Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-02-15
JHEP 0304 (2003) 040
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, LaTex
Scientific paper
10.1088/1126-6708/2003/04/040
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 $G_2$ 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.
Carrión Hector L.
Rojas M.
Toppan Francesco
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