Geometric quantization and non-perturbative Poisson sigma model. (English) Zbl 1123.53047

Bonechi, Francesco; Cattaneo, Alberto S.; Zabzine, Maxim

Adv. Theor. Math. Phys. 10, No. 5, 683-712 (2006).

Classical systems are described by Poisson manifolds. With a Poisson manifold \(M\), namely with the space \(C^{\infty}(M)\), a deformation called the “deformation quantization” is associated. The similar (but different) construction of the geometric quantization, especially the first step of this construction is considered.

Reviewer: Peter M. Akhmet’ev (Izmiran)

MSC:

53D50	Geometric quantization
53D55	Deformation quantization, star products

Keywords:

Poisson manifold; action functional