  We derive the first two moment sum rules of the conduction electron retarded
self-energy for both the Falicov-Kimball model and the Hubbard model coupled to
an external spatially uniform and time-dependent electric field (this
derivation also extends the known nonequilibrium moment sum rules for the
Green's functions to the third moment). These sum rules are used to further
test the accuracy of nonequilibrium solutions to the many-body problem; for
example, we illustrate how well the self-energy sum rules are satisfied for the
Falicov-Kimball model in infinite dimensions and placed in a uniform electric
field turned on at time t=0. In general, the self-energy sum rules are
satisfied to a significantly higher accuracy than the Green's functions sum
rules.
