CrasyDSE: A framework for solving Dyson-Schwinger equations

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• Computational Physics

Background:

• Dyson-Schwinger equations are crucial for non-perturbative quantum field theory analyses.
• Their complexity often impedes progress in areas like quantum chromodynamics.
• Automation of calculations is needed for future investigations.

Purpose of the Study:

• To present a computational framework for automating Dyson-Schwinger equation calculations.
• To provide a tool that can handle a large number of Green functions.
• To facilitate investigations in complex quantum field theories.

Main Methods:

• Developed a C++ code to manage numerous Green functions.
• Utilized a Mathematica notebook for automating the creation of integral expressions.
• Integrated Mathematica and C++ for numerical solutions.
• Demonstrated the workflow with examples from Yang-Mills theory.

Main Results:

• Successfully automated parts of Dyson-Schwinger equation calculations.
• Illustrated the framework's utility with examples from Yang-Mills theory and pure Yang-Mills theory.
• The code can handle a large number of Green functions efficiently.
• The framework can be combined with existing tools like DoFun.

Conclusions:

• The developed framework offers a significant advancement for tackling complex Dyson-Schwinger equations.
• It serves as a foundation for future research in non-perturbative quantum field theory.
• Automating these calculations enables deeper insights into theories like quantum chromodynamics.