Stability of an electron embedded in Higgs condensate
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2015
- DOI:
- 10.48550/arXiv.1502.00983
- arXiv:
- arXiv:1502.00983
- Bibcode:
- 2015arXiv150200983S
- Keywords:
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- Physics - General Physics;
- High Energy Physics - Phenomenology
- E-Print:
- 14 pages