Riemann-Finsler Geometry and Lorentz-Violating Scalar Fields

Understand

The correspondence between Riemann-Finsler geometries and effective field theories with spin-independent Lorentz violation is explored.

• We obtain the general quadratic action for effective scalar field theories in any spacetime dimension with Lorentz-violating operators of arbitrary mass dimension.
• Classical relativistic point-particle lagrangians are derived that reproduce the momentum-velocity and dispersion relations of quantum wave packets.
• The correspondence to Finsler structures is established, and some properties of the resulting Riemann-Finsler spaces are investigated.