关于四分体（Vielbeins）的评论
Comments on the Tetrad (Vielbeins)
摘要：
我们希望纠正许多教科书或评论文章中出现的对四分体（或一般意义上的面纱）的误解。四分体的定义不应附加任何条件。局部Lorentz坐标$X_a$的$e_{μa}=\partial_μX_a$在许多方面是错误的：它给出了条件$\partial_μe_{νa}=\partial_νe_{μa}$，这导致我们得到循环系数同为零的平凡结果和零黎曼张量。此外，$e_{μa}e_ν^a=g_{μν}$是不是标量下的局部洛伦兹变换等，我们展示了如何弥补这些赤字的正确定义，$e_{μa}=D_μZ_a$与当地（反）德西特坐标$Z_A$。
英文摘要：
We want to correct the misunderstandings on the tetrad (or veilbeins in general) appeared in many text books or review articles. The tetrad should be defined without any condition. $e_{μa}=\partial_μX_a$ with local Lorentz coordinates $X_a$ ia wrong in many sences: it gives the condition $\partial_μe_{νa}=\partial_νe_{μa}$, which leads us to the trivial result that the cyclic coefficients vanish identically and to the null Riemannian tensor. Also $e_{μa}e_ν^a=g_{μν}$ is not scalar under the local Lorentz transformation etc. We show how these deficits are remedied by the correct definition, $e_{μa}=D_μZ_a$ with local (Anti) de Sitter coordinates $Z_A$.
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。
