标题： 兰佐斯张量的物理解释 显示英文标题

标题： The Physical Interpretation of the Lanczos Tensor

摘要： 广义相对论的场方程可以写成威克尔张量的一阶微分方程，反过来，威克尔张量也可以写成一个三指标张量即兰奇洛斯张量的一阶微分方程。 兰奇洛斯张量在广义相对论中的作用类似于电磁理论中的矢量势。 阿哈罗诺夫-玻姆效应表明，当量子力学应用于电磁理论时，矢量势在动力学上是重要的，即使电磁场张量$F_{ab}$为零。 在这里假设在量子领域中，兰奇洛斯张量在动力学上是重要的，这导致尝试通过矢量场和兰奇洛斯张量之间的类比来对引力场进行量子化。 显示英文摘要

摘要： The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamically significant, even when the electro-magnetic field tensor $F_{ab}$ vanishes. Here it is assumed that in the quantum realm the Lanczos tensor is dynamically significant, and this leads to an attempt to quantize the gravitational field by pursuing the analogy between the vector field and the Lanczos tensor.