Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
We present the Mathematica application DoFun(1) 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 summary 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, 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.: 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 ill 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 (C) 2012 Elsevier B.V. All rights reserved.
functional renormalization group equations dyson-schwinger equations quantum field theory correlation functions