论文标题
Dirac-Coulomb传播器的衍射
Diffraction for the Dirac-Coulomb propagator
论文作者
论文摘要
$ \ mathbb {r}^{1,3} $带有Z/r的dirac方程是一个相对论场方程，对氢原子进行建模。我们分析了该方程式的传播器的奇异性结构，表明传播器的Schwartz核的奇异性沿着不断扩展的球形波远离射线，而射线却错过了原点的潜在奇异性，但也可能包括从起源中散发出的衍射奇异性的附加球形波。这种衍射的波前比主要奇异性更平滑1-0个衍生物，并且是一种吻合的奇异性。
The Dirac equation in $\mathbb{R}^{1,3}$ with potential Z/r is a relativistic field equation modeling the hydrogen atom. We analyze the singularity structure of the propagator for this equation, showing that the singularities of the Schwartz kernel of the propagator are along an expanding spherical wave away from rays that miss the potential singularity at the origin, but also may include an additional spherical wave of diffracted singularities emanating from the origin. This diffracted wavefront is 1-0 derivatives smoother than the main singularities and is a conormal singularity.
