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CrasyDSE: A framework for solving Dyson-Schwinger equations.

Markus Q Huber1, Mario Mitter2

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Summary
This summary is machine-generated.

This study introduces CrasyDSE, a computational framework automating complex Dyson-Schwinger equation calculations in quantum field theory. The tool aids researchers in non-perturbative analyses, particularly in quantum chromodynamics and Yang-Mills theory.

Keywords:
Correlation functionsDyson–Schwinger equationsQuantum field theory

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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.