  A method for deriving quantum kinetic equations with initial correlations is
developed on the basis of the nonequilibrium Green's function formalism. The
method is applicable to a wide range of correlated initial states described by
nonequilibrium statistical thermodynamics. Initial correlations and the
real-time evolution are treated by a unified technique employing many-component
``mixed'' Green's functions. The Dyson equation for the mixed Green's function
leads to a set of equations for real-time Green's functions and new (cross)
components linking initial correlations with dynamical processes. These
equations are used to formulate a generalized Kadanoff-Baym ansatz for
correlated initial states. A non-Markovian short-time kinetic equation is
derived within the T-matrix approximation for the self-energies. The properties
of the memory kernels in this equation are considered in detail in Born
approximation for the T-matrices. The kinetic equation is demonstrated to
conserve the total energy of the system. An explicit expression for the
time-dependent correlation energy is obtained.
