GENERAL KINETIC DESCRIPTION OF RELATIVISTIC MIXED NEUTRINOS

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