  Consistency with the Maxwell equations determines how matter must be coupled
to the electro-magnetic field (EMF) within the minimal coupling scheme.
Specifically, if the Hamiltonian includes just a short-range repulsion among
the conduction electrons, as is commonly the case for models of correlated
metals, those electrons must be coupled to the full internal EMF, whose
longitudinal and transverse components are self-consistently related to the
electron charge and current densities through Gauss's and circuital laws,
respectively. Since such self-consistency relation is hard to implement when
modelling the non-equilibrium dynamics caused by the EMF, as in pump-probe
experiments, it is common to replace in model calculations the internal EMF by
the external one. Here we show that such replacement may be extremely
dangerous, especially when the frequency of the external EMF is below the
intra-band plasma edge.
