Constructive $\phi^4$ field theory without tears

TL;DR

This paper introduces a simplified constructive approach to $$ Euclidean field theory using a novel loop vertex expansion, eliminating the need for complex cluster and Mayer expansions.

Contribution

It presents a new loop vertex expansion method that simplifies the constructive treatment of $$ field theory, removing traditional technical complexities.

Findings

Simplified constructive proof of $$ field theory

Elimination of cluster and Mayer expansions

Introduction of a new loop vertex expansion technique

Abstract

We propose to treat the $\phi^4$ Euclidean theory constructively in a simpler way. Our method, based on a new kind of "loop vertex expansion", no longer requires the painful intermediate tool of cluster and Mayer expansions.