Is There Really No Extensive Self-Consistent Perturbation Theory?

Abstract

Many-particle perturbation theory is dominated by the Rayleigh–Schrödinger expansion, because at fixed particle density each term of the power series in the strength of the interaction has the right dependence on the particle number N. The first self-consistent generalization, the Brillouin–Wigner expansion, however, is non-extensive already in 2nd order. In Feenberg's generalization the same feature is found within iterative perturbation theory, but the series can be rearranged in such a way that lower orders are extensive. Applications are suggested.