Dirac neutrinos in dense matter

The evolution of a supernova core can be dramatically different if the neutrinos trapped in the core mix and/or flip helicity and escape as ''sterile, right-handed'' neutrinos. Thus the observation of neutrinos from supernova SN1987A constrains the mass and mixings of neutrinos. Here we develop the general description of neutrino mixing and spin flip in a background of matter when the nonforward scattering rate is important. The constraints are estimated