We provide an analysis and statement of the source term in the classical Kaluza field equations, by considering the 5-dimensional (5D) energy-momentum tensor corresponding to the 5D geodesic hypothesis that is typically presumed in the Kaluza theory. By providing the 5D matter Lagrangian, this work completes a Lagrangian analysis of the classical Kaluza theory that began by establishing the proper form of the unique Kaluza field Lagrangian. This work considers the transformation properties necessitated by general covariance of the Kaluza source terms, to establish the correct form for the source terms in the field equations, and to establish the 5D matter Lagrangian that corresponds to the 5D geodesic hypothesis. In addition to the effects of a scalar field expected from other scalar-tensor or scalar-electromagnetic theories, a peculiar Kaluza coupling coefficient arises for charged matter which acts to vary the source strengths in ways unknown to conventional physics. We briefly evaluate the implied modifications to source terms in the field equations. We find an ADM-like neutralization of gravity at high specific charge states and a saturation in field strength at high specific charge-to-mass ratios.

中文翻译：

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Kaluza能量动量张量的场方程和Lagrangian

通过考虑与Kaluza理论中通常假定的5D测地线假说相对应的5维（5D）能量动量张量，我们对经典Kaluza场方程中的源项进行了分析和陈述。通过提供5D物质拉格朗日，这项工作完成了对经典Kaluza理论的拉格朗日分析，首先建立了独特的Kaluza场拉格朗日的适当形式。这项工作考虑了Kaluza源项的一般协方差所必需的变换特性，以便在场方程中为源项建立正确的形式，并建立与5D测地线假设相对应的5D物质拉格朗日。除了其他标量张量或标量电磁理论所预期的标量场的影响外，带电物质会产生奇特的Kaluza耦合系数，其作用是以传统物理学未知的方式改变源强度。我们简要地评估了场方程中对源项的隐含修改。我们发现，在高比电荷态下，ADM状的重力中和，而在高比电荷质量比下，场强达到饱和。