论文标题
在二维中对三角功能点散射体的无奇异性处理及其概念上的含义
Singularity-free treatment of delta-function point scatterers in two dimensions and its conceptual implications
论文作者
论文摘要
在两个维度上，散射问题的标准处理潜力的标准处理，$ v（\ mathbf {r}）= \ mathfrak {z} \，δ（\ m athbf {r}）$，导致对数的奇异性随后通过renuloralation n o renumalization n couplation $ coupling $ coupling $ coupling $ couplefrand $ c。最近，我们开发了一种固定散射（DFSS）的动态公式，该公式提供了对该潜力的无奇异性处理。我们阐明了负责DFSS隐式正规化属性的基本机制，从而避免了对数奇异性在标准方法中遇到的对数奇异性。我们提供了这种奇点的替代解释，这表明它发生了，因为问题的标准处理考虑到对散射波的贡献，其动量与检测器的屏幕平行。用于消除这种奇异性的重新规范化方案具有减去这些非物理贡献的作用，而DFSS具有实现此目标的内置机制。
In two dimensions, the standard treatment of the scattering problem for a delta-function potential, $v(\mathbf{r})=\mathfrak{z}\,δ(\mathbf{r})$, leads to a logarithmic singularity which is subsequently removed by a renormalization of the coupling constant $\mathfrak{z}$. Recently, we have developed a dynamical formulation of stationary scattering (DFSS) which offers a singularity-free treatment of this potential. We elucidate the basic mechanism responsible for the implicit regularization property of DFSS that makes it avoid the logarithmic singularity one encounters in the standard approach to this problem. We provide an alternative interpretation of this singularity showing that it arises, because the standard treatment of the problem takes into account contributions to the scattered wave whose momentum is parallel to the detectors' screen. The renormalization schemes used for removing this singularity has the effect of subtracting these unphysical contributions, while DFSS has a built-in mechanics that achieves this goal.
