Neutrino self-energy in external magnetic field

Using the exact propagators in a constant magnetic field, the neutrino self-energy has been calculated to all orders in the field strength B within the minimal extension of the Weinberg-Salam model with massive Dirac neutrinos. A simple and very accurate formula for the self-energy is obtained, that is valid for 0 < B << m^2_W/e and for and for neutrino transverse momentum to the magnetic field p_{\perp} << m_W. I discuss the implications of this finding to the dispersion of massless neutrinos in vacuum and in a charge-symmetric medium, and to the magnetic field induced resonance transitions of massive neutrinos inside supernovae and magnetars, and calculate the neutrino magnetic moment.