In this work we study the propagation of massive Dirac neutrinos in matter with flavor mixing, using statistical techniques based on Relativistic Wigner Functions. First, we consider neutrinos in equilibrium within the Hartree approximation, and obtain the corresponding relativistic dispersion relations and effective masses. After this, we analyze the same system out of equilibrium. We verify that, under the appropiate physical conditions, the well known equations for the MSW effect are recovered. The techniques we used here appear as an alternative to describe neutrino properties and transport equations in a consistent way.

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 selfinteractions 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.

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SummaryWe study a neutrino gas in equilibrium both at T = 0 and at finite temperature. The neutrinos are assumed to be massive Dirac particles with two generations interacting with each other via neutral currents and with a background of matter. We analyze the main properties of the neutrino eigenmodes in the medium, such as effective masses and mixing angle.