2020/05/25 by Mahouton Norbert Hounkonnou, Hounkonnou, Mahouton Norbert, Francis Atta Howard +4 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.2005.12274
arxiv created 2020/05/25 · openalex publication_date 2020/05/25 · arxiv updated 2020/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we focus on the characterization of Lie algebras of fermionic, bosonic and parastatistic operators of spin particles. We provide a method to construct a Lie group structure for the quantum spin particles. We show the semi-simplicity of a quantum spin particle Lie algebra, and extend the results to the Lie group level. Besides, we perform the Iwasawa decomposition of spin particles at both the Lie algebra and Lie group levels. Finally, we investigate the coupling of angular momenta of spin half particles, and give a general construction for such a study.