Spinors: A Mathematica package for doing spinor calculus in General Relativity

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 summaryProgram title: SpinorsCatalogue identifier: AEMQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMQ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s 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.: 117039No. of bytes in distributed program, including test data, etc.: 300404Distribution format: tar.gzProgramming 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.)