  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. The results provide support
for open conjectures about Riemann-Finsler geometries associated with
Lorentz-violating field theories.
