论文标题
在普通氢和氢离子上
On general-relativistic hydrogen and hydrogenic ions
论文作者
论文摘要
本文研究了具有负裸质量的点核的静态非线性电磁磁性时空如何影响一般性偏见的dirac hamiltonian对于没有和没有异常磁矩的测试电子的自我接触性。 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奇异性。 得出的主要结论是：{在严格负裸质量的点核的静电空间上（可能为$ - \ infty $）基本的自相关失败，除非径向电场在核的核电场上足够快地差异很快，并且要考虑电子的异常磁矩。 因此，在霍夫曼时空上（严格）（严格的）负裸质量，具有或没有异常的磁矩的测试电子的狄拉克·哈密顿量本质上不是自我相关的。 但是，所有这些操作员都具有自相关扩展，并具有通常的必需频谱$（ - \ infty， - \ mel c^2] \ cup [\ mel c^2，\ infty）$，并且位于gap $（ - \ mel c^2，\ mel c^2），\ mel c^2）$（\ mel c^2）$（
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 $(-\mEL c^2,\mEL c^2)$
