CrasyDSE: A framework for solving Dyson-Schwinger equations.

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Dyson-Schwinger equations are important tools for non-perturbative analyses of quantum field theories. For example, they are very useful for investigations in quantum chromodynamics and related theories. However, sometimes progress is impeded by the complexity of the equations. Thus automating parts of the calculations will certainly be helpful in future investigations. In this article we present a framework for such an automation based on a code that can deal with a large number of Green functions. Since also the creation of the expressions for the integrals of the Dyson-Schwinger equations needs to be automated, we defer this task to a notebook. We illustrate the complete workflow with an example from Yang-Mills theory coupled to a fundamental scalar field that has been investigated recently. As a second example we calculate the propagators of pure Yang-Mills theory. Our code can serve as a basis for many further investigations where the equations are too complicated to tackle by hand. It also can easily be combined with , a program for the derivation of Dyson-Schwinger equations.

PROGRAM SUMMARY

: CrasyDSE : AEMY _v1_0 : http://cpc.cs.qub.ac.uk/summaries/AEMY_v1_0.html : CPC Program Library, Queen's University, Belfast, N. Ireland : Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html : 49030 : 303958 : tar.gz : Mathematica 8 and higher, . : All on which Mathematica and are available. : All on which Mathematica and are available (Windows, Unix, Mac OS). : 11.1, 11.4, 11.5, 11.6. : Solve (large) systems of Dyson-Schwinger equations numerically. : Create functions in Mathematica to be used for the numeric code in . This code uses structures to handle large numbers of Green functions. : Provides a tool to convert Mathematica expressions into expressions including conversion of function names. : Depending on the complexity of the investigated system solving the equations numerically can take seconds on a desktop PC to hours on a cluster.