Effect of matter motion and polarization in neutrino flavour oscillations

The Lorentz invariant formalism for description of neutrino flavour oscillations in moving and polarized matter is developed. It is shown that the neutrino effective potential, which determines the effective mass difference between neutrinos in matter can be significantly changed by relativistic motion of matter. In the case of matter motion parallel to neutrino propagation, matter effects in neutrino flavour oscillations are suppressed. In the case of relativistic motion of matter in the opposite direction substantial increase of effects of matter in neutrino oscillations is predicted. The dependence of the matter term in neutrino effective potential on the values and correlations of the three vectors, the neutrino and matter speeds and matter polarization, is discussed in detail.