  We consider a Lorentz non-invariant dispersion relation for the neutrino,
which would produce unexpected effects with neutrinos of few eV, exactly where
the tritium beta-decay anomaly is found. We use this anomaly to put bounds on
the violation of Lorentz invariance. We discuss other consequences of this
non-invariant dispersion relation in neutrino experiments and high-energy
cosmic-ray physics.
