A note on the many-body perturbation theory

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