A field theory in Randers-Finsler spacetime

Universidade Federal do Cariri (UFCA) - Av. Tenente Raimundo Rocha, Cidade Universitária, Juazeiro do Norte, Ceará, CEP 63048-080, Brazil

Received: 4 September 2020
Accepted: 8 December 2020

Abstract

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.