  We derive the most general evolution equations describing in-medium
(anti)neutrino propagation in the mean-field approximation. In particular, we
consider various types of neutrino-antineutrino mixing, for both Dirac and
Majorana fields, resulting either from nontrivial pair correlations or from
helicity coherence due to the nonvanishing neutrino masses. We show that,
unless the medium is spatially homogeneous and isotropic, these correlations
are sourced by the usual neutrino and antineutrino densities. This may be of
importance in astrophysical environments such as core-collapse supernovae.
