Stability of an electron embedded in Higgs condensate

TL;DR

This paper investigates the stability of an electron within a Higgs condensate cavity, proposing a model that yields an extremely small equilibrium radius and suggests gravitational energy can offset quantum energies.

Contribution

It introduces a novel model replacing Coulomb energy with fermion self-energy and incorporates Higgs condensate effects to explain electron stability at a tiny scale.

Findings

Equilibrium radius is approximately 9.2 x 10^{-32} cm.

Gravitational energy can cancel quantum zero-point and kinetic energies.

Model extends Dirac's 1962 approach with Higgs condensate considerations.

Abstract

We study stability of an electron distributed on the surface of a spherical cavity in Higgs condensate. The surface tension of the cavity prevents the electron from flying apart due to Coulomb repulsion. A similar model was introduced by Dirac in 1962, though without reference to Higgs condensate. In his model, the equilibrium radius of the electron equals the classical electron radius, $R^{c}_{e} \simeq 2.8 \times 10^{-13}$ cm, that is about $10^{5}$ times the radius consistent with experimental data. To address this problem, we replace the Coulomb term in the total energy of the electron by fermion self-energy involving screening by electrons occupying the negative energies of the vacuum. The tension of the cavity is obtained using the approximation $\xi_{0} \ll R_{0}$ where $\xi_{0}$ is the coherence length. For $\xi_{0} = 10^{-3} R_{0}$, the equilibrium radius in this model is $R_{0} \simeq 9.2 \times 10^{-32}$ cm. For such a small radius, we find the gravitational energy of the electron to be large enough to cancel the energy $\hbar c/R$, coming from the vibrational zero point energy and the kinetic energy of the embedded electron.