An Explicit Large Versus Small Field Multiscale Cluster Expansion

TL;DR

This paper introduces a new multiscale cluster expansion method that generalizes previous formulas, enabling explicit non-perturbative formulas for Schwinger functions, tested on the infrared ^4 model.

Contribution

It presents a novel cluster expansion technique suitable for phase-space multiscale analysis in renormalizable theories, with explicit non-perturbative formulas and a large vs small field expansion.

Findings

Polymer amplitudes satisfy the polymer bound.

Method is model independent, demonstrated on ^4 model.

Allows explicit non-perturbative formulas for Schwinger functions.

Abstract

We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just renormalizable theory, and allows the writing of explicit non-perturbative formulas for the Schwinger functions. The procedure is quite model independent, but for simplicity we chose the infrared $\ph^4_4$ model as a testing ground. We used also a large field versus small field expansion. The polymer amplitudes, corresponding to graphs without almost local two and for point functions, are shown to satisfy the polymer bound.