Neutrinos in Strong Magnetic Fields

We compute the dispersion curves for neutrinos propagating in an extremely dense electroweak plasma, in the presence of very strong magnetic fields of order $B \le M_W^2/e$. The neutrino self-energy is calculated in the one-loop approximation. We consider only contributions of the first Landau level to the propagator of the W-bosons, and distinguish between motion parallel or perpendicular to the external magnetic field. We find that the neutrino dispersion curve for parallel propagation to the field suggests a superfluid behavior. An interesting analogy with fractional QHE is pointed out. We obtain a neutrino effective mass which increases with the magnetic field.