Resonant Conversion of Massless Neutrinos in Supernovae

It has been noted for a long time that, in some circumstances, {\sl massless} neutrinos may be {\sl mixed} in the leptonic charged current. Conventional neutrino oscillation searches in vacuum are insensitive to this mixing. We discuss the effects of resonant massless-neutrino conversions in the dense medium of a supernova. In particular, we show how the detected $\bar\nu_e$ energy spectra from SN1987a and the supernova $r$-process nucleosynthesis may be used to provide very stringent constraints on the mixing of {\sl massless} neutrinos.