  We propose an alternative formulation of Many-Body Perturbation Theory that
uses the density-functional concept. Instead of the usual four-point integral
equation for the polarizability, we obtain a two-point one, that leads to
excellent optical absorption and energy loss spectra. The corresponding
three-point vertex function and self-energy are then simply calculated via an
integration, for any level of approximation. Moreover, we show the direct
impact of this formulation on the time-dependent density-functional theory.
Numerical results for the band gap of bulk silicon and solid argon illustrate
corrections beyond the GW approximation for the self-energy.
