Geometric Quantization of Vector Bundles

TL;DR

This paper introduces a new method for geometric quantization of vector bundles on compact Kähler manifolds, extending existing techniques to a broader class of bundles with a functorial dependence on connections.

Contribution

It provides a functorial construction for quantizing any smooth vector bundle on a compact Kähler manifold, generalizing previous approaches for Toeplitz and geometric quantization.

Findings

Quantization depends functorially on the choice of connection.

The method applies to all smooth vector bundles on compact Kähler manifolds.

Extension of existing quantization techniques to a broader class of bundles.

Abstract

I repeat my definition for quantization of a vector bundle. For the case of Toeplitz and geometric quantization of a compact Kaehler Manifold, I give a construction for quantizing any smooth vector bundle which depends functorially on a choice of connection on the bundle.