  Using a real-time formalism of equilibrium and nonequilibrium quantum-field
theory, we derive the reaction-rate formula for neutrino-conversion ($\nu \to
\nu'$) process and $\nu \bar{\nu}'$ annihilation process, which take place in a
hot and dense QED plasma with background (anti)neutrinos out of equilibrium.
Also derived is the formula for the inverse processes to the above ones. Using
the hard-thermal-loop resummation scheme, we include the contribution from the
coherent processes. The decay/production of a neutrino causes an evolution of
its spatial distribution. A scheme for dealing with this evolution is
presented. For the case of isotropic neutrino distribution, numerical
computation is carried out for the parameter region of type-II super-nova
explosion. Defferential reaction rate exhibits characteristic peak structure,
which comes from the coherent processes. The contribution from the above
processes to the decay or damping rate of a parent neutrino $\nu$ is also
studied.
