  We derive exact operator average expressions for the first two spectral
moments of nonequilibrium Green's functions for the Falicov-Kimball model and
the Hubbard model in the presence of a spatially uniform, time-dependent
electric field. The moments are similar to the well-known moments in
equilibrium, but we extend those results to systems in arbitrary time-dependent
electric fields. Moment sum rules can be employed to estimate the accuracy of
numerical calculations; we compare our theoretical results to numerical
calculations for the nonequilibrium dynamical mean-field theory solution of the
Falicov-Kimball model at half-filling.
