  A method is presented for deducing classical point-particle Lagrange
functions corresponding to a class of quartic dispersion relations. Applying
this to particles violating Lorentz symmetry in the minimal Standard-Model
Extension leads to a variety of novel lagrangians in flat spacetime. Morphisms
in these classical systems are studied that echo invariance under field
redefinitions in the quantized theory. The Lagrange functions found offer new
possibilities for understanding Lorentz-breaking effects by exploring parallels
with Finsler-like geometries.
