Mathematical foundations for field theories on Finsler spacetimes

Abstract

The paper introduces a general mathematical framework for action based field theories on Finsler spacetimes. As most often fields on Finsler spacetime (e.g., the Finsler fundamental function or the resulting metric tensor) have a homogeneous dependence on the tangent directions of spacetime, we construct the appropriate configuration bundles whose sections are such homogeneous fields; on these configuration bundles, the tools of coordinate free calculus of variations can be consistently applied to obtain field equations. Moreover, we prove that general covariance of natural Finsler field Lagrangians leads to an averaged energy-momentum conservation law which, in the particular case of Lorentzian spacetimes, is equivalent to the usual, pointwise energy-momentum covariant conservation law.

48 pages, 1 figure

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• Multimetric Finsler Geometry
• Generalized Finsler geometry and the anisotropic tearing of skin
• Revisiting Legendre transformations in Finsler geometry
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• Birkhoff Theorem for Berwald Finsler spacetimes
• Weak equivalence principle and nonrelativistic limit of general dispersion relations
• Muon accelerators -- Muon lifetime measurements as window to Planck scale physics
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• From kinetic gases to an exponentially expanding universe - The Finsler-Friedmann equation
• Single-Particle Quantum Mechanics of the Free Klein-Gordon Equation with Lorentz Violation
• Characteristic tensors for almost Finsler manifolds
• Kinetic gases in static spherically symmetric modified dispersion relations
• Experimental Bounds on Deformed Muon Lifetime Dilation