Stationary and non-stationary solutions of the evolution equation for neutrino in matter

• Main Authors: Chukhnova, A.V., Lobanov, A.E.
• Format: Conference Proceeding
• Language: English
• Subjects: Coherence; Economic models; Evolution; Field theory; Flavor (particle physics); Green's functions; Helicity; Neutrinos; Quantum field theory; Quantum theory; Wave functions
• ISSN: 2100-014X; 2101-6275; 2100-014X
• DOI: 10.1051/epjconf/201819103002

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.