{"title":"A space-time calculus based on symmetric 2-spinors","authors":"Steffen Aksteiner, Thomas Bäckdahl","doi":"10.1007/s10714-023-03088-6","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we present a space-time calculus for symmetric spinors, including a product with a number of index contractions followed by symmetrization. As all operations stay within the class of symmetric spinors, no involved index manipulations are needed. In fact spinor indices are not needed in the formalism. It is also general because any covariant tensor expression in a 4-dimensional Lorentzian spacetime can be translated to this formalism. The computer algebra implementation <i>SymSpin</i> as part of <i>xAct</i> for <i>Mathematica</i> is also presented.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"55 3","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10714-023-03088-6.pdf","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Relativity and Gravitation","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10714-023-03088-6","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper we present a space-time calculus for symmetric spinors, including a product with a number of index contractions followed by symmetrization. As all operations stay within the class of symmetric spinors, no involved index manipulations are needed. In fact spinor indices are not needed in the formalism. It is also general because any covariant tensor expression in a 4-dimensional Lorentzian spacetime can be translated to this formalism. The computer algebra implementation SymSpin as part of xAct for Mathematica is also presented.
本文给出了对称旋量的一个时空演算，其中包括一个具有若干指标收缩的乘积，然后是对称。由于所有操作都在对称自旋量类中，因此不需要涉及索引操作。实际上，在形式主义中不需要旋量指标。它也是一般的，因为任何四维洛伦兹时空中的协变张量表达式都可以转化为这种形式。本文还介绍了作为xAct for Mathematica的一部分的计算机代数实现SymSpin。
期刊介绍：
General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation.
It welcomes in particular original articles on the following topics of current research:
Analytical general relativity, including its interface with geometrical analysis
Numerical relativity
Theoretical and observational cosmology
Relativistic astrophysics
Gravitational waves: data analysis, astrophysical sources and detector science
Extensions of general relativity
Supergravity
Gravitational aspects of string theory and its extensions
Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations
Quantum field theory in curved spacetime
Non-commutative geometry and gravitation
Experimental gravity, in particular tests of general relativity
The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.
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