Abstract
Weak magnetic monopoles with a continuum of charges less than the minimum implied by Dirac's quantization condition may be possible in nonassociative quantum mechanics. If a weakly magnetically charged proton in a hydrogen atom perturbs the standard energy spectrum only slightly, magnetic charges could have escaped detection. Testing this hypothesis requires entirely new methods to compute energy spectra in nonassociative quantum mechanics. Such methods are presented here, and evaluated for upper bounds on the magnetic charge of elementary particles.
Highlights
In 1931, Dirac [1] showed that magnetic monopoles with charge g can be consistently described by wave functions provided the quantization condition eg 1⁄4 Nħ holds with half-integer N
Nonassociative quantum mechanics can be defined by replacing the operator product of observables with an abstract product, such that a 1ða 2a 3Þ ≠ ða 1a 2Þa 3 in general
We show that even a small magnetic charge of the nucleus would significantly shift the ground-state energy of a hydrogen atom
Summary
Martin Bojowald,1,* Suddhasattwa Brahma,2,∥ Umut Büyükçam,1,† Jonathan Guglielmon,1,‡ and Martijn van Kuppeveld1,§. If a weakly magnetically charged proton in a hydrogen atom perturbs the standard energy spectrum only slightly, magnetic charges could have escaped detection. Testing this hypothesis requires entirely new methods to compute energy spectra in nonassociative quantum mechanics. Such methods are presented here, and evaluated for upper bounds on the magnetic charge of elementary particles. The methods used here are closely related to these papers but provide a new application to energy spectra In this way, we will set up a method to compute eigenvalues without using wave functions or boundary conditions.
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