  The effects of perturbative Lorentz and CPT violation on neutrino
oscillations are studied. Features include neutrino-antineutrino oscillations,
direction dependence, and unconventional energy behavior. Leading-order
corrections arising from renormalizable operators are derived in the general
three-flavor effective field theory. The results are applied to neutrino-beam
experiments with long baselines, which offer excellent sensitivity to the
accompanying effects. Key signatures of Lorentz and CPT violation using
neutrino beams include sidereal variations in the oscillation probabilities
arising from the breakdown of rotational symmetry, and CPT asymmetries
comparing neutrino and antineutrino modes. Attainable sensitivities to
coefficients for Lorentz violation are estimated for several existing and
future experiments.
