  We revisit the derivation of the time-dependent Hartree-Fock equation for
interacting fermions in a regime coupling a mean-field and a semiclassical
scaling, contributing two comments to the result obtained in 2014 by
Benedikter, Porta, and Schlein. First, the derivation holds in arbitrary space
dimension. Second, by using an explicit formula for the unitary implementation
of particle-hole transformations, we cast the proof in a form similar to the
coherent state method of Rodnianski and Schlein for bosons.
