A field theory in Randers-Finsler spacetime

Abstract

Finsler geometry is a natural arena to investigate the physics of spacetimes with local Lorentz violating. The directional dependence of the Finsler metric provides a way to encode the Lorentz violating effects into the geometric structure of spacetime. Here, a classical field theory is proposed in a special Finsler geometry, the so-called Randers-Finsler spacetime, where the Lorentz violation is produced by a background vector field. By promoting the Randers-Finsler metric to a differential operator, a Finsler-invariant action for the scalar, gauge and fermions are proposed. The theory contains nonlocal terms, as in the Very Special Relativity based theories. By expanding the Lagrangian, minimal and nonminimal Standard Model Extension terms arises, revealing a perturbative Lorentz violation. For a CPT-even term, the Carrol-Field-Jackiw and derivative extensions are obtained.

arXiv comment12 pages. arXiv admin note: substantial text overlap with arXiv:1602.07345

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• Applications of the Schwarzschild-Finsler-Randers model
• Classical Lagrangians for the nonminimal spin-nondegenerate Standard-Model Extension at higher orders in Lorentz violation
• The Finsler spacetime condition for (α,β)-metrics and their isometries
• Anisotropic Conformal Dark Gravity on the Lorentz Tangent Bundle Spacetime
• Trajectories of astroparticles in pseudo-Finsler spacetime with the most general modified dispersion