Magnetic monopoles and nonassociative deformations of quantum theory

TL;DR

This paper explores nonassociative deformations of quantum mechanics and gravity caused by magnetic monopoles, introducing a new framework with testable predictions and connections to octonion algebra and M-theory.

Contribution

It develops a quantitative framework for nonassociative quantum mechanics related to magnetic monopoles and links it to octonion algebra and non-geometric M-theory backgrounds.

Findings

New effects in nonassociative quantum mechanics due to magnetic monopoles

Connection between nonassociative algebra and octonions

Proposal of a non-geometric M-theory background

Abstract

We examine certain nonassociative deformations of quantum mechanics and gravity in three dimensions related to the dynamics of electrons in uniform distributions of magnetic charge. We describe a quantitative framework for nonassociative quantum mechanics in this setting, which exhibits new effects compared to ordinary quantum mechanics with sourceless magnetic fields, and the extent to which these theoretical consequences may be experimentally testable. We relate this theory to noncommutative Jordanian quantum mechanics, and show that its underlying algebra can be obtained as a contraction of the alternative algebra of octonions. The uncontracted octonion algebra conjecturally describes a nonassociative deformation of three-dimensional quantum gravity induced by magnetic monopoles, which we propose is realised by a non-geometric Kaluza-Klein monopole background in M-theory.