  Time-dependent (current) density functional theory for many-electron systems
strongly coupled to quantized electromagnetic modes of a microcavity is
proposed. It is shown that the electron-photon wave function is a unique
functional of the electronic (current) density and the expectation values of
photonic coordinates. The Kohn-Sham system is constructed, which allows to
calculate the above basic variables by solving selfconsistent equations for
noninteracting particles. We suggest possible approximations for the
exchange-correlation potentials and discuss implications of this approach for
the theory of open quantum systems.
