Fedosov Quantization of Fractional Lagrange Spaces

TL;DR

This paper develops a Fedosov-type geometric quantization framework for fractional Lagrange spaces using Caputo derivatives, enabling the modeling of quantum fractional Finsler geometries and potential applications in fractional gravity.

Contribution

It introduces a novel Fedosov deformation quantization method for fractional Lagrange geometries with Caputo derivatives, unifying classical and quantum fractional models.

Findings

Geometrization of classical and quantum fractional Lagrange interactions.

Construction of fractional almost Kahler models encoding fractional Euler-Lagrange equations.

Extension of the scheme to fractional Hamilton systems and gravity models.

Abstract

The main goal of this work is to perform a nonolonomic deformation (Fedosov type) quantization of fractional Lagrange geometries. The constructions are provided for a (fractional) almost Kahler model encoding equivalently all data for fractional Euler-Lagrange equations with Caputo fractional derivative. For homogeneous generating Finsler functions, the geometric models contain quantum versions of fractional Finsler spaces. The scheme can be generalized for fractional Hamilton systems and various models of fractional classical and quantum gravity. We conclude that the approach with Caputo fractional derivative allows us to geometrize both classical and quantum (Fedosov type) fractional regular Lagrange interactions.