 Zbl 1083.53505

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