  We perform a perturbative analysis for the nonequilibrium Green functions of
the spinless Falicov-Kimball model in the presence of an arbitrary external
time-dependent but spatially uniform electric field. The conduction electron
self-energy is found from a strictly truncated second-order perturbative
expansion in the local electron-electron repulsion U. We examine the current at
half-filling, and compare to both the semiclassical Boltzmann equation and
exact numerical solutions for the contour-ordered Green functions from a
transient-response formalism (in infinite dimensions) on the
Kadanoff-Baym-Keldysh contour. We find a strictly truncated perturbation theory
in the two-time formalism cannot reach the long-time limit of the steady state;
instead it illustrates pathological behavior for times larger than
approximately 2/U.
