Higgs凝聚体中电子的稳定性
Stability of an electron embedded in Higgs condensate
摘要：
本文研究了Higgs凝聚体中分布在球腔表面的电子的稳定性。腔的表面张力防止电子由于库仑排斥而飞离。狄拉克在1962年提出了一个类似的模型，但没有提到希格斯凝聚。在他的模型中，电子的平衡半径等于经典电子半径$R^{c}_{e} \simeq 2.8 \times 10^{-13}$ cm，即大约是半径的$10^{5}$倍，与实验数据一致。为了解决这个问题，我们用费米子自能代替电子总能量中的库仑项，费米子自能涉及占据真空负能量的电子的屏蔽。使用近似$ξ_{0} \ll R_{0}$获得腔的张力，其中$ξ_{0}$是相干长度。对于$ξ_{0} = 10^{-3} R_{0}$，该模型中的平衡半径为$R_{0} \simeq 9.2 \times 10^{-32}$ cm。对于这样一个小的半径，我们发现电子的引力能大到足以抵消能量$\hbar c/R$，来自振动零点能量和嵌入电子的动能。
英文摘要：
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 $ξ_{0} \ll R_{0}$ where $ξ_{0}$ is the coherence length. For $ξ_{0} = 10^{-3} R_{0}$, 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.
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