  We combine the single site dynamical mean field theory (DMFT) with the
non-local GW method. This is done fully self-consistently and we apply our
formalism to a one-band Hubbard model. Eventually at self-consistency the full
self-energy and polarization operator of the system are retrieved. Some
numerical results, in the metallic as well as the insulator regime, are
presented and briefly discussed. Depending on the involved interaction (GW)
parameters, substantial changes are found when the GW self-energy is
incorporated. However, the main point of this work is to demonstrate the
applicability of the method not to make any strict comparison with exact
results and experiments.
