Fedosov Quantization of Fractional Lagrange Spaces

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.

14 pages, latex2e, v2 with up-dated references and minor typos corrections

References in corpus (4)

• Finsler and Lagrange Geometries in Einstein and String Gravity
• Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
• Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
• Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity

Cited by in corpus (1)

• Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics