Proof of the Bogoliubov-Parasiuk theorem on renormalization. (English) Zbl 1222.81219

Summary: 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 \(\varphi^{4}\)-theory.


81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
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