Neutrino conversions in hot plasma

We discuss the excitation of sterile neutrinos in the early universe using general quantum kinetic equations, which also incorporate a possible primordial magnetic field $B$. We find a new contribution to the excitation propability, which has its origin in the shrinkage of the spin vector. In the absence of $B$ nucleosynthesis implies the constraint $\mid \Delta m^2\mid\sin^22\theta_0\lsim 1.6\times 10^{-6}~{\rm eV}^2$ which is more restrictive than previous estimates. We also present examples of possible stringent limits for $B\ne 0$.