Spinors: A Mathematica package for doing spinor calculus in General Relativity
Spinors: A Mathematica package for doing spinor calculus in General Relativity
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Spinors：用于在广义相对论中进行旋量微积分的 Mathematica 软件包
DOI：
10.1016/j.cpc.2012.04.024
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
J. Martin
中科院分区：
文献类型：
--
作者：
A. Gómez;J. Martin
Spinors 软件是一个 Mathematica 软件包，它实现了 Penrose 在 3+1 维广义相对论中设计的 2 分量旋量微积分。 Spinors 软件是 xAct 系统的一部分，该系统是用于通过计算机进行张量分析的 Mathematica 软件包的集合。在本文中，我们对旋量进行了全面的描述，并给出了实际的使用示例。程序摘要 程序标题：Spinors 目录标识符：AEMQ_v1_0 程序摘要 URL：http://cpc.cs.qub.ac.uk/summaries/AEMQ_v1_0.html 程序可从以下位置获取：CPC 程序图书馆，女王大学，贝尔法斯特，北爱尔兰 许可规定：标准 CPC 许可证，http://cpc.cs.qub.ac.uk/licence/licence.html 分布式程序中的行数，包括测试数据等：117039 分布式程序字节数，包括测试数据等：300404 分发格式：tar.gz 编程语言：Mathematica。计算机：任何运行 Mathematica 7.0 或更高版本的计算机。操作系统：与 Mathematica 7.0 或更高版本兼容的任何操作系统。 RAM：Mathematica 8.0 中为 94Mb。分类：1.5。外部例程：Mathematica 封装了 xCore、xPerm 和 xTensor，它们是 xAct 系统的一部分。这些可以从 http://www.xact.es 获取。问题的性质：广义相对论中旋量表达式的操纵和简化。求解方法：针对四维洛伦兹几何中旋量微积分的具体情况，调整 xAct 系统的张量函数。限制：该软件仅适用于签名度量为 (1, −1, −1, −1) 的 4 维洛伦兹时空。狄拉克旋量没有直接支持。不寻常的功能：将张量表达式转换为旋量表达式并返回的简单规则。旋量表达式的抽象索引操作与分量计算的无缝集成。运行时间：不到一秒即可处理和规范化具有几十个索引的标准旋量表达式。 （这些表达式在旋量表达式到张量表达式的转换中自然出现，反之亦然。）
The Spinors software is a Mathematica package which implements 2-component spinor calculus as devised by Penrose for General Relativity in dimension 3+1. The Spinors software is part of the xAct system, which is a collection of Mathematica packages to do tensor analysis by computer. In this paper we give a thorough description of Spinors and present practical examples of use. Program summary Program title: Spinors Catalogue identifier: AEMQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMQ_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.: 117039 No. of bytes in distributed program, including test data, etc.: 300404 Distribution format: tar.gz Programming language: Mathematica. Computer: Any computer running Mathematica 7.0 or higher. Operating system: Any operating system compatible with Mathematica 7.0 or higher. RAM: 94Mb in Mathematica 8.0. Classification: 1.5. External routines: Mathematica packages xCore, xPerm and xTensor which are part of the xAct system. These can be obtained at http://www.xact.es. Nature of problem: Manipulation and simplification of spinor expressions in General Relativity. Solution method: Adaptation of the tensor functionality of the xAct system for the specific situation of spinor calculus in four dimensional Lorentzian geometry. Restrictions: The software only works on 4-dimensional Lorentzian space-times with metric of signature (1, −1, −1, −1). There is no direct support for Dirac spinors. Unusual features: Easy rules to transform tensor expressions into spinor ones and back. Seamless integration of abstract index manipulation of spinor expressions with component computations. Running time: Under one second to handle and canonicalize standard spinorial expressions with a few dozen indices. (These expressions arise naturally in the transformation of a spinor expression into a tensor one or vice versa.)