Self-consistent nonperturbative anomalous dimensions

TL;DR

This paper develops a self-consistent nonperturbative approach to determine anomalous dimensions in models with trilinear interactions, using Dyson-Schwinger equations and vertex modeling to derive transcendental relations.

Contribution

It introduces a method to extract anomalous dimensions nonperturbatively by solving truncated Dyson-Schwinger equations with a modeled vertex that matches perturbative results.

Findings

Derived transcendental equations relating anomalous dimension and coupling constant.

Confirmed that the equations agree with known perturbative results up to order g^4.

Provided a framework for nonperturbative analysis of anomalous dimensions in trilinear interaction models.

Abstract

A self-consistent treatment of two and three point functions in models with trilinear interactions forces them to have opposite anomalous dimensions. We indicate how the anomalous dimension can be extracted nonperturbatively by solving and suitably truncating the topologies of the full set of Dyson-Schwinger equations. The first step requires a sensible ansatz for the full vertex part which conforms to first order perturbation theory at least. We model this vertex to obtain typical transcendental equations between anomalous dimension and coupling constant $g$ which coincide with know results to order $g^4$.