Running coupling expansion for the renormalized $\phi^4_4$-trajectory from renormalization invariance

TL;DR

This paper develops a finite, renormalization-invariant expansion for the beta function and potential of the four-dimensional phi^4 theory, avoiding bare quantities and ensuring all-order perturbative finiteness.

Contribution

It introduces a renormalized running coupling expansion based solely on renormalization invariance, with a rigorous proof of all-order finiteness in perturbation theory.

Findings

Expansion is finite to all orders of perturbation theory.

Uses renormalization invariance as a fundamental principle.

Provides a large momentum bound on propagator amputated vertices.

Abstract

We formulate a renormalized running coupling expansion for the $\beta$--function and the potential of the renormalized $\phi^4$--trajectory on four dimensional Euclidean space-time. Renormalization invariance is used as a first principle. No reference is made to bare quantities. The expansion is proved to be finite to all orders of perturbation theory. The proof includes a large momentum bound on the connected free propagator amputated vertices.