Algorithmic derivation of Dyson-Schwinger Equations

Abstract

We present an algorithm for the derivation of Dyson-Schwinger equations of general theories that is suitable for an implementation within a symbolic programming language. Moreover, we introduce the Mathematica package DoDSE which provides such an implementation. It derives the Dyson-Schwinger equations graphically once the interactions of the theory are specified. A few examples for the application of both the algorithm and the DoDSE package are provided. The package can be obtained from physik.uni-graz.at/~mah/DoDSE.html.

17 pages, 11 figures, downloadable Mathematica package v2: adapted to version 1.2 of DoDSE package with simplified handling and improved plotting of graphs; references added

References in corpus (3)

• Infrared behaviour of the ghost-gluon vertex in Landau gauge Yang-Mills theory
• U_A(1) anomaly and eta' mass from an infrared singular quark-gluon vertex
• Propagator Dyson-Schwinger Equations of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism

Cited by in corpus (37)

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• A Dyson-Schwinger study of the four-gluon vertex
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• Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: Continuum results
• Recent developments in bound-state calculations using the Dyson-Schwinger and Bethe-Salpeter equations
• Correlation functions of three-dimensional Yang-Mills theory from Dyson-Schwinger equations
• Infrared Behavior of Three-Point Functions in Landau Gauge Yang-Mills Theory
• Techniques for n-Particle Irreducible Effective Theories
• Infrared analysis of Dyson-Schwinger equations taking into account the Gribov horizon in Landau gauge
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• CrasyDSE: A framework for solving Dyson-Schwinger equations
• DoFun 3.0: Functional equations in Mathematica
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• Features of ghost-gluon and ghost-quark bound states related to BRST quartets
• On the Infrared Behavior of Landau Gauge Yang-Mills Theory with a Fundamentally Charged Scalar Field
• Spurious divergences in Dyson-Schwinger equations
• Dense two-color QCD from Dyson-Schwinger equations
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• Phase structure and propagators at nonvanishing temperature for QCD and QCD-like theories
• Vertex functions of Coulomb gauge Yang--Mills theory
• Truncating first-order Dyson-Schwinger equations in Coulomb-Gauge Yang-Mills theory
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• A new method to calculate the n-Particle Irreducible Effective Action
• The analytic structure of three-point functions from contour deformations
• An exploratory study of Yang-Mills three-point functions at non-zero temperature
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• Infrared scaling solutions beyond the Landau gauge: The maximally Abelian gauge and Abelian infrared dominance
• Exploring the Tan contact term in Yang-Mills theory
• A Closer Look at Gluons
• On the connection between Hamilton and Lagrange formalism in Quantum Field Theory
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