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

TL;DR

This paper derives explicit solutions for neutrino evolution in dense matter, revealing stationary and spin-flavor coherent states, and connects quantum field theory results with quasi-classical approximations for transition probabilities.

Contribution

It provides explicit Green function solutions and dispersion relations for neutrinos in matter within a quantum field theory framework, including stationary and coherent states.

Findings

Existence of both stationary and spin-flavor coherent solutions.

Stationary states can differ from mass eigenstates.

Quasi-classical approximation aligns with quantum solutions in ultra-relativistic limit.

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. It is shown that there exist both the solutions describing the stationary states and the solutions describing the spin-flavor coherent states of the neutrino. The stationary states may be different from the mass eigenstates, 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.