Non-associativity as gravity

TL;DR

This paper explores gravity as a non-associative phenomenon by extending the Dirac equation's vector potential using octonionic algebra, proposing a novel mathematical framework for gravitational interactions.

Contribution

It introduces a new approach by incorporating octonionic algebra into the Dirac equation to model gravity as a non-associative interaction.

Findings

Extended vector potential for Dirac equation using octonions

Proposed a matrix set solution combining $BS$ and $O_4$

Suggests non-associativity as a fundamental aspect of gravity

Abstract

Gravitation interactions are treated as non-associative part of the field's interactions. Vector-potential of the Dirac equation is extended for the octonionic algebra. The solution is considered as element of matrix set $BS\times O_4$.