Within the recently proposed [1][2][3] Lorentz invariant formalism for description of neutrino spin evolution in presence of an arbitrary electromagnetic fields matter motion and polarization effects are considered. It is shown that in the case of matter moving with relativistic speed parallel to neutrino propagation, matter effects in neutrino spin (and also flavour) oscillations are suppressed. In the case of relativistic motion of matter in the opposite direction in respect to neutrino propagation, sufficient increase of effects of matter in neutrino oscillations is predicted. These phenomena could have important consequences in different astrophysical environments.In [1-3] the Lorentz invariant formalism for neutrino motion in nonmoving and isotropic matter under the influence of an arbitrary configuration of electromagnetic fields have been developed. We have derived the neutrino spin evolution Hamiltonian that accounts not only for the transversal to the neutrino momentum components of electromagnetic field but also for the longitudinal components. With the using of the proposed Hamiltonian it is possible to consider neutrino spin precession in an arbitrary configuration of electromagnetic fields including those that contain strong longitudinal components. We have also considered the new types of resonances in the neutrino spin precession ν L ↔ ν R that could appear when neutrinos propagate in matter under the influence of different electromagnetic field configurations. Within the proposed approach the parametric resonance of neutrino oscillations in electromagnetic wave field with periodically varying time-dependent amplitude has been also studied [4].In the studies [1][2][3] of the neutrino spin evolution we have focused mainly on description of influence of different electromagnetic fields, while modelling the matter we confined ourselves to the most simple case of non-moving and unpolarised matter. Now we should like to go further ( see also [5]) and to generalize our approach for the case of moving and polarized homogeneous 1

Oscillations of neutrinos ν L ↔ ν R in presence of an arbitrary electromagnetic field are considered. We introduce the Hamiltonian for the neutrino spin evolution equation that accounts for possible effects of interaction of neutrino magnetic µ and electric ǫ dipole moments with the transversal (in respect to the neutrino momentum) and also the longitudinal components of electromagnetic field. Using this Hamiltonian we predict the new types of resonances in the neutrino oscillations ν L ↔ ν R in the presence of the field of an electromagnetic wave and in combination of an electromagnetic wave and constant magnetic field. The possible influence of the longitudinal magnetic field on neutrino oscillations is emphasized.The electromagnetic properties of neutrinos are among the most interesting issues in particle physics. Studies of the neutrino electromagnetic properties could provide an important information about the structure of theoretical model of particle interaction. For instance, the discovery of the non-vanishing neutrino magnetic moment, as well as the neutrino mass, would clearly indicate that the Standard Model has to be generalized.The non-vanishing neutrino magnetic moment has also crucial consequences in astrophysics. As it has been shown in plenty of studies (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]) that have emerged during past decades, the neutrino conversions and oscillations produced under the influence of transversal constant or constant and twisting (in space) magnetic fields could be important for evolution of astrophysical object, like the Sun and neutron stars, or could result in sufficient effects while neutrinos propagate through interstellar galactic media 2 .In the previously performed studies of neutrino spin precession only effects of the neutrino magnetic (or flavour transition) moment interaction 1 E-mail: studenik@srdlan.npi.msu.su 2 It should be noted here that the neutrino helicity flip could be caused not only by the interaction with an external magnetic field (or, as it is shown below with an electromagnetic wave) but also by the scattering with charged fermions in the background (see, for example, [19] and references therein)

The quantum theory of spin light (electromagnetic radiation emitted by a Dirac massive neutrino propagating in dense matter due to the weak interaction of a neutrino with background fermions) is developed. In contrast to the Cherenkov radiation, this effect does not disappear even if the medium refractive index is assumed to be equal to unity. The formulas for the transition rate and the total radiation power are obtained. It is found out that radiation of photons is possible only when the sign of the particle helicity is opposite to that of the effective potential describing the interaction of a neutrino (antineutrino) with the background medium. Due to the radiative self-polarization the radiating particle can change its helicity. As a result, the active left-handed polarized neutrino (right-handed polarized antineutrino) converting to the state with inverse helicity can become practically ``sterile''. Since the sign of the effective potential depends on the neutrino flavor and the matter structure, the spin light can change a ratio of active neutrinos of different flavors. In the ultra relativistic approach, the radiated photons averaged energy is equal to one third of the initial neutrino energy, and two thirds of the energy are carried out by the final ``sterile'' neutrinos.Comment: 12 pages, Latex. To appear in Phys. Lett.

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The quantum theory of the "spin light" (electromagnetic radiation emitted by a massive neutrino propagating in dense matter due to the weak interaction of a neutrino with background fermions) is developed. In contrast to the Cherenkov radiation, this effect does not disappear even if the medium refractive index is assumed to be equal to unity. The formulas for the transition rate and the total radiation power are obtained. It is found out that radiation of photons is possible only when the sign of the particle helicity is opposite to that of the effective potential describing the interaction of a neutrino (antineutrino) with the background medium. Due to the radiative self-polarization the radiating particle can change its helicity.As a result, the active left-handed polarized neutrino (right-handed polarized antineutrino) converting to the state with inverse helicity can become practically "sterile". Since the sign of the effective potential depends on the neutrino flavor and the matter structure, the "spin light" can change a ratio of active neutrinos of different flavors. In the ultra relativistic approach, the radiated photons averaged energy is equal to one third of the initial neutrino energy, and two thirds of the energy are carried out by the final "sterile" neutrinos. This fact can be important for the understanding of the "dark matter" formation mechanism on the early stages of evolution of the Universe.A massive neutrino propagating in dense matter can emit electromagnetic radiation due to the weak interaction of a neutrino with background fermions [1,2]. As a result of the radiation, neutrino can change its helicity due to the radiative self-polarization. In contrast to the Cherenkov