  The Keldysh boundary problem in a nonequilibrium Falicov-Kimball model in
infinite dimensions is studied within the truncated and self-consistent
perturbation theories, and the dynamical mean-field theory. Within the model
the system is started in equilibrium, and later a uniform electric field is
turned on. The Kadanoff-Baym-Wagner equations for the nonequilibrium Green
functions are derived, and numerically solved. The contributions of initial
correlations are studied by monitoring the system evolution. It is found that
the initial correlations are essential for establishing full electron
correlations of the system and independent on the starting time of preparing
the system in equilibrium. By examining the contributions of the initial
correlations to the electric current and the double occupation, we find that
the contributions are small in relation to the total value of those physical
quantities when the interaction is weak, and significantly increase when the
interaction is strong. The neglect of initial correlations may cause artifacts
in the nonequilibrium properties of the system, especially in the strong
interaction case.
