  An ab initio QED approach to treat a valence-hole excitation in closed shell
systems is developed in the framework of the two-time-Green function method.
The derivation considers a redefinition of the vacuum state and its excitation
as a valence-hole pair. The proper two-time Green function, whose spectral
representation confirms the poles at valence-hole excitation energies is
proposed. An contour integral formula which connects the energy corrections and
the Green function is also presented. First-order corrections to the
valence-hole excitation energy involving self-energy, vacuum polarization, and
one-photon-exchange terms are explicitly derived in the redefined vacuum
picture. Reduction to the usual vacuum electron propagators is given that
agrees in the Breit approximation with the many-body perturbation theory
expressions for the valence-hole excitation energy.
