ABSTRACT
In the last section we proved that, for the many-electron system with a short range potential (that is, V (x) ∈ L1), an n’th order diagram Gn allows the following bounds. If Gn has no two-and four-legged subgraphs, it is bounded by constn (measured in a suitable norm), if Gn has no two-legged but may have some four-legged subgraphs it is bounded by n! constn (and it was shown that the factorial is really there by computing n’th order ladder diagrams with dispersion relation ek = k2/2m−µ), and if Gn contains two-legged subdiagrams it is in general divergent. The large contributions from two-and four-legged subdiagrams have to be eliminated by some kind of renormalization procedure. After that, one is left with a sum of diagrams where each n’th order diagram allows a constn bound.
