类氢原子在弱奇性时空中Dirac哈密顿量的谱
Spectrum of the Dirac Hamiltonian for Hydrogenic atoms on spacetimes with mild singularities
摘要：
我们将单电子离子（类氢原子）建模为静态的球对称电真空时空，其中原子核被视为类时线奇点，电子被视为狄拉克方程的测试粒子。时空是具有非线性真空定律的爱因斯坦-麦克斯韦方程组的解。一个例子是霍夫曼的时空使用玻恩-因菲尔德定律获得。狄拉克哈密顿量被证明是本质上自伴的，独立的原子序数。其本质谱和绝对连续谱与具有库仑势的Minkowski空间上的Dirac哈密顿量相同。存在无穷多个特征值，并得到聚类结果。
英文摘要：
We model a single-electron ion (hydrogenic atom) as a static, spherically symmetric electrovacuum spacetime in which the nucleus is treated as a timelike line-singularity and the electron is treated as a test particle following Dirac's equation. The spacetime is a solution of Einstein-Maxwell equations with a non-linear vacuum law. An example is Hoffmann's spacetime obtained using the Born-Infeld law. The Dirac Hamiltonian is shown to be essentially self-adjoint, independent of the atomic number. The essential spectrum and absolutely continuous spectrum are the same as in Dirac's Hamiltonian on Minkowski space with a Coulomb potential. Presence of infinitely many eigenvalues is shown and a clustering result is obtained.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
