On the canonical normalization of a trace density of deformation quantization. (English) Zbl 0943.53052

Karabegov, A. V.

Lett. Math. Phys. 45, No. 3, 217-228 (1998).

The author gives a scheme to normalize a canonical trace density of arbitrary deformation quantization, as defined by Fedorov on a symplectic manifold. Certain characteristics of a formal trace density, such as characteristics of arbitrary deformation quantization calculated on any contractible subset, is given. It is shown that the canonical normalization of a trace density of an arbitrary deformation quantization can be described in terms of quantization itself, without referring to the Moyal deformation quantization. The scheme is applied to give an explicit expression of the canonical formal trace density of deformation quantization with separation of variables on a pseudo-Kähler manifold.

Reviewer: M.Rajabov (Baku)

MSC:

53D55	Deformation quantization, star products
81S30	Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics

Keywords:

deformation quantisation; trace density; pseudo-Kähler manifold