The renormalized $\phi^4_4$-trajectory by perturbation theory in a running coupling II: the continuous renormalization group

TL;DR

This paper studies the renormalized trajectory of massless ^4 theory in four dimensions using a perturbative approach to the continuous renormalization group, establishing finiteness of the expansion to all orders.

Contribution

It introduces a perturbative method to analyze the renormalized ^4 trajectory via a functional differential equation, proving the expansion's finiteness at all orders.

Findings

Finite perturbative expansion to all orders.

Large momentum bounds on Green's functions.

Characterization of the ^4 trajectory as a renormalization group invariant curve.

Abstract

The renormalized trajectory of massless $\phi^4$-theory on four dimensional Euclidean space-time is investigated as a renormalization group invariant curve in the center manifold of the trivial fixed point, tangent to the $\phi^4$-interaction. We use an exact functional differential equation for its dependence on the running $\phi^4$-coupling. It is solved by means of perturbation theory. The expansion is proved to be finite to all orders. The proof includes a large momentum bound on amputated connected momentum space Green's functions.