论文标题
相对论和差异几何形状中的维度分析
Dimensional analysis in relativity and in differential geometry
论文作者
论文摘要
该注释为洛伦兹和一般相对论以及差异几何形状中的维度分析提供了简短的指南。它试图恢复多格洛和舒顿的“固有”或“绝对”维度的概念。固有维度独立于坐标的尺寸，并表达张量的物理和操作含义。总结了几个重要的张量和张量操作的尺寸分析。特别是表明，张量的组件不需要所有相同的维度，并且Riemann（曾经逆转和三次协变），Ricci（两次协变）和Einstein（两次协变）曲率张力量无尺寸。讨论了度量和应力 - 能量量张量的维度与操作意义之间的关系。审查了这两个张量的尺寸和爱因斯坦恒定$κ$的尺寸的可能惯例，其中包括奇怪的可能性$κ=8πg$，而无需$ c $ co $。
This note provides a short guide to dimensional analysis in Lorentzian and general relativity and in differential geometry. It tries to revive Dorgelo and Schouten's notion of 'intrinsic' or 'absolute' dimension of a tensorial quantity. The intrinsic dimension is independent of the dimensions of the coordinates and expresses the physical and operational meaning of a tensor. The dimensional analysis of several important tensors and tensor operations is summarized. In particular it is shown that the components of a tensor need not have all the same dimension, and that the Riemann (once contravariant and thrice covariant), Ricci (twice covariant), and Einstein (twice covariant) curvature tensors are dimensionless. The relation between dimension and operational meaning for the metric and stress-energy-momentum tensors is discussed; and the possible conventions for the dimensions of these two tensors and of Einstein's constant $κ$, including the curious possibility $κ= 8πG$ without $c$ factors, are reviewed.
