论文标题
dirac Hamiltonian的频谱，用于与奇异性的空间上的氢原子
Spectrum of the Dirac Hamiltonian for Hydrogenic atoms on spacetimes with mild singularities
论文作者
论文摘要
我们将单电子离子（氢原子）建模为静态的球形对称电动赛车，其中核被视为及时线性的线性，并且在Dirac方程后将电子视为测试粒子。时空是具有非线性真空定律的爱因斯坦 - 马克斯韦方程的解决方案。一个例子是霍夫曼的时空，使用了犯罪法律获得。 Dirac Hamiltonian证明本质上是自我偶的，独立于原子数。基本的频谱和绝对连续的光谱与Minkowski空间的Dirac的哈密顿量相同，具有库仑潜力。显示了无限的许多特征值的存在，并获得了聚类结果。
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.
