Further illustration of the use of the Frobenius-Schwinger-Dyson equations

TL;DR

This paper explores the application of Frobenius-Schwinger-Dyson equations to the Thirring model, advancing understanding of their solutions beyond Gaussian cases in quantum field theory.

Contribution

It demonstrates the use of Frobenius-Schwinger-Dyson equations in a non-trivial quantum field theory model, the Thirring model, extending previous work beyond Gaussian actions.

Findings

Illustrated solutions of Frobenius-Schwinger-Dyson equations for the Thirring model

Extended the application of these equations beyond Gaussian actions

Provided insights into non-trivial quantum field theory models

Abstract

The Frobenius-Schwinger-Dyson equations are a rather high-brow abstract nonsense type of equations describing n-point functions of arbitrarily high composite insertions. It is not clear how to solve or even find approximate solutions of these equations in general, but they are worth investigating because (a certain preferred type of) renormalization of composite insertions has been performed in advance: it just remains to find solutions given an action and renormalization conditions. Earlier work in this field involved only Gaussian actions or variable transformations thereof. In this work we illustrate the use of Frobenius-Schwinger-Dyson at a less obviously trivial level, that of the Thirring model.