Algorithmic derivation of Dyson–Schwinger equations

• Published in: Computer physics communications Vol. 180; no. 6; pp. 965 - 976
• Main Authors: Alkofer, R., Huber, M.Q., Schwenzer, K.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2009
• Subjects: Dyson–Schwinger equations; Quantum field theory; 03.70.+k; 11.10.-z; Dyson–Schwinger equations; Quantum field theory; 11.15.Tk
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2008.12.009

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 1 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. Program title: DoDSE Catalogue identifier: AECT_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECT_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 105 874 No. of bytes in distributed program, including test data, etc.: 262 446 Distribution format: tar.gz Programming language: Mathematica 6 and higher Computer: all on which Mathematica is available Operating system: all on which Mathematica is available Classification: 11.1, 11.4, 11.5, 11.6 Nature of problem: Derivation of Dyson–Schwinger equations for a theory with given interactions. Solution method: Implementation of an algorithm for the derivation of Dyson–Schwinger equations. Unusual features: The results can be plotted as Feynman diagrams in Mathematica. Running time: Less than a second to minutes for Dyson–Schwinger equations of higher vertex functions.