Variational total energies from Phi and Psi derivable theories
The old variational functional for the total energy of a many-electron system proposed by Luttinger and Ward (LW) in 1960 is here tested on the electron gas at the level of the GW approximation. Using a simple non-interacting Green function to evaluate the fuctional we obtain a correlation energy very close to that of a fully self-consistent $GW$ calculation which, in turn, is very close to that o
