  A single-time quantum transport equation, which includes effects beyond the
quasiparticle approximation, is derived for Fermi-systems in the framework of
non-equilibrium real-time Green's functions theory. Ternary correlations are
incorporated in the kinetic description via a cluster expansion for the
self-energies (e.g., the transport vertex and the width) truncated at the level
of three-body scattering amplitudes. A finite temperature/density formulation
of the three-body problem is given. Corresponding three-body equations reduce
to the well-known Faddeev equations in the vacuum limit. In equilibrium the
equation of state contains virial corrections proportional to the third quantum
virial coefficient.
