On Fedosov’s approach to deformation quantization with separation of variables

Abstract

The description of all deformation quantizations with separation of variables on a Kahler manifold from [8] is used to identify the Fedosov star-product of Wick type constructed by M. Bordemann and S. Waldmann in [3]. This star-product is shown to be the one with separation of variables which corresponds to the trivial deformation of the Kahler form in the sense of [8]. To this end a formal Fock bundle on a Kahler manifold is introduced and an associative multiplication on its sections is defined.