Magnetic properties of neutrinos in high temperature SU(2)XU(1) gauge theory

We calculate the finite temperature self-energy for neutrinos in the presence of a constant magnetic field in a medium in the unbroken $SU(2) \otimes U(1)$ model. We obtain the exact dispersion relation for such neutrinos and find that the thermal effective mass is modified by the magnetic field. We also find a simple analytic expression for the dispersion relation and obtain the index of refraction for large neutrino momentum.