Magnetic Charge in a Nonassociative Field Theory

TL;DR

This paper explores a nonassociative octonionic field theory to incorporate magnetic charges, revealing simplified dynamics with dyonic charges and potential links to string theory for resolving quantization issues.

Contribution

It introduces a nonassociative field theory framework using octonions to model magnetic charge and discusses its implications for quantization and string theory extensions.

Findings

Simplified dynamics with dyonic charges in the nonassociative theory

Quantization problems persist despite the new framework

Potential resolution of difficulties via string theory extension

Abstract

The violation of the Jacobi identity by the presence of magnetic charge is accomodated by using an explicitly nonassociative theory of octonionic fields. It is found that the dynamics of this theory is simplified if the Lagrangian contains only dyonic charges, but certain problems in the constrained quantisation remain. The extension of these concepts to string theory may however resolve these difficulties.