Quantum transport theory for neutrinos with flavor and particle-antiparticle mixing

We derive quantum kinetic equations for mixing neutrinos including consistent forward scattering terms and collision integrals for coherent neutrino states. In practice, we reduce the general Kadanoff--Baym equations in a few clearly justified steps to a generalized density matrix equation that describes both the flavour- and particle-antiparticle coherences and is valid for arbitrary neutrino masses and kinematics. We then reduce this equation to a simpler particle-antiparticle diagonal limit and eventually to the ultra-relativistic limit. Our derivation includes simple Feynman rules for computing collision integrals with the coherence information. We also expose a novel spectral shell structure underlying the mixing phenomenon and quantify how the prior information on the system impacts on the QKE's, leading to a direct effect on its evolution. Our results can be used for example to accurately model neutrino distributions in hot and dense environments and to study the production and decay of mixing heavy neutrinos in colliders.