Quantizable functions on K\"ahler manifolds and non-formal quantization

TL;DR

This paper constructs a non-formal deformation quantization for a dense subset of smooth functions on Kähler manifolds using Fedosov connections, linking quantizable functions to twisted differential operators and quantum moment maps.

Contribution

It introduces a method to quantize a dense subset of functions on Kähler manifolds via Fedosov connections, connecting to twisted differential operators and quantum moment maps.

Findings

Existence of a dense subsheaf of functions admitting non-formal deformation quantization.

Quantization of these functions yields sheaves of twisted differential operators.

Quantizable functions include images of quantum moment maps.

Abstract

Applying the Fedosov connections constructed in our previous work, we find a (dense) subsheaf of smooth functions on a K\"ahler manifold $X$ which admits a non-formal deformation quantization. When $X$ is prequantizable and the Fedosov connection satisfies an integrality condition, we prove that this subsheaf of functions can be quantized to a sheaf of twisted differential operators (TDO), which is isomorphic to that associated to the prequantum line bundle. We also show that examples of such quantizable functions are given by images of quantum moment maps.