GENERAL KINETIC DESCRIPTION OF RELATIVISTIC MIXED NEUTRINOS

We derive a general Boltzmann-type collision integral for mixed neutri nos interacting with each other and with a medium. Our treatment is fu lly relativistic in that antineutrino degrees of freedom are included. This collision integral allows one to account for the simultaneous ef fects of neutrino oscillations in a medium and for the effects of coll isions. Our result generalizes previous attempts of unify the first- a nd second-order interaction effects in a single self-consistent equati on. Most importantly, our equation includes effects non-linear in the neutrino density matrices (or occupation numbers) such as Pauli blocki ng of neutrino final states or neutrino refraction in a medium of neut rinos. We apply the definition of the entropy of a non-equilibrium Fer mi gas to the case of mixed neutrinos, and we prove that our collision integrals obey the relevant thermodynamic inequalities.