Division Algebras, (1,9)-Space-Time, Matter-Antimatter Mixing

TL;DR

This paper explores how the tensor product of division algebras relates to (1,9)-space-time and the Standard Model, revealing matter-antimatter transitions that can be controlled by dimensional restrictions.

Contribution

It introduces a novel connection between division algebras, (1,9)-space-time, and matter-antimatter transitions within the Standard Model framework.

Findings

Matter-antimatter transitions arise from the (1,9)-Dirac operator.

Restricting hyperfield dependencies eliminates these transitions.

The extra six dimensions appear as a complex triple.

Abstract

The tensor product of the division algebras, which is a kernel for the structure of the Standard Model, is also a root for the Clifford algebra of (1,9)-space-time. A conventional Dirac Lagrangian, employing the (1,9)-Dirac operator acting on the Standard Model hyperfield, gives rise to matter into antimatter transitions not mediated by any gauge field. These transitions are eliminated by restricting the dependencies of the components of the hyperfield on the extra six dimensions, which appear in this context as a complex triple.