Noncommutative Kahler-like structures in quantization

TL;DR

This paper introduces C*-algebras with polarization as quantum Kahler structures, connecting them to geometric quantization and exploring their properties via coherent states methods.

Contribution

It proposes a new framework for quantum Kahler structures using polarized C*-algebras and links it to existing geometric quantization theories.

Findings

Established the concept of C*-algebra with polarization as quantum Kahler structure

Connected polarized C*-algebras to Kostant-Souriau geometric quantization

Analyzed polarized C*-algebras using coherent states methods

Abstract

One introduces the notion of C*-algebra with polarization which could be considered as the quantum Kahler structure. The connection of these algebras with Kostant-Souriou geometric quantization is shown. The theory of polarized C*-algebra is investigated by the use of the coherent states method.