arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2012.11606hep-thhep-phquant-ph
收藏

量子力学的沼泽地

The Quantum Mechanics Swampland

Aditya Parikh

摘要:

我们研究了由各类QFT算子产生的费米子之间的非相对论量子力学势,并评估了它们的奇异结构。这些势可以由四费米子算符产生,也可以通过交换标量或矢量介体来产生,介体通过可重整化或不可重整化算符耦合。在非相对论区域,用这些势求解薛定谔方程提供了散射过程的精确描述。这个过程需要提供一组边界条件。我们首先概括的程序设置边界条件匹配的第一玻恩近似在量子力学的树级QFT近似。使用这个程序,我们表明,潜在的是非奇异的,尽管存在的条款成比例的$r^{-3}$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{Quantum Mechanics Swampland},其中景观由非相对论性量子力学势组成,可以被UV完成为QFT,而沼泽地由病理性势组成,不能。我们确定了初步的标准,用于区分居住在景观中的潜力,居住在沼泽地。我们还考虑了在更高的维度潜力的扩展,并发现库仑潜力是非奇异的在任意数量的时空维度。

英文摘要:

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.

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。

↑