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Equilibrium properties of self-interacting neutrinos in the quasi-particle approach

In this work a neutrino gas in equilibrium is studied both at T=0 and at finite temperature. Neutrinos are treated as massive Dirac quasi-particles with two generations. We include self-interactions among the neutrinos via neutral currents, as well as the interaction with a background of matter. To obtain the equilibrium properties we use Wigner function techniques. To account for corrections beyond the Hartree approximation, we also introduce correlation functions. We prove that, under the quasi-particle approximation, these correlation functions can be expressed as products of Wigner functions. We analyze the main properties of the neutrino eigenmodes in the medium, such as effective masses and mixing angle. We show that the formulae describing these quantities will differ with respect to the case with no self-interactions.