{"title":"Application of the double numbers in the representation of the Lorentz transformations","authors":"G. F. Torres del Castillo","doi":"10.31349/revmexfise.20.010204","DOIUrl":null,"url":null,"abstract":"We show that the orthochronous proper Lorentz transformations that leave one of the Cartesian coordinates fixed can be represented by $2 \\times 2$ unitary matrices with determinant equal to 1, whose entries are double numbers. This representation is employed in the calculation of the Wigner angle, which arises in the composition of two boosts in arbitrary directions.","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Mexicana De Fisica E","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31349/revmexfise.20.010204","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Social Sciences","Score":null,"Total":0}
引用次数: 1
Abstract
We show that the orthochronous proper Lorentz transformations that leave one of the Cartesian coordinates fixed can be represented by $2 \times 2$ unitary matrices with determinant equal to 1, whose entries are double numbers. This representation is employed in the calculation of the Wigner angle, which arises in the composition of two boosts in arbitrary directions.
期刊介绍：
The Revista Mexicana de Física (Rev. Mex. Fis.) publishes original papers of interest to our readers from the physical science com unity. Language may be English or Spanish, however, given the nature of our readers, English is recommended. Articles are classified as follows:
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