Stationary and non-stationary solutions of the evolution equation for neutrino in matterстатья
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Аннотация:We study solutions of the equation which describes the evolution
of a neutrino propagating in dense homogeneous medium in the framework of
the quantum field theory. In the two-flavor model the explicit form of Green
function is obtained, and as a consequence the dispersion law for a neutrino in
matter is derived. Both the solutions describing the stationary states and the
spin-flavor coherent states of the neutrino are found. It is shown that the stationary
states of the neutrino are different from the mass states, and the wave
function of a state with a definite flavor should be constructed as a linear combination
of the wave functions of the stationary states with coefficients, which
depend on the mixing angle in matter. In the ultra-relativistic limit the wave
functions of the spin-flavor coherent states coincide with the solutions of the
quasi-classical evolution equation. Quasi-classical approximation of the wave
functions of spin-flavor coherent states is used to calculate the probabilities of
transitions between neutrino states with definite flavor and helicity.