A simple electromagnetic model of the electron

TL;DR

This work proposes a torus-based electromagnetic model in which the electron is a rotating phase-vortex EM wave confined to a torus, and shows this configuration satisfies Maxwell's equations while reproducing key QED electron properties. By treating charge as a geometrical consequence of the field divergence and fitting four free parameters, the model simultaneously matches the electron's charge $e$, spin $S=\\hbar/2$, and magnetic moment $\\mu_B(1 + \alpha/(2\\pi))$, including the Schwinger correction. The analysis yields a phase velocity of $2c$, Compton-scale major radius, Dirac-frequency-consistent oscillation, and a rest energy near $0.8 m_e c^2$, with field amplitudes approaching the Schwinger limit. The approach offers a classical electromagnetic visualization (POEM) of the QED electron and motivates further refinement of boundary conditions and the exploration of a broader class of nonplane-wave solutions.

Abstract

We present a toroidal electromagnetic ansatz that provides a realistic microscopic model of the QED electron. The proposed toroidal electromagnetic wave satisfies Maxwell's equations and reproduces fundamental properties of the electron as described in quantum electrodynamics (QED). Within this framework, the electron is modeled as a rotating electromagnetic wave confined to a toroidal geometry. Parameter optimization yields quantitative agreement with the electron charge e, spin $\hbar/2$, and magnetic moment $μ_B(1 + α/2π)$, incorporating the Schwinger anomalous magnetic moment correction. The model yields an amplitude on the order of the Schwinger scale where electron-positron pair production occurs. The major radius corresponds to the Compton wavelength scale, while the monochromatic frequency is consistent with the de Broglie-Dirac frequency. The phase velocity is found to be $2c$, and the computed rest energy approximates $0.8 m_e c^2$. This representation provides a microscopic classical electromagnetic framework that encapsulates the properties of the QED electron.

Figures (2)

• Figure 1: The fields are defined inside the torus. The mask will be the step function effectively selecting the open inner volume as the domain where the EM field is defined. $R_0$ is the major radius, $r_0$ the minor radius. $\vec{R}$ is the position from origin to a given point inside the torus with $\vec{R} = \vec{R_0}+\vec{r}$
• Figure 2: E and B fields. Note the left handed nature. While the fields are represented flat in the (a) picture, they should be imagined as laid out along the circle on (b). There is one wavelength fitting in the circle given the phase $\Psi= (\phi - \omega t)$.