Testing non-associative quantum mechanics

TL;DR

This paper explores non-associative quantum mechanics, deriving testable physical predictions for exotic systems like magnetic monopoles, revealing effects that differ fundamentally from standard quantum mechanics.

Contribution

It provides the first derivation of testable results in non-associative quantum mechanics using effective potentials, expanding understanding of exotic quantum systems.

Findings

Potentially observable effects unique to non-associative quantum systems

Effective potentials reveal new physical phenomena

Differences from standard quantum mechanics with magnetic fields

Abstract

The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to non-associative algebras. Their quantum physics has remained obscure. This letter presents the first derivation of potentially testable physical results in non-associative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.