  In this work we establish a density-functional reformulation of coupled
matter-photon problems subject to general external electromagnetic fields and
charge currents. We first show that for static minimally-coupled matter-photon
systems an external electromagnetic field is equivalent to an external charge
current. We employ this to show that scalar external potentials and transversal
external charge currents are in a one-to-one correspondence to the expectation
values of the charge density and the vector-potential of the correlated
matter-photon ground state. This allows to establish a Maxwell-Kohn-Sham
approach, where in conjunction with the usual single-particle Kohn-Sham
equations a classical Maxwell equation has to be solved. In the magnetic
mean-field limit this reduces to a current-density-functional theory that does
not suffer from non-uniqueness problems and if furthermore the magnetic field
is zero recovers standard density-functional theory.
