CRITERION FOR VALIDITY OF MANY-BODY PERTURBATION-THEORY OF THE ELECTRON-GAS

The purpose of this paper is to point out the steps in conventional many-body perturbation theory which require separate, additional justification over and above convergence of the perturbation series. The questionable step is the cancellation of the renormalized energy shift by the chemical potential, neglecting any possible modification of the wave functions as well as state-dependent energy shifts.