  We present a formulation of the quantum kinetic equations (QKEs) which govern
the evolution of neutrino flavor at high density and temperature. Here, the
QKEs are derived from the ground up, using fundamental neutrino interactions
and quantum field theory. We show that the resulting QKEs describe coherent
flavor evolution with an effective mass when inelastic scattering is
negligible. The QKEs also contain a collision term. This term can reduce to the
collision term in the Boltzmann equation when scattering is dominant and the
neutrino effective masses and density matrices become diagonal in the
interaction basis. We also find that the QKE's include equations of motion for
a new dynamical quantity related to neutrino spin. This quantity decouples from
the equations of motion for the density matrices at low densities or in
isotropic conditions. However, the spin equations of motion allow for the
possibility of coherent transformation between neutrinos and antineutrinos at
high densities and in the presence of anisotropy. Although the requisite
conditions for this exist in the core collapse supernova and compact object
merger environments, it is likely that only a self consistent incorporation of
the QKEs in a sufficiently realistic model could establish whether or not
significant neutrino-antineutrino conversion occurs.
