zbMATH — the first resource for mathematics

Cohomological classification of deformation quantizations with separation of variables. (English) Zbl 0938.53049
A second cohomology class for the deformation quantization with separation of variables on a Kähler manifold has been calculated. It turns out that for deformation quantizations with separation of variables \(A\) and \(\overline A\) the calculation of the Deligne classes \([\overline A,A]\) is rather straightforward. The definition of a specific class \(cl\) based on Deligne’s classes is given and then \(cl(A)\) is calculated.

53D55 Deformation quantization, star products
81S10 Geometry and quantization, symplectic methods
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
Full Text: DOI