Almost Kaehler deformation quantization

TL;DR

This paper develops a Fedosov-type deformation quantization method for almost-Kaehler manifolds using a special affine connection that preserves the structure.

Contribution

It introduces a novel approach to deformation quantization on almost-Kaehler manifolds employing a torsion-inclusive affine connection.

Findings

Constructed a Fedosov-type star product for almost-Kaehler manifolds.

Extended deformation quantization techniques to manifolds with torsion.

Provided a framework for quantization respecting the almost-Kaehler structure.

Abstract

We use a natural affine connection with nontrivial torsion on an arbitrary almost-Kaehler manifold which respects the almost-Kaehler structure to construct a Fedosov-type deformation quantization on this manifold.