Lorentz violation, scalar fields, and Finsler geometry

The quadratic scalar field theory incorporating general violations of Lorentz symmetry is presented, and the classical relativistic point-particle lagrangian yielding the corresponding dispersion relation is obtained. Point-particle motions in the presence of Lorentz violation are associated with a Finsler geometry. A method to extract these Finsler spaces is described, and some of their properties are studied.