论文标题
量子力学滚动
The Quantum Mechanics Swampland
论文作者
论文摘要
我们研究了各类QFT操作员产生的费米之间的非相关量子机械电位，并评估其奇异性结构。这些电势可以由四个特里米昂操作员或通过可通过可降低或不可降低的操作员耦合的标量或矢量介体交换。在非权威主义制度中，用这些电势求解Schrödinger方程提供了对散射过程的准确描述。此过程需要提供一组边界条件。我们首先通过将量子力学中的第一个诞生近似与树级QFT近似相匹配来概括设置边界条件的过程。使用此过程，我们表明电势是非语言的，尽管术语的存在与$ r^{ - 3} $和$ \ nabla_ {i} \ nabla_ {j}Δ^3}（\ vec {r}）$。这一令人惊讶的特征使我们提出了\ emph {量子力学swampland}，其中景观由可以将紫外线固定在QFT上完成的非相关量子力学潜力组成，而swampland由无法做到的病理潜力组成。我们确定了区分景观中存在的潜力的初步标准，这些标准与居住在沼泽地的景观中。我们还考虑在更高维度的电势上扩展，并发现库仑电位在任意数量的时空维度中是非发挥作用的。
We investigate non-relativistic quantum mechanical potentials between fermions generated by various classes of QFT operators and evaluate their singularity structure. These potentials can be generated either by four-fermion operators or by the exchange of a scalar or vector mediator coupled via renormalizable or non-renormalizable operators. In the non-relativistic regime, solving the Schrödinger equation with these potentials provides an accurate description of the scattering process. This procedure requires providing a set of boundary conditions. We first recapitulate the procedure for setting the boundary conditions by matching the first Born approximation in quantum mechanics to the tree-level QFT approximation. Using this procedure, we show that the potentials are nonsingular, despite the presence of terms proportional to $r^{-3}$ and $\nabla_{i}\nabla_{j}δ^{3}(\vec{r})$. This surprising feature leads us to propose the \emph{Quantum Mechanics Swampland}, in which the Landscape consists of non-relativistic quantum mechanical potentials that can be UV completed to a QFT, and the Swampland consists of pathological potentials which cannot. We identify preliminary criteria for distinguishing potentials which reside in the Landscape from those that reside in the Swampland. We also consider extensions to potentials in higher dimensions and find that Coulomb potentials are nonsingular in an arbitrary number of spacetime dimensions.
