Proof of the Bogoliubov-Parasiuk theorem on renormalization

Abstract

A new proof is given that the subtraction rules of Bogoliubov and Parasiuk lead to well-defined renormalized Green's distributions. A collection of the counter-terms in "trees" removes the difficulties with overlapping divergences and allows fairly simple estimates and closed expressions for renormalized Feynman integrals. The renormalization procedure, which also applies to conventionally non-renormalizable theories, is illustrated in the φ{symbol}4-theory. © 1966 Springer-Verlag.