外场引起的真空极化密度
On the Vacuum Polarization Density Caused by an External Field
摘要：
我们考虑由一个或多个原子核产生的外电势$-λϕ$。按照狄拉克图像，这样的势使真空极化。在众所周知的重整化过程之后，在物理文献中导出的极化密度决定性地取决于$λ$的强度。对于小的$λ$，更准确地说，只要相应狄拉克算子的最低本征值$e_1(λ)$保持在本质谱的间隙中，密度上的积分为零。换句话说，真空保持中性。但是一旦$e_1(λ)$潜入较低的连续谱，真空就会自发地充入电荷$ 2e$。整体电荷守恒意味着两个正电子从真空中发射出来，也就是说，一个足够大的外势可以产生电子-正电子对。我们对这一现象给出了严格的证明。
英文摘要：
We consider an external potential, $-λϕ$, due to one or more nuclei. Following the Dirac picture such a potential polarizes the vacuum. The polarization density as derived in physics literature, after a well known renormalization procedure, depends decisively on the strength of $λ$. For small $λ$, more precisely as long as the lowest eigenvalue, $e_1(λ)$, of the corresponding Dirac operator stays in the gap of the essential spectrum, the integral over the density vanishes. In other words the vacuum stays neutral. But as soon as $e_1(λ)$ dives into the lower continuum the vacuum gets spontaneously charged with charge $ 2e$. Global charge conservation implies that two positrons were emitted out of the vacuum, this is, a large enough external potential can produce electron-positron pairs. We give a rigorous proof of that phenomenon.
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