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

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.