Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity

TL;DR

This paper develops a Fedosov-like quantization method for gravity using nonholonomic almost Kahler structures on (pseudo) Riemannian manifolds, integrating nonlinear connection formalism into Einstein gravity.

Contribution

It introduces a novel approach to quantize gravity by combining nonholonomic geometry with Fedosov quantization, extending classical Einstein gravity frameworks.

Findings

Successful formulation of gravity in almost Kahler geometry

Implementation of Fedosov-like quantization for Einstein gravity

Extension of nonlinear connection formalism to quantum gravity

Abstract

Nonholonomic distributions and adapted fame structures on (pseudo) Riemannian manifolds of even dimension are employed to build structures equivalent to almost Kahler geometry and which allows to perform a Fedosov-like quantization of gravity. The nonlinear connection formalism that was formally elaborated for Lagrange and Finsler geometry is implemented in classical and quantum Einstein gravity.