引力理论作为局部惯性系理论
Theory of Gravity as Theory of Local Inertial Frames
AI总结：
本文证明完整黎曼张量的仿射理论是扩展引力理论，将引力视为局部惯性系场，并首次全面考察从仿射到度量图像的转换。
AI中文摘要：
本文证明了完整黎曼张量的仿射理论构成了引力的扩展理论。这里的基本对象是一个时空对称连接。其物理解释是局部惯性系的场。在这种方法中，引力以自然的方式作为牛顿第一定律的局部版本出现。基于本文作者与其中一位导师合著文章中引入的结果，提出了该理论的变分表述。一般框架由几个例子支持。本论文的一个核心结果是从仿射图像到度量图像的过渡。该过程的一个简化版本——适用于特定类别的拉格朗日量。在那里证明了仿射图像中的非度量性可以在度量图像中被解释为物质场。这正是赫尔曼·外尔对电磁学的解释。在这里，从完整黎曼张量理论到传统度量理论的变换首次以完全一般性进行了检验，并使用先前引入的例子进行了说明。
英文摘要：
It is proved that the affine theory of the full Riemann tensor constitutes the extended theory of gravity. The fundamental object here is a spacetime symmetric connection. Its physical interpretation is that of a field of local inertial frames. In this approach, gravity arises, in a natural way, as a local version of Newton's First Law. A variational formulation of the theory is presented, based on the results introduced in the article co-authored by the present author and one of the supervisors. The general framework is supported by several examples. A central result of the dissertation is the transition from the affine picture to the metric picture. A simplified version of this procedure -- valid for a specific class of Lagrangians. It was proved there that the non-metricity in the affine picture can be interpreted as a matter field in the metric picture. This is precisely Hermann Weyl's interpretation of electromagnetism. Here, the transformation from the full Riemann tensor theory to the conventional metric theory is examined in full generality for the first time and illustrated using the previously introduced examples.
