Neutrino Flavor Conversion in a Supernova Core

If $\nu_\mu$ or $\nu_\tau$ mix with $\nu_e$, neutrino oscillations and collisions in a supernova (SN) core allow these flavors effectively to participate in $\beta$ equilibrium and thus to obtain a large chemical potential. If a sterile species mixes with $\nu_e$, these effects lead to an anomalous loss of energy and lepton number. We study flavor conversion in a SN core on the basis of a new kinetic equation which rigorously includes neutrino interference and degeneneracy effects. Our discussion serves as an example and illustration of the properties of this ``non-abelian Boltzmann equation''.