Explicit Formulae for Noncommutative Deformations of CP^N and CH^N

TL;DR

This paper provides explicit formulas for deformation quantization of complex projective and hyperbolic spaces, including star products and Fock representations, advancing the mathematical understanding of noncommutative Kähler manifolds.

Contribution

It introduces explicit deformation quantization formulas and Fock representations for noncommutative CP^N and CH^N, expanding on Karabegov's method.

Findings

Explicit star product formulas in all orders.

Fock representations for noncommutative CP^N and CH^N.

Enhanced mathematical framework for noncommutative Kähler manifolds.

Abstract

We give explicit expressions of a deformation quantization with separation of variables for CP^N and CH^N. This quantization method is one of the ways to perform a deformation quantization of Kahler manifolds, which is introduced by Karabegov. Star products are obtained as explicit formulae in all order in the noncommutative parameter. We also give the Fock representations of the noncommutative CP^N and CH^N.