A field theory in Randers-Finsler spacetime

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