An Octonionic Gauge Theory

TL;DR

This paper develops a gauge theory based on octonions, addressing nonassociativity through bimodule representations, leading to new interactions in the gauge field kinetic term.

Contribution

It introduces a novel octonionic gauge theory framework that incorporates nonassociativity via bimodule representations, expanding the scope of gauge symmetries.

Findings

Constructed a gauge theory using octonion algebra.

Identified nonassociativity as a source of new interactions.

Demonstrated modifications to the gauge field kinetic term.

Abstract

The nonassociativity of the octonion algebra necessitates a bimodule representation, in which each element is represented by a left and a right multiplier. This representation can then be used to generate gauge transformations for the purpose of constructing a field theory symmetric under a gauged octonion algebra, the nonassociativity of which appears as a failure of the representation to close, and hence produces new interactions in the gauge field kinetic term of the symmetric Lagrangian.