Three Natural Generalizations of Fedosov Quantization

TL;DR

This paper extends Fedosov's deformation quantization method to supermanifolds, non-Weyl star products, and structures depending on Planck's constant, broadening its applicability in mathematical physics.

Contribution

It introduces three natural generalizations of Fedosov quantization without adding new variables, enhancing the framework's flexibility and scope.

Findings

Generalization to supermanifolds

Allowing non-Weyl star products

Structures depending on Planck's constant

Abstract

Fedosov's simple geometrical construction for deformation quantization of symplectic manifolds is generalized in three ways without introducing new variables: (1) The base manifold is allowed to be a supermanifold. (2) The star product does not have to be of Weyl/symmetric or Wick/normal type. (3) The initial geometric structures are allowed to depend on Planck's constant.