Large Momentum bounds from Flow Equations

TL;DR

This paper uses Wilson's flow equations to derive near-optimal bounds on the large momentum behavior of correlation functions in 4D massive Euclidean Phi-4 theory, enhancing understanding of renormalization.

Contribution

It provides a new, sharper inductive proof of large momentum bounds, closely related to Weinberg's theorem, for Phi-4 theory using flow equations.

Findings

Established near-optimal bounds on correlation functions at large momenta

Provided a simplified inductive proof of perturbative renormalizability

Linked bounds to Weinberg's theorem in quantum field theory

Abstract

We analyse the large momentum behaviour of 4-dimensional massive euclidean Phi-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.