The Fuzzy Kaehler Coset Space by the Fedosov Formalism

TL;DR

This paper explores the deformation quantization of Kaehler coset spaces using Fedosov formalism, demonstrating that Killing potentials form fuzzy algebras in irreducible cases.

Contribution

It introduces a method to quantize Kaehler coset spaces via Fedosov formalism and shows the emergence of fuzzy algebrae for Killing potentials.

Findings

Killing potentials satisfy fuzzy algebrae in irreducible Kaehler coset spaces.

Fedosov formalism effectively applies to deformation quantization of these spaces.

The approach bridges geometric quantization and fuzzy geometry.

Abstract

We discuss deformation quantization of the Kaehler coset space by using the Fedosov formalism. We show that the Killing potentials of the Kaehler coset space satisfy the fuzzy algebrae, when the coset space is irreducible.