Quaternionic and octonionic spinors. A classification

Abstract

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.

On nonminimal ${\cal N}=4$N=4 supermultiplets in 1D and their associated σ-models

“…The supersymmetry transformations are here explicitly obtained by dressing the N = 8 root supermultiplet expressed in terms of the octonionic structure constants C ijk , see [34,4] …”

See-Saw Mechanism and Dimensional Reduction in Connection with Exotic Metrics

“…We can write down a possible set of (2 5 × 2 5 ) gamma-matrices, in the Weyl representation [8], satisfying the Clifford algebra given in Eq. (2.1):…”

New Results in Supersymmetric Quantum Mechanics

“…On the other hand, it is well-known [15], that the seven 8 × 8 antisymmetric gamma matrices of Cl(0, 7) can be recovered by the left-action of the imaginary octonions on the octonionic space. As a result, the entries of the seven antisymmetric gamma-matrices of Cl(0, 7) can be expressed in terms of the totally antisymmetric octonionic structure constants C i jk 's.…”