The isolated electron: De Broglie's "hidden" thermodynamics, SU(2) Quantum Yang-Mills theory, and a strongly perturbed BPS monopole

TL;DR

This paper models the electron as a vortex loop in SU(2) Yang-Mills theory, linking its size and mass to monopole structures and thermodynamics, providing a novel quantum field theoretical perspective.

Contribution

It introduces a new model of the electron as a vortex loop in SU(2) Yang-Mills theory, connecting its properties to monopoles and thermodynamic phases.

Findings

The electron's radius is comparable to the Bohr radius.

The monopole core size matches the electron's Compton wavelength.

Coulomb energy correction to the electron's mass is approximately 2%.

Abstract

Based on a recent numerical simulation of the temporal evolution of a spherically perturbed BPS monopole, SU(2) Yang-Mills thermodynamics, Louis de Broglie's deliberations on the disparate Lorentz transformations of the frequency of an internal "clock" on one hand and the associated quantum energy on the other hand, and postulating that the electron is represented by a figure-eight shaped, self-intersecting center vortex loop in SU(2) Quantum Yang-Mills theory we estimate the spatial radius $R_0$ of this self-intersection region in terms of the electron's Compton wave length $\lambda_C$. This region, which is immersed into the confining phase, constitutes a blob of deconfining phase of temperature $T_0$ mildly above the critical temperature $T_c$ carrying a frequently perturbed BPS monopole (with a magnetic-electric dual interpretation of its charge w.r.t. U(1)$\subset$SU(2)). We also establish a quantitative relation between rest mass $m_0$ of the electron and SU(2) Yang-Mills scale $\Lambda$, which in turn is defined via $T_c$. Surprisingly, $R_0$ turns out to be comparable to the Bohr radius while the core size of the monopole matches $\lambda_C$, and the correction to the mass of the electron due to Coulomb energy is about 2\,\%.