FIELD-THEORETIC TREATMENT OF MIXED NEUTRINOS IN A NEUTRINO AND MATTER BACKGROUND

We use the method of finite temperature field theory to examine the propagation of mixed neutrinos through dense media, putting the emphasis in those situations in which the neutrinos themselves are in the background. The evolution equation for the flavor amplitudes is deduced, and the expressions for the corresponding hamiltonian matrix are given explicitly. We find that, in order to include the nonlinear effects due to the $\nu$-$\nu$ interactions, the neutrino propagator that must be used in the calculation of the neutrino self-energy diagrams that contain neutrinos in the internal lines is the propagator for the neutrino modes in the medium instead of the thermal free-field propagator. We also show how the absorptive contributions are included in terms of a non-hermitian part of the hamiltonian matrix, which we indicate how it is calculated. Our treatment provides a consistent generalization of a method that has been successfully applied to the study of neutrino oscillations in matter.