Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles

Abstract

We provide a method of converting Lagrange and Finsler spaces and their Legendre transforms to Hamilton and Cartan spaces into almost Kaehler structures on tangent and cotangent bundles. In particular cases, the Hamilton spaces contain nonholonomic lifts of (pseudo) Riemannian / Einstein metrics on effective phase spaces. This allows us to define the corresponding Fedosov operators and develop deformation quantization schemes for nonlinear mechanical and gravity models on Lagrange- and Hamilton-Fedosov manifolds.

latex2e, 11pt, 35 pages, v3, accepted to J. Math. Phys. (2009)

References in corpus (6)

• General Very Special Relativity is Finsler Geometry
• Planck-scale modified dispersion relations and Finsler geometry
• Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
• Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity
• Doubly Special Relativity and Finsler geometry
• Lorentz Invariance Violation from String Theory

Cited by in corpus (7)

• Nonholonomic Ricci Flows: II. Evolution Equations and Dynamics
• String Quantum Gravity, Lorentz-Invariance Violation and Gamma-Ray Astronomy
• Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li
• Quantum-Gravity Induced Lorentz Violation and Dynamical Mass Generation
• Fedosov Quantization of Fractional Lagrange Spaces
• Einstein Gravity in Almost Kahler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics
• Stringy Space-Time Foam and High-Energy Cosmic Photons