Cosserat/Maxwell/Weyl理论的一种普通方法
A pedestrian approach to cosserat / Maxwell / weyl theory
摘要：
本文的目的是对偏微分方程和李伪群系统的形式理论在工程中的应用所得到的一些结果作一个初步的总结（弹性理论，电磁学，耦合现象）和数学（规范理论，广义相对论）沿着以下方案：1）变换的李群可以被认为是变换的李伪群，但由于参数不再出现，所以不能使用作用型方法。2)工作的卡尔丹是取代使用的规范斯宾塞序列，而工作的Vessiot是取代使用的规范珍妮特序列，但这两个序列之间的联系，因此这两个工程是不知道今天。3)利用对偶理论，时空变换的共形群的Spencer算子的形式伴随提供了Cosserat方程，Maxwell方程和Weyl方程的平等基础，但这样的结果导致了深刻的矛盾。因此，由此获得的结果证明，工程和数学物理的基础必须在喷流理论的框架内重新审视，尽管对于已建立的理论来说，这可能看起来很惊人。
英文摘要：
The purpose of this short notice is to present an elementary summary of a few recent results obtained through the application of the formal theory of systems of partial differential equations and Lie pseudo groups to engineering (elasticity theory, electromagnetism, coupling phenomena) and mathematical (gauge theory, general relativity) along the following scheme: 1) Lie groups of transformations may be considered as Lie pseudo groups of transformations but no action type method can be used as parameters never appear any longer. 2) The work of Cartan is superseded by the use of the canonical Spencer sequence while the work of Vessiot is superseded by the use of the canonical Janet sequence but the link between these two sequences and thus these two works is not known today. 3)Using duality theory, the formal adjoint of the Spencer operator for the conformal group of transformations of space-time provides the Cosserat equations, the Maxwell equations and the Weyl equations on equal footing but such a result leads to deep contradictions. Accordingly, the results thus obtained prove that the foundations of engineering and mathematical physics must be revisited within the framework of jet theory though striking it may look like for established theories.
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