Positive Kernels and Quantization

TL;DR

This paper introduces a generalized quantization method based on positive definite kernels on principal G-bundles, extending geometric and coherent state quantizations to arbitrary compact groups.

Contribution

It proposes a new quantization framework using positive kernels on principal G-bundles, generalizing existing geometric and coherent state quantizations.

Findings

Unifies geometric and coherent state quantizations under a kernel-based framework.

Extends quantization methods to general compact groups beyond U(1).

Provides a mathematical foundation for kernel-based quantization on principal bundles.

Abstract

In the paper we investigate a method of quantization based on the concept of positive definite kernel on a principal $G$-bundle with compact structural group G. For G=U(1) our approach leads to Kostant-Souriau geometric quantization as well as to coherent state method of quantization. So, the theory proposed here can be treated as a generalization of both mentioned quantizations to the case of general compact group.