A field theory in Randers-Finsler spacetime

Finsler geometry is a natural arena to investigate the physics of spacetimes with local Lorentz violation. The directional dependence of the Finsler metric provides a way to encode the Lorentz-violating effects into the geometric structure of the 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 arise, revealing a perturbative Lorentz violation. For a CPT-even term, the Carrol-Field-Jackiw and derivative extensions are obtained. Copyright (C) 2021 EPLA

Automated summary

Finsler geometry serves as a natural arena for studying spacetime physics with local Lorentz violation by encoding these effects through the directional dependence of the Finsler metric. A classical field theory is proposed in a special Randers-Finsler spacetime, where Lorentz violation is introduced by a background vector field, leading to nonlocal terms and Standard Model Extension terms that reveal perturbative Lorentz violation.