By J.R. Sabin (Eds.)
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It is a well-known fact that the sum of the most divergent terms in a perturbation series, when convergent, leads often to remarkably accurate results [9–11]. The GW method, defined by Hedin in 1965  (see also Ref. ), accomplishes such a partial sum for S. The GW method is thoroughly reviewed in Aryasetiawan and Gunnarsson (AG)  and Aulburn et al. (AJW)  in publications through 2000. Much of previous work relies heavily on DFT-zeroth order calculations, and few attempts are made to achieve convergence.
Can we go back to those days, Jens? Happy birthday! What follows can be rightly seen as a (long-delayed) afterthought to our happy Utah sojourns. 2. MOTIVATION When considering truly rigorous, ab initio studies of periodic systems one implicitly adopts a number of criteria that the needed methods and numerical techniques have to satisfy. These are 1. Adoption of a many-body theory that is systematically improvable (at least in principle) and testable for its numerical convergence; 2. Avoidance of unphysical, analytical ‘pathologies’ intrinsic to a particular truncation of the hierarchy of sophistication levels in that theory; 3.