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

Abstract

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 summaryProgram title:DoFunCatalogue identifier: AELN_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELN_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 35 506No. of bytes in distributed program, including test data, etc.: 571 837Distribution format: tar.gzProgramming language: Mathematica 7 and higherComputer: PCs and workstationsOperating system: All on which Mathematica is available (Windows, Unix, MacOS)Classification: 11.1, 11.4, 11.5, 11.6Nature 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