相对论量子电动力学中类氢原子的指数局域化
Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics
摘要：
我们考虑两种不同的模型中的氢原子在量子化的电磁场，处理电子相对论。第一个是自由图像中的无对模型，第二个是由半相对论的Pauli-Fierz哈密顿量给出的。我们证明了没有对运营商是半有界的电离阈值以下的能量对应的光谱子空间是指数本地化。对于精细结构常数$e^2$和紫外截止值$Λ$的任意值，以及对于所有小于无辐射场临界电荷$Z_c=e^{-2}2/(2/π+π/2)$的核电荷，这两个结果都成立。对于半相对论性的Pauli-Fierz算子，对于$e^2$和$Λ$的所有值以及小于$e^{-2}2/π$的核电荷，我们也得到了类似的结果。
英文摘要：
We consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the semi-relativistic Pauli-Fierz Hamiltonian. We prove that the no-pair operator is semi-bounded below and that its spectral subspaces corresponding to energies below the ionization threshold are exponentially localized. Both results hold true, for arbitrary values of the fine-structure constant, $e^2$, and the ultra-violet cut-off, $Λ$, and for all nuclear charges less than the critical charge without radiation field, $Z_c=e^{-2}2/(2/π+π/2)$. We obtain similar results for the semi-relativistic Pauli-Fierz operator, again for all values of $e^2$ and $Λ$ and for nuclear charges less than $e^{-2}2/π$.
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