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Ground-state properties of materials, such as the total energy, the electronic density and the atomic structure, have been extensively investigated in the last 40 years by the successful [S. Redner, Physics Today 58, 49 (June 2005)] ab initio density-functional theory, to be considered today as the standard model of condensed matter theory. On the other hand, excited-state properties such as the electronic structure measured in ARPES experiments, were relatively unexplored from first principles until the appearance, in the late eighties, of the first ab initio calculations using Hedin's GW approximation.
We will briefly review the Green's function based functional approach to many-body quantum field theory leading to the in principle exact Hedin's equations and to the GW approximation. We will then present some of the results it is possible to get, and review in general the achievements and the shortcomings of the GW approximation. The last part will be devoted to open issues and new developments beyond the GW approximation. |
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