{"title":"量子物理中的李代数","authors":"I. Kikuchi, Akihito Kikuchi","doi":"10.17605/OSF.IO/YRG7V","DOIUrl":null,"url":null,"abstract":"This article explains how to apply the computer algebra package GAP (this http URL) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct weight modules, and to count correctly the degeneracy). \nThis short article is a complement to the article \"Computer Algebra and Material Design\" [arXiv:1612.02275] by one of the authors (A.K.). The latter article is also available in the arXiv.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":"20 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2017-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Lie algebra in quantum physics by means of computer algebra\",\"authors\":\"I. Kikuchi, Akihito Kikuchi\",\"doi\":\"10.17605/OSF.IO/YRG7V\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article explains how to apply the computer algebra package GAP (this http URL) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct weight modules, and to count correctly the degeneracy). \\nThis short article is a complement to the article \\\"Computer Algebra and Material Design\\\" [arXiv:1612.02275] by one of the authors (A.K.). The latter article is also available in the arXiv.\",\"PeriodicalId\":8424,\"journal\":{\"name\":\"arXiv: Computational Physics\",\"volume\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Computational Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17605/OSF.IO/YRG7V\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Computational Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17605/OSF.IO/YRG7V","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Lie algebra in quantum physics by means of computer algebra
This article explains how to apply the computer algebra package GAP (this http URL) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct weight modules, and to count correctly the degeneracy).
This short article is a complement to the article "Computer Algebra and Material Design" [arXiv:1612.02275] by one of the authors (A.K.). The latter article is also available in the arXiv.