Algorithmic derivation of functional renormalization group equations and Dyson–Schwinger equations

We present the Mathematica application DoFun1 which allows to derive Dyson–Schwinger equations and renormalization group flow equations for n-point functions in a simple manner. DoFun offers several tools which considerably simplify the derivation of these equations from a given physical action. We...

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Bibliographic Details
Published in:Computer physics communications 2012-06, Vol.183 (6), p.1290-1320
Main Authors: Huber, Markus Q., Braun, Jens
Format: Article
Language:English
Subjects:
Correlation functions
Dyson–Schwinger equations
Functional renormalization group equations
Quantum field theory
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Summary:We present the Mathematica application DoFun1 which allows to derive Dyson–Schwinger equations and renormalization group flow equations for n-point functions in a simple manner. DoFun offers several tools which considerably simplify the derivation of these equations from a given physical action. We discuss the application of DoFun by means of two different types of quantum field theories, namely a bosonic O(N) theory and the Gross–Neveu model. Program title:DoFun Catalogue identifier: AELN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELN_v1_0.html Program obtainable from: CPC Program Library, Queenʼs 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.: 35 506 No. of bytes in distributed program, including test data, etc.: 571 837 Distribution format: tar.gz Programming language: Mathematica 7 and higher Computer: PCs and workstations Operating system: All on which Mathematica is available (Windows, Unix, MacOS) Classification: 11.1, 11.4, 11.5, 11.6 Nature of problem: Derivation of functional renormalization group equations and Dyson–Schwinger equations from the action of a given theory. Solution method: Implementation of an algorithm to derive functional renormalization group and Dyson–Schwinger equations. Unusual features: The results can be plotted as Feynman diagrams in Mathematica. The output is compatible with the syntax of many other programs and is therefore suitable for further (algebraic) computations. Running time: Seconds to minutes
ISSN:0010-4655
1879-2944
DOI:10.1016/j.cpc.2012.01.014