The ground state of non-associative hydrogen and upper bounds on the magnetic charge of elementary particles

TL;DR

This paper explores a non-associative quantum mechanics framework to analyze the ground state of hydrogen with magnetic charge, deriving new upper bounds on elementary particles' magnetic charges that challenge traditional Dirac quantization.

Contribution

It introduces a mathematically consistent algebraic formulation of non-associative quantum mechanics allowing fractional magnetic charges and applies it to hydrogen's ground state.

Findings

Derived spectral properties for non-associative quantum systems.

Established new upper bounds on magnetic charges of elementary particles.

Challenged traditional Dirac quantization constraints.

Abstract

Formulations of magnetic monopoles in a Hilbert-space formulation of quantum mechanics require Dirac's quantization condition of magnetic charge, which implies a large value that can easily be ruled out for elementary particles by standard atomic spectroscopy. However, an algebraic formulation of non-associative quantum mechanics is mathematically consistent with fractional magnetic charges of small values. Here, spectral properties in non-associative quantum mechanics are derived, applied to the ground state of hydrogen with a magnetically charged nucleus. The resulting energy leads to new strong upper bounds for the magnetic charge of various elementary particles that can appear as the nucleus of hydrogen-like atoms, such as the muon or the antiproton.