Abstract
In this paper we considered semiclassical neutrino spin precession in a transversal matter current and quantum case of the neutrino spin oscillations in the mass and flavor bases induced by a moving media. In the first part we have verified, that even without presence of an electromagnetic field, in presence of a matter, when the transverse matter term is not zero, the neutrino spin oscillations can be induced. In the second part there were some calculations, that in the end led us to the evolution equations which include an effective Hamiltonian of the weak interactions. From these equations one can see the influence of the transverse component of a matter velocity on a spin oscillations and of the longitudinal component of a matter velocity on the neutrino energy spectrum.
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