Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces

Abstract

Finsler and Lagrange spaces can be equivalently represented as almost Kahler manifolds enabled with a metric compatible canonical distinguished connection structure generalizing the Levi Civita connection. The goal of this paper is to perform a natural Fedosov-type deformation quantization of such geometries. All constructions are canonically derived for regular Lagrangians and/or fundamental Finsler functions on tangent bundles.

arXiv commentthe latex 2e variant of the manuscript accepted for JMP, 11pt, 23 pages

References in corpus (11)

• Deformation quantization of Poisson manifolds, I
• Operads and Motives in Deformation Quantization
• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$
• Exact Solutions with Noncommutative Symmetries in Einstein and Gauge Gravity
• Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity
• Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity
• Clifford-Finsler Algebroids and Nonholonomic Einstein-Dirac Structures
• Lagrange-Fedosov Nonholonomic Manifolds
• Wick type deformation quantization of Fedosov manifolds
• Finsler-Lagrange Geometries and Standard Theories in Physics: New Methods in Einstein and String Gravity
• Generalized Lagrange Transforms: Finsler Geometry Methods and Deformation Quantization of Gravity

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