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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 λ 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)⊂SU(2)). We also establish a quantitative relation between rest mass m 0 of the electron and SU(2) Yang-Mills scale Λ , 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 λ C , and the correction to the mass of the electron due to Coulomb energy is about 2%.
Highlights
The electron and other charged leptons are considered fundamental particles in the presentStandard Model of particle physics
To describe the spatial probability density for the presence of a point-like electron in terms of the square of a wave function based on de Broglie’s particle-wave duality [3], whose time evolution is governed by the Hamiltonian of the isolated system, is an extremely successful and useful concept: About a century ago, it started to revolutionize our understanding of atomic stability and of the discreteness of the spectra of light emitted by excited atoms [4,5,6,7,8,9,10,11,12,13,14,15,16,17], the chemical bond [18], and the role of and interplay between electrons in condensed matter and hot plasmas thanks to the development of Entropy 2017, 19, 575; doi:10.3390/e19110575
The intersection region—a blob of deconfining phase, whose center-of-mass position essentially is a modulus of this solitonic configuration, contains a BPS monopole responding to perturbations issued by the surrounding thermodynamics
Summary
The electron and other charged leptons are considered fundamental particles in the present. The condensate of monopoles and antimonopoles together with its massive gauge-mode excitations (Meissner-Ochsenfeld effect or Abelian Higgs mechanism [54]) is not stable immediately at Tc since the energy density of the deconfining phase is lower within the following temperature range [31,32]: T∗ ≡ 0.88Tc ≤ T ≤ Tc. Shortly below T∗ the entropy density of the system approaches zero, and the thermal ground state of the preconfining phase decays into (spatial) n-fold self-intersecting center-vortex loops (n = 0, 1, 2, · · · ).
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