Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces

TL;DR

This paper develops a Fedosov-type deformation quantization method for Finsler and Lagrange spaces modeled as almost Kahler manifolds, providing a geometric framework for quantization in these settings.

Contribution

It introduces a canonical deformation quantization approach for almost Kahler models of Finsler and Lagrange spaces, extending geometric quantization techniques.

Findings

Constructs a Fedosov-type deformation quantization for these geometries

Provides a canonical method derived from regular Lagrangians and Finsler functions

Bridges Finsler geometry with quantum deformation frameworks

Abstract

Finsler and Lagrange spaces can be equivalently represented as almost Kahler manifolds enabled with a metric compatible canonical distinguished connection structure generalizing the Levi Civita connection. The goal of this paper is to perform a natural Fedosov-type deformation quantization of such geometries. All constructions are canonically derived for regular Lagrangians and/or fundamental Finsler functions on tangent bundles.