关于广义相对论氢和类氢离子
On general-relativistic hydrogen and hydrogenic ions
摘要：
本文研究了具有负裸质量的点核的静态非线性电磁真空时空对测试电子广义相对论Dirac哈密顿量的自伴性的影响，包括有和无反常磁矩的情形.该研究在之前研究的测试电子的极端情况之间进行了插值：（a）Reissner-Weyl-Nordström时空（麦克斯韦电磁真空），它支持具有负无限裸质量的非常强的曲率奇异性，和（b）霍夫曼时空（Born或Born--因菲尔德电磁真空）具有消失的裸质量，具有最温和的可能曲率奇异性。得出的主要结论是：{在具有严格负裸质量的点核的静电时空}（可能是$-\infty$）上，除非径向电场在核处足够快地发散，并考虑电子的反常磁矩，否则本质自伴性失效。因此，在具有（严格）负裸质量的霍夫曼时空上，无论有无反常磁矩，测试电子的狄拉克哈密顿量本质上都不是自伴的。所有这些算子都具有自伴扩张，具有通常的本质谱$(-\infty,-\mEL c^2]\cup[\mEL c^2,\infty)$和位于间隙$(-\mEL c^2,\mEL c^2)$中的无限离散谱
英文摘要：
This paper studies how the static non-linear electromagnetic-vacuum spacetime of a point nucleus with negative bare mass affects the self-adjointness of the general-relativistic Dirac Hamiltonian for a test electron, without and with an anomalous magnetic moment. The study interpolates between the previously studied extreme cases of a test electron in (a) the Reissner--Weyl--Nordström spacetime (Maxwell's electromagnetic vacuum), which supports a very strong curvature singularity with negative infinite bare mass, and (b) the Hoffmann spacetime (Born or Born--Infeld's electromagnetic vacuum) with vanishing bare mass, which features the mildest possible curvature singularity. The main conclusion reached is: {on electrostatic spacetimes of a point nucleus with a strictly negative bare mass} (which may be $-\infty$) essential self-adjointness fails unless the radial electric field diverges sufficiently fast at the nucleus and the anomalous magnetic moment of the electron is taken into account. Thus on the Hoffmann spacetime with (strictly) negative bare mass the Dirac Hamiltonian of a test electron, with or without anomalous magnetic moment, is not essentially self-adjoint. All these operators have self-adjoint extensions, though, with the usual essential spectrum $(-\infty,-\mEL c^2]\cup[\mEL c^2,\infty)$ and an infinite discrete spectrum located in the gap $(-\mEL c^2,\mEL c^2)$
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