Generalized Lagrange Transforms: Finsler Geometry Methods and Deformation Quantization of Gravity

Abstract

We propose a natural Fedosov type quantization of generalized Lagrange models and gravity theories with metrics lifted on tangent bundle, or extended to higher dimension, following some stated geometric/ physical conditions (for instance, nonholonomic and/or conformal transforms to some physically important metrics or mapping into a gauge model). Such generalized Lagrange transforms define canonical nonlinear connection, metric and linear connection structures and model almost Kahler geometries with induced canonical symplectic structure and compatible affine connection. The constructions are possible due to a synthesis of the nonlinear connection formalism developed in Finsler and Lagrange geometries and deformation quantization methods.

latex 2e, 11pt, 17 pages, to be published: An. St. Univ. Al. I. Cuza, Iasi, s I a, Matematica, vol LIII (suplement), 2007

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Cited by in corpus (9)

• Principles of Einstein-Finsler Gravity and Perspectives in Modern Cosmology
• Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity
• Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
• Einstein Gravity as a Nonholonomic Almost Kahler Geometry, Lagrange-Finsler Variables, and Deformation Quantization
• Pseudo-Finslerian spacetimes and multi-refringence
• Fractional Almost Kahler - Lagrange Geometry
• Finsler-Lagrange Geometries and Standard Theories in Physics: New Methods in Einstein and String Gravity
• Loop Quantum Gravity in Ashtekar and Lagrange-Finsler Variables and Fedosov Quantization of General Relativity
• Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity