The renormalized $\phi^4_4$-trajectory by perturbation theory in the running coupling

TL;DR

This paper develops a perturbative method to compute the renormalized trajectory of four-dimensional phi^4 theory using a running coupling, introducing an iterative scheme that is finite at all orders.

Contribution

It presents a novel iterative perturbation scheme for phi^4_4 theory that does not rely on a bare action and guarantees finiteness at every perturbative order.

Findings

Successfully computes the renormalized trajectory using the new scheme.

Proves the perturbation expansion is finite at all orders.

Provides a framework for non-bare action based renormalization in quantum field theory.

Abstract

We compute the renormalized trajectory of $\phi^4_4$-theory by perturbation theory in a running coupling. We introduce an iterative scheme without reference to a bare action. The expansion is proved to be finite to every order of perturbation theory.