  Spin-flavor oscillations of Dirac neutrinos in matter and a magnetic field
are studied using the method of relativistic quantum mechanics. Using the exact
solution of the wave equation for a massive neutrino, taking into account
external fields, the effective Hamiltonian governing neutrino spin-flavor
oscillations is derived. Then the The consistency of our approach with the
commonly used quantum mechanical method is demonstrated. The obtained
correction to the usual effective Hamiltonian results in the appearance of the
new resonance in neutrino oscillations. Applications to spin-flavor neutrino
oscillations in an expanding envelope of a supernova are discussed. In
particular, transitions between right-polarized electron neutrinos and
additional sterile neutrinos are studied for realistic background matter and
magnetic field distributions. The influence of other factors such as the
longitudinal magnetic field, the matter polarization, and the non-standard
contributions to the neutrino effective potential, is also analyzed.
