  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.
