  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 neutrino dispersion relation, effective potential and effective mass have
been obtained that depend on $B$. The consequences of this effective potential
on neutrino oscillations have been explored, and resonance conditions have been
obtained for magnetic fields $0<eB \le 4m^2_e$, where $e$ is the elementary
charge and $m_e$ is the electron mass. The oscillation length has also been
obtained, showing that $\nu_e$-$\nu_\mu$ resonant oscillations in magnetic
field are likely to occur in the proximity of most stars generating high
magnetic fields.
