  A relativistic density-functional theory based a Fock-space effective
quantum-electrodynamics (QED) Hamiltonian using the Coulomb or Coulomb-Breit
two-particle interaction is developed. This effective QED theory properly
includes the effects of vacuum polarization through the creation of
electron-positron pairs but does not include explicitly the photon degrees of
freedom. It is thus a more tractable alternative to full QED for atomic and
molecular calculations. Using the constrained-search formalism, a Kohn-Sham
scheme is formulated in a quite similar way to non-relativistic
density-functional theory, and some exact properties of the involved density
functionals are studied, namely charge-conjugation symmetry and uniform
coordinate scaling. The usual no-pair Kohn-Sham scheme is obtained as a
well-defined approximation to this relativistic density-functional theory.
