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Deformation quantization of Poisson manifolds. (English) Zbl 1058.53065

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.

This important article circulated since 1997 as a frequently cited preprint (q-alg/9709040).


MSC:
53D55Deformation quantization, star products
16E40Homology and cohomology theories for associative rings
18G55Nonabelian homotopical algebra
53D17Poisson manifolds; Poisson groupoids and algebroids
81S10Geometric quantization, symplectic methods (quantum theory)