论文标题
Schrödinger方程的Cartan连接。真空的性质
Cartan Connection for Schrödinger equation. The nature of vacuum
论文作者
论文摘要
我们将Schrödinger方程式作为空间中的连续性方程式重新诠释，并通过在特定的喷射空间上缩放Lie-Bäcklund组给出了cartan连接。在这个空间中，波函数及其梯度坐标被视为独立坐标。这种方法使完整的cartan连接形成了无差异的条件。构造后，连接可以研究构建该schrödinger-cartan连接的空间的几何形状。这是一种以几何方式概括de Broglie-Bohm（Pilot Wave）理论中存在的概念的想法。我们还提供了此程序，用于为一般部分微分方程构建（非唯一）无扭转的曲cant曲连接。
We reinterpret the Schrödinger equation as a continuity equation in the space with the Cartan connection given by scaling Lie-Bäcklund group on a specific jet space. In this space, the wave function and their gradient coordinates are treated as independent coordinates. This approach gives a full Cartan connection form a divergence-free condition. Once constructed, the connection makes it possible to investigate the geometry of the space on which this Schrödinger-Cartan connection is constructed. This is the idea that generalizes the concepts present in de Broglie-Bohm (pilot wave) theory in a geometric way. We also present this procedure for constructing (non-uniquely) torsion-free Cartan connections for general Partial Differential Equations.
