Wilson renormalization group and improved perturbation theory

TL;DR

This paper introduces a resummed perturbation theory utilizing Wilson renormalization group flow, demonstrating its consistency with gauge invariance and its applicability to asymptotically free theories like 5^3_6 and QED.

Contribution

It presents a novel formulation of perturbation theory that incorporates Wilsonian flowing couplings directly into loop expansions, ensuring well-defined couplings in asymptotically free theories.

Findings

Flowing couplings are well-defined without infrared Landau poles in asymptotically free theories.

The formulation is extended to QED and shown to be gauge invariant.

Application to 5^3_6 demonstrates the absence of Landau poles in the infrared.

Abstract

We discuss a resummed perturbation theory based on the Wilson renormalization group. In this formulation the Wilsonian flowing couplings, which generalize the running coupling, enter directly into the loop expansion. In the case of an asymptotically free theory the flowing coupling is well defined since the infrared Landau pole is absent. We show this property in the case of the $\phi^3_6$ theory. We also extend this formulation to the QED theory and we prove that it is consistent with gauge invariance.