Misuse of the minimal coupling to the electromagnetic field in quantum many-body systems

Consistency with the Maxwell equations determines how matter must be coupled to the electromagnetic 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 modeling the nonequilibrium 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 misleading, especially when the frequency of the external EMF is below the intraband plasma edge.