Classical Lagrangians for the nonminimal Standard-Model Extension at higher orders in Lorentz violation

The current paper is dedicated to determining perturbative expansions for Lagrangians describing classical, relativistic, pointlike particles subject to Lorentz violation parameterized by the nonminimal Standard-Model Extension (SME). An iterative technique recently developed and applied to a Lorentz-violating scalar field theory is now adopted to treat the spin-degenerate SME fermion sector. Lagrangians are obtained at third order in Lorentz violation for the operators $\hat{a}_{\mu}$, $\hat{c}_{\mu}$, $\hat{e}$, $\hat{f}$, and $\hat{m}$ for arbitrary mass dimension. The results demonstrate the impact of nonzero spin on classical particle propagation. They will be useful for phenomenological studies of modified gravity and could provide useful insights into explicit Lorentz violation in curved spacetimes.