Kontsevich quantization formula explained

In mathematics, the Kontsevich quantization formula describes how to construct a generalized ★-product operator algebra from a given arbitrary finite-dimensional Poisson manifold. This operator algebra amounts to the deformation quantization of the corresponding Poisson algebra. It is due to Maxim Kontsevich.^{[1] [2]}

Deformation quantization of a Poisson algebra

Given a Poisson algebra, a deformation quantization is an associative unital product

on the algebra of formal power series in

Notes and References

1. M. Kontsevich (2003), Deformation Quantization of Poisson Manifolds, Letters of Mathematical Physics 66, pp. 157 - 216.
2. . . 2000 . A Path Integral Approach to the Kontsevich Quantization Formula . Communications in Mathematical Physics . 212 . 3 . 591–611 . 10.1007/s002200000229. math/9902090. 2000CMaPh.212..591C. 8510811 .