{"title":"The \\(q\\)-Analog of the Quantum Theory of Angular Momentum: a Review from Special Functions","authors":"R. Álvarez-Nodarse, A. Arenas-Gómez","doi":"10.1134/S106192084010023","DOIUrl":null,"url":null,"abstract":"<p> In the present paper, we review the <span>\\(q\\)</span>-analog of the Quantum Theory of Angular Momentum based on the <span>\\(q\\)</span>-algebra <span>\\(su_q(2)\\)</span> with a special emphasis on the representation of the Clebsch–Gordan coefficients in terms of <span>\\(q\\)</span>-hypergeometric series. This representation allows us to obtain several known properties of the Clebsch–Gordan coefficients in an unified and simple way. </p><p> <b> DOI</b> 10.1134/S106192084010023 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 1","pages":"24 - 43"},"PeriodicalIF":1.7000,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S106192084010023","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In the present paper, we review the \(q\)-analog of the Quantum Theory of Angular Momentum based on the \(q\)-algebra \(su_q(2)\) with a special emphasis on the representation of the Clebsch–Gordan coefficients in terms of \(q\)-hypergeometric series. This representation allows us to obtain several known properties of the Clebsch–Gordan coefficients in an unified and simple way.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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