Quantum kinetics of neutrinos in the early universe and supernovae

In this talk I will review recent progress in neutrino quantum kinetics, obtained in the context of an LDRD-ER project. After a short motivation I will review a first-principle derivation of the neutrino quantum kinetic equations appropriate to describe the evolution of neutrinos in hot and dense environments. I will then focus on new spin oscillation effects which may lead to coherent neutrino-antineutrino conversion in astrophysical environments. Finally, I will describe recent work on the inelastic collision term and plans for the immediate future.