Neutrino Propagation and Oscillations in a Strong Magnetic Field

We review the results on neutrino propagation in neutral and charged media under strong magnetic fields $M_{W}^{2}\gg B\gg m_{e}^{2}$. It is shown that the neutrino energy density gets a magnetic contribution in both charged and neutral media, which is linear in the magnetic field, of first order in $G_{F}$, and independent of the charge density. This new term enters as a correction to the neutrino kinetic energy and produces an anisotropic contribution to the neutrino index of refraction. As a consequence, in a neutral medium a highly anisotropic resonant level-crossing condition takes place for the oscillation between electron-neutrinos and the other neutrino species. Possible cosmological applications are presented.