Huber Markus Q, Mitter Mario
Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstr. 2, 64289 Darmstadt, Germany.
Institut für Physik, Karl-Franzens-Universität Graz, Universitätsplatz 5, 8010 Graz, Austria.
Comput Phys Commun. 2012 Nov;183(11):2441-2457. doi: 10.1016/j.cpc.2012.05.019.
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.
: 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.
戴森 - 施温格方程是量子场论非微扰分析的重要工具。例如，它们在量子色动力学及相关理论的研究中非常有用。然而，有时方程的复杂性会阻碍进展。因此，在未来的研究中，将部分计算自动化肯定会有所帮助。在本文中，我们基于一个能够处理大量格林函数的代码，提出了这样一种自动化框架。由于戴森 - 施温格方程积分表达式的创建也需要自动化，我们将此任务推迟到一个笔记本中。我们用一个最近研究的与基本标量场耦合的杨 - 米尔斯理论的例子来说明完整的工作流程。作为第二个例子，我们计算纯杨 - 米尔斯理论的传播子。我们的代码可以作为许多进一步研究的基础，在这些研究中，方程过于复杂难以手动处理。它也可以很容易地与一个用于推导戴森 - 施温格方程的程序相结合。
：CrasyDSE：AEMY_v1_0：http://cpc.cs.qub.ac.uk/summaries/AEMY_v1_0.html：北爱尔兰贝尔法斯特女王大学CPC程序库：标准CPC许可，http://cpc.cs.qub.ac.uk/licence/licence.html：49030：303958：tar.gz：Mathematica 8及更高版本，。：所有可使用Mathematica和的系统。：所有可使用Mathematica和的系统（Windows、Unix、Mac OS）。：11.1、11.4、11.5、11.6。：数值求解（大型）戴森 - 施温格方程组。：在Mathematica中创建用于中的数值代码的函数。此代码使用结构来处理大量格林函数。：提供将Mathematica表达式转换为表达式的工具，包括函数名的转换。：根据所研究系统的复杂性，在台式机上数值求解方程可能需要几秒到在集群上需要数小时。
