In this manuscript we provide a fully geometric formulation for the induced electromagnetic fields and their corresponding constitutive relations in moving media. To this end, we present the reader with a brief geometric summary to show how vector calculus electromagnetic theory is embedded in the more general language of differential forms. Then, we consider the class of \emph{metric} constitutive relations describing the medium in which electromagnetic fields propagate. We explicitly obtain the components of the induced fields in a moving medium, as seen in the the lab \emph{rest} frame. This allows us to read the expressions for the permitivity, permeability and magnetoelectric matrices for the moving medium which, in turn, can be interpreted as a different physical material from the lab point of view

中文翻译：

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运动介质中感应电磁场的几何结构

在这份手稿中，我们为运动介质中的感应电磁场及其相应的本构关系提供了完整的几何公式​​。为此，我们向读者提供了一个简短的几何总结，以展示矢量微积分电磁理论如何嵌入到更一般的微分形式语言中。然后，我们考虑描述电磁场传播介质的 \emph{metric} 本构关系类。我们明确地获得了运动介质中感应场的分量，如实验室 \emph{rest} 框架中所见。这使我们能够阅读运动介质的介电常数、磁导率和磁电矩阵的表达式，反过来，从实验室的角度来看，可以将其解释为不同的物理材料