On quantizations of complex contact manifolds

Abstract

Abstract. A (holomorphic) quantization of a complex contact manifold is a filtered algebroid stack which is locally equivalent to the ring E of microdifferential operators and which has trivial graded. The existence of a canonical quantization has been proved by Kashiwara. In this paper we consider the classification problem, showing that the above quantizations are classified by the first cohomology group with values in a certain sheaf of homogeneous forms. Secondly, we consider the problem of existence and classification for quantizations given by algebras.

Dynamical Quantization of Contact Structures

“…Regarding the scientific context, it is worth noting that [38,39] discuss the deformation quantization of complex contact structures in terms of a Moyal-Weyl star product and microlocal sheaf theory, and [40,41] address quantization for contact structures via the virtual representation given by the index of the contact Dirac operator and as a bracket deformation, respectively. It would be enlightening to compare these algebraic constructions with the geometry-based quantizations of Definitions 1.1 and 1.2, which follow from the fact that maximal non-integrability of the contact structure forces a BRST quantization with a maximal set of second class constraints.…”