Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case

TL;DR

This paper presents a new proof of perturbative renormalizability and infrared finiteness for massless scalar theories using Wilson renormalization group techniques, emphasizing a systematic organization of Feynman graphs.

Contribution

It introduces a novel proof method based on the Wilson renormalization group and Polchinski equation, avoiding traditional topological graph analysis.

Findings

Proof of perturbative renormalizability for massless scalar theories

Demonstration of infrared finiteness using iterative methods

Automatic generation of counterterms through physical condition fixing

Abstract

A new proof of perturbative renormalizability and infrared finiteness for a scalar massless theory is obtained from a formulation of renormalized field theory based on the Wilson renormalization group. The loop expansion of the renormalized Green functions is deduced from the Polchinski equation of renormalization group. The resulting Feynman graphs are organized in such a way that the loop momenta are ordered. It is then possible to analyse their ultraviolet and infrared behaviours by iterative methods. The necessary subtractions and the corresponding counterterms are automatically generated in the process of fixing the physical conditions for the ``relevant'' vertices at the normalization point. The proof of perturbative renormalizability and infrared finiteness is simply based on dimensional arguments and does not require the usual analysis of topological properties of Feynman graphs.