  This article gives a brief summary on recently obtained classical lagrangians
for the nonminimal fermion sector of the Standard-Model Extension (SME). Such
lagrangians are adequate descriptions of classical particles that are subject
to a Lorentz-violating background field based on the SME. Explicitly,
lagrangians were obtained for the leading nonminimal contributions of the m, a,
c, e, and f coefficients. These results were then used to interpret classical,
kinematic tests of Special Relativity in the framework of the nonminimal SME.
This led to new constraints on certain nonminimal controlling coefficients.
Although the experiments were very sophisticated in the era when they were
carried out, their sensitivities for detecting Lorentz violation were still far
away from the Planck scale. Obtaining the novel constraints can be considered
as a proof-of-principle demonstrating the applicability of the classical
lagrangians computed.
