A note on the many-body perturbation theory

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.