Single-angle to multi-angle transition in the collective flavor dynamics of neutrinos in supernovae

In this paper we study in detail the dynamics of flavor transformation for neutrinos propagating in the very dense environment of astrophysical compact objects as Type II supernova in post collapse phase and proto-neutron stars. The analysis is based on the formalism by Strack and Burrows, who introduced the generalized Boltzmann equation for Wigner phase space density. In appropriate limits the formalism reduces to the usual evolution equations for the wave functions or for density matrix elements of Liouville equation. We incorporate the most important aspects of neutrino propagation physics: the phenomenology of standard oscillations with MSW resonance induced by ordinary matter, collective behavior due to self-interaction, which can produce bipolar and synchronized flavor oscillations, whose relevance is recognized by recent literature, the combination of these effects with collisions including scattering, emission and absorption of neutrinos.