Abstract
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.
Highlights
Neutrino wave equationThe phenomenological theory of oscillations based on the ideas of B
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
Maki et al [2] describes the general properties of neutrino oscillations. As this theory was initially developed to describe neutrinos of rather high energies, it is not appropriate for study of low-energy neutrinos including the relic neutrinos, which play an important role in many cosmological models
Summary
The phenomenological theory of oscillations based on the ideas of B. One-particle wave functions are elements of the representation space of the direct product of the Poincaré group and the internal symmetry group S U(3) Within this approach, the phenomenon of neutrino oscillations arises as a direct consequence of the general principles of quantum field theory. As it is well-known [5], neutrinos propagating in matter interact with the medium via forward elastic scattering on background fermions. These representations are connected by the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix UPMNS.
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