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Large momentum bounds from flow equations. (English) Zbl 1027.81022
Summary: We analyze the large momentum behaviour of 4-dimensional massive Euclidean \(\varphi^4\) theory using the flow equations of Wilson’s renormalization group. The flow equations give access to a simple inductive proof of perturbative renormalizability. By sharpening the induction hypothesis we prove new and, as it seems, close to optimal bounds on the large momentum behaviour of the correlation functions. The bounds are related to what is generally called Weinberg’s theorem.

MSC:
81T08 Constructive quantum field theory
81T17 Renormalization group methods applied to problems in quantum field theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T10 Model quantum field theories
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