2003/02/15 by Hector L. Carrión, H. L. Carrion, Moisés Rojas +3 · 45 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Clifford algebra #Combinatorics #Coset #Geometry #Lorentz transformation #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Quaternion #Quaternionic representation #Spinor #Superstring theory #Supersymmetry #hep-th
paper · pdf · doi:10.1088/1126-6708/2003/04/040
published in Journal of High Energy Physics 2003(04), 040 (Springer Nature) · 24 pages, LaTex
arxiv created 2003/02/15 · openalex publication_date 2003/04/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quaternionic and octonionic realizations of Clifford algebras and spinors are classified and explicitly constructed in terms of recursive formulas. The most general free dynamics in arbitrary signature space-times for both quaternionic and octonionic spinors is presented. In the octonionic case we further provide a systematic list of results and tables expressing, e.g., the relations of the octonionic Clifford algebras with the G2 cosets over the Lorentz algebras, the identities satisfied by the higher-rank antisymmetric octonionic tensors and so on. Applications of these results range from the classification of octonionic generalized supersymmetries, the construction of octonionic superstrings, as well as the investigations concerning the recently discovered octonionic M-superalgebra and its superconformal extension.