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.

arXiv commentlatex2e, 11pt, 35 pages, v3, accepted to J. Math. Phys. (2009)

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• Implications of a Stochastic Microscopic Finsler Cosmology
• Modified Dispersion Relations in Horava-Lifshitz Gravity and Finsler Brane Models
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• Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
• String Quantum Gravity, Lorentz-Invariance Violation and Gamma-Ray Astronomy
• Finsler Black Holes Induced by Noncommutative Anholonomic Distributions in Einstein Gravity
• Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li
• Quantum-Gravity Induced Lorentz Violation and Dynamical Mass Generation
• Einstein Gravity as a Nonholonomic Almost Kahler Geometry, Lagrange-Finsler Variables, and Deformation Quantization
• CPT-Violating Leptogenesis induced by Gravitational Defects
• On General Solutions for Field Equations in Einstein and Higher Dimension Gravity
• Fractional Almost Kahler - Lagrange Geometry
• Decoherence and CPT Violation in a Stringy Model of Space-Time Foam
• Fedosov Quantization of Fractional Lagrange Spaces
• Rainbows without unicorns: Metric structures in theories with Modified Dispersion Relations
• Einstein Gravity in Almost Kahler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics
• Loop Quantum Gravity in Ashtekar and Lagrange-Finsler Variables and Fedosov Quantization of General Relativity
• The Algebraic Index Theorem and Fedosov Quantization of Lagrange-Finsler and Einstein Spaces
• Black Holes, Ellipsoids, and Nonlinear Waves in Pseudo-Finsler Spaces and Einstein Gravity
• Two-Connection Renormalization and Nonholonomic Gauge Models of Einstein Gravity
• Nonassociative geometry of nonholonomic phase spaces with star R-flux string deformations and (non) symmetric metrics
• Stringy Space-Time Foam and High-Energy Cosmic Photons
• On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles
• A Novel Foamy Origin for Singlet Fermion Masses
• A Kähler Structure on Cartan Spaces
• Branes and Quantization for an A-Model Complexification of Einstein Gravity in Almost Kahler Variables
• Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity