Abstract
We give a field-theoretic treatment of the behavior of mixed neutrinos in media such as the early universe or the core of a supernova, where the neutrinos themselves are part of the background. The contributions to the self-energy coming from the neutrino internal lines must be calculated in terms of the propagator corresponding to the neutrino modes in the medium, instead of the thermal free propagator. The use of the effective field associated with these modes allows us to express the neutrino densities in terms of the dynamical flavor amplitudes in precise form. We show how the damping terms in the Hamiltonian matrix that governs the flavor evolution are determined from the absorptive part of the self-energy. Our work extends the thermal-field-theory method to a nonlinear problem where it was thought not to be applicable, and provides a simpler alternative to the Boltzmann-type kinetic approach.
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