Many-body perturbation theory using the density-functional concept:   beyond the GW approximation
  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. 
Fabien Bruneval, Francesco Sottile, Valerio Olevano, Rodolfo Del Sole   and Lucia Reining