2018/03/31 by A. Yanes, A Y Martinho, R. da Rocha +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Algebraic number #Bilinear interpolation #Geometric Analysis and Curvature Flows #Parallelizable manifold #Product (mathematics) #Spinor #Spinor field #hep-th #math-ph #math.MP
paper · pdf · doi:10.1093/ptep/pty068
published in Progress of Theoretical and Experimental Physics 2018(6) (University of Oxford) · 16 pages
openalex created_date 2018/03/29 · openalex publication_date 2018/05/23 · arxiv created 2021/02/16 · arxiv updated 2021/02/17 · openalex updated_date 2026/08/05
The geometric Fierz identities are employed to generate new emergent fermionic fields on the parallelizable (curvatureless, torsionfull) 7-sphere (|S7|). Employing recently found classes of spinor fields on the |S7| spin bundle, new classes of fermionic fields are obtained from their bilinear covariants by a generalized reconstruction theorem on the parallelizable |S7|. Using a generalized non-associative product on the octonionic bundle on the parallelizable |S7|, these new classes of algebraic spinor fields, lifted onto the parallelizable |S7|, are shown to correctly transform under the Moufang loop generators on |S7|.