  The Larkin-Migdal approach to a cold superfluid Fermi liquid is generalized
for a non-equilibrium system. The Schwinger-Keldysh diagram technique is
applied. The developed formalism is applicable to the pairing in the states
with arbitrary angular momenta. We consider the white body radiation problem by
calculating probabilities of different direct reactions from a piece of a
fermion superfluid. The closed diagram technique is formulated in terms of the
full Green's functions for systems with the pairing correlation. The cutting
rules are used to classify the diagrams representing one-nucleon, two-nucleon,
etc. processes in the matter. The important role of multi-piece diagrams for
the vector-current conservation is demonstrated. In the case of equilibrated
systems, dealing with dressed Green's functions, we demonstrate correspondence
between calculations in the Schwinger-Kadanoff-Baym-Keldysh formalism and the
ordinary Matsubara technique. As an example we consider neutrino radiation from
the neutron pair breaking and formation processes in case of a singlet pairing.
Necessary correlation effects are included. The in-medium renormalization of
normal and anomalous vertices is performed.
