Additional fermionic fields onto parallelizable 7-spheres

TL;DR

This paper employs geometric Fierz identities to generate and analyze new classes of fermionic fields on the parallelizable 7-sphere, revealing their algebraic and transformation properties within a non-associative octonionic framework.

Contribution

It introduces novel fermionic fields on the parallelizable 7-sphere derived from spinor bilinears and explores their algebraic structure using a generalized octonionic product.

Findings

New classes of fermionic fields on S^7 identified

Fermionic fields transform correctly under Moufang loop actions

Algebraic properties of spinor fields established

Abstract

The geometric Fierz identities are here employed to generate new emergent fermionic fields on the parallelizable (curvatureless, torsionfull) 7-sphere ($S^7$). Employing recently found new classes of spinor fields on the $S^7$ spin bundle, new classes of fermionic fields are obtained from their bilinear covariants by a generalized reconstruction theorem, on the parallelizable $S^7$. Using a generalized non-associative product on the octonionic bundle on the parallelizable $S^7$, these new classes of algebraic spinor fields, lifted onto the parallelizable $S^7$, are shown to correctly transform under the Moufang loop generators on $S^7$.