CrasyDSE: A framework for solving Dyson-Schwinger equations

TL;DR

CrasyDSE is a computational framework that automates the derivation and solution of Dyson-Schwinger equations, facilitating non-perturbative quantum field theory analyses, especially in complex scenarios.

Contribution

The paper introduces a C++ and Mathematica-based framework for automating Dyson-Schwinger equation calculations, enhancing efficiency and handling complex Green functions.

Findings

Successfully applied to Yang-Mills theory with scalar fields

Calculated propagators in pure Yang-Mills theory

Framework integrates with DoFun for derivation automation

Abstract

Dyson-Schwinger equations are important tools for non-perturbative analyses of quantum field theories. For example, they are very useful for investigations in quantum chromodynamics and related theories. However, sometimes progress is impeded by the complexity of the equations. Thus automatizing parts of the calculations will certainly be helpful in future investigations. In this article we present a framework for such an automatization based on a C++ code that can deal with a large number of Green functions. Since also the creation of the expressions for the integrals of the Dyson-Schwinger equations needs to be automatized, we defer this task to a Mathematica notebook. We illustrate the complete workflow with an example from Yang-Mills theory coupled to a fundamental scalar field that has been investigated recently. As a second example we calculate the propagators of pure Yang-Mills theory. Our code can serve as a basis for many further investigations where the equations are too complicated to tackle by hand. It also can easily be combined with DoFun, a program for the derivation of Dyson-Schwinger equations.