The relationship of flux quantization to charge quantization and the fine structure constant

Abstract

In the preceding communication [Int. J. Quantum Chem., 11 S, 373 (1968)l we discussed the background for a theory which considers quantized flux as the primary phenomenon underlying an electromagnetic theory of elementary particles. We start developing that theory by applying it to muons and electrons only.Quantized flux is an option which quantum mechanics offers us because the phase 612 of a field lepton may be multivalued even though its y function is singlevalued. Such quantized flux lines may be assumed to be closed lines, i.e. loops, so that magnetic monopoles need not be introduced into this theory. I t was assumed that one quantized flux line is associated with each charged source lepton, the flux line may have the forms shown by the magnetic field lines of that source lepton, i.e. closed loops. Such a variety of "alternative" forms may be adopted by a flux loop, and each alternative "loopform" of quantized flux is given a complex probability amplitude, in a manner somewhat resembling Feynman's superposition of path histories in his space-time approach to quantum mechanics. In this way a magnetic field of the strength of a muon magneton or an electron's Bohr magneton may be reconstructed.The purpose of the present paper is to show that it is possible to accommodate, qualitatively, the main properties of a charged lepton within such a model. We show that the lepton's magnetic field may be formulated in terms of an appropriate superposition of alternative forms of a loop of quantized flux,-that its electric field follows from that magnetic field if one assumes the loopforms to spin with an angular velocity 2mc2/h, without the explicit introduction of a source of size e,-and that the energy mc2 and the angular momentum h/2 of the lepton may be interpreted as electromagnetic energy and electromagnetic angular momentum. We also considered it necessary that a qualitative understanding of the fine structure constant e2/hc and of the mass ratio of muon to electron should result from this picture.The picture employed here is oversimplified and therefore not expected to give accurate numbers; even factors of the order two may separate the present qualitative approach from a more sophisticated and precise theory of quantized flux loopforms applied to charged leptons. 269

Topological Quantum Interplay between Magnetic Flux and Mass in an Electron

“…According to the literature, the topic has been investigated to some extent in the past and for a decade by Jehle [38][39][40][41][42][43]. Indeed, in Jehle's works, it is reported about the possibility to formulate a theory of the electromagnetic field of charged leptons as resulting from quantized magnetic flux.…”

“…Indeed, in Jehle's works, it is reported about the possibility to formulate a theory of the electromagnetic field of charged leptons as resulting from quantized magnetic flux. Jehle pointed out that the magnetic flux is an option that electrodynamics provides to investigate the nature of charged leptons and proved that the Coulomb potential can be obtained as arising from the quantization of the magnetic flux [39]. Although the formulated model was phenomenological and in contradiction with the standard formulation of QED, because of the electromagnetic origin of the mass of the electron, his formulation was an embryonal case of a topological property associated with the magnetic flux of the electron.…”