Spinors and Octonions

TL;DR

This paper explores the mathematical structure of octonions via spin representations, revealing connections to exceptional groups and suggesting potential applications in fundamental physics theories like M- and F-theory.

Contribution

It introduces a novel perspective on octonions through spin representations and elucidates their relation to exceptional Lie groups, with implications for theoretical physics.

Findings

Octonions are linked to spin representations and exceptional groups.

The paper suggests physical applications in M- and F-theory.

Provides a new mathematical framework for understanding octonions.

Abstract

Octonions are introduced through some spin representations. The groups $G_2$, $F_4$ and the $E$ series appear in a natural manner; one way to understand octonions is as the "second coming" of the reals, but with the spinors instead of vectors. Some physical applications in $M$- and $F$-theory as putative "theories of everything" are suggested.