Neutrino flavor oscillations in background matter

We study the evolution of two mixed Dirac neutrinos in an external axial-vector field. The dynamics of this system is described in the framework of relativistic wave equations approach on the basis of the known solutions of the Dirac equation in an external field with a given initial condition. The general solution of the initial condition problem, exactly accounting for the external field, is obtained. Then we consider special form of the external field which corresponds to the standard model neutrino interactions with the background matter. In this limit we derive the transition probability and compare it with the previously known results.