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

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Cited by in corpus (6)

• Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
• Fractional Nonholonomic Ricci Flows
• Fractional Almost Kahler - Lagrange Geometry
• Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics
• Fractional Analogous Models in Mechanics and Gravity Theories
• Fractional Exact Solutions and Solitons in Gravity