The conventional many-body perturbation theory suffers from three major ill
s (i) some terms in the perturbation series may be unbounded; (ii) the seri
es as a whole may not have a limit and (iii) despite convergence,the calcul
ated limit may be false ('bogus' convergence). In renormalizable field theo
ries, as the name indicates, problem (i) can be bypassed. Problems (ii) and
(iii) remain. Here we demonstrate that these two problems can also be reso
lved, by choosing an appropriate Kohn-Sham Hamiltonian as the 'unperturbed'
Hamiltonian. For this to be possible, some pertinent ground-state densitie
s must be pure-state non-interacting v-representable. We illustrate our fin
dings by means of two examples.