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首页> 外文期刊>Journal of Gravity >Field Equations and Lagrangian for the Kaluza Metric Evaluated with Tensor Algebra Software
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Field Equations and Lagrangian for the Kaluza Metric Evaluated with Tensor Algebra Software

机译：用Tensor代数软件评估Kaluza度量的场方程和Lagrangian

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This paper calculates the Kaluza field equations with the aid of a computer package for tensor algebra, xAct. The xAct file is provided with this paper. We find that Thiry’s field equations are correct, but only under limited circumstances. The full five-dimensional field equations under the cylinder condition are provided here, and we see that most of the other references miss at least some terms from them. We go on to establish the remarkable Kaluza Lagrangian, and verify that the field equations calculated from it match those calculated with xAct, thereby demonstrating self-consistency of these results. Many of these results can be found scattered throughout the literature, and we provide some pointers for historical purposes. But our intent is to provide a definitive exposition of the field equations of the classical, five-dimensional metric ansatz of Kaluza, along with the computer algebra data file to verify them, and then to recover the unique Lagrangian for the theory. In common terms, the Kaluza theory is an “ω=0” scalar field theory, but with unique electrodynamic couplings.
机译：本文借助张量代数xAct的计算机软件包来计算Kaluza场方程。本文随附xAct文件。我们发现Thiry的场方程是正确的，但仅在有限的情况下。此处提供了圆柱条件下的完整五维场方程，我们看到大多数其他参考文献中至少缺少一些术语。我们继续建立非凡的Kaluza Lagrangian，并验证由此计算出的场方程与xAct计算的场方程匹配，从而证明了这些结果的自洽性。在整个文献中可以找到许多这样的结果，并且我们为历史目的提供了一些指示。但是，我们的目的是对Kaluza的经典五维度量ansatz的场方程以及计算机代数数据文件进行验证，从而为该理论提供唯一的Lagrangian。通俗地讲，Kaluza理论是“ω= 0”标量场理论，但具有独特的电动耦合。

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