Lorentz violating effects in the neutrino sector have been
considered by many authors [86, 182, 181, 180, 83, 55, 18, 126,
191, 82]. To illustrate how Lorentz violation affects neutrino
propagation, we consider the simplest case, where the limiting
speeds for mass eigenstates of the neutrino are different, i.e.
neutrinos have dispersions We can immediately see from Equation
(108) that Lorentz violation can have a number of consequences
for standard neutrino oscillation experiments. The first is
simply that neutrino oscillation still occurs even if the mass
is zero. In fact, some authors have proposed that Lorentz
violation could be partly responsible for the observed
oscillations . Oscillations due to the type of Lorentz violation
above vary as . Current data support neutrino oscillations that
vary as a function of [35, 125], so it seems unlikely that
Lorentz violation could be the sole source of neutrino
oscillations. It is possible, however, that Lorentz violation
may explain some of the current problems in