论文标题
非线性共形电磁和重力
Nonlinear Conformal Electromagnetism and Gravitation
论文作者
论文摘要
1909年，E。和F. cosserat兄弟发现了一种新的非线性群体理论方法（EL），唯一的实验需要测量EL常数。用一种现代语言，他们的想法是使用非线性的Spencer序列，而不是用于定义空间刚性动作的lie groupoid的非线性珍妮特序列。遵循H. weyl，我们的目的是首次计算定义时空的共形组的非线性Spencer序列，以提供电磁（EM）和引力的物理基础，唯一需要实验性的需要测量真空中的EM常数和引力常数。有了尺寸$ n $的流形，困难是处理E. Cartan在1922年被称为“兴高采烈”的$ n $非线性转换。使用尺寸$ n = 4 $具有非常具体的属性来计算Spencer共生学的计算，我们认为Cosserat El Field El Field El El eel eel eel eel eel eel eel eel eel eel eel eel em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em em。作为副产品，可以抽象地描述众所周知的田间/物质耦合（PIEZOZOELECTRICTICITICY，光弹性，...），唯一的实验需要测量相应的耦合常数。在引力的Sudy中，尺寸$ n = 4 $还允许在任何地方定义一个共形因子，但在中央有吸引力的质量和严格的二阶Jets制造的下组的反转定律将吸引力转化为排斥。
In 1909 the brothers E. and F. Cosserat discovered a new nonlinear group theoretical approach to elasticity (EL), with the only experimental need to measure the EL constants. In a modern language, their idea has been to use the nonlinear Spencer sequence instead of the nonlinear Janet sequence for the Lie groupoid defining the group of rigid motions of space. Following H. Weyl, our purpose is to compute for the first time the nonlinear Spencer sequence for the Lie groupoid defining the conformal group of space-time in order to provide the physical foundations of both electromagnetism (EM) and gravitation, with the only experimental need to measure the EM constant in vacuum and the gravitational constant. With a manifold of dimension $n$, the difficulty is to deal with the $n$ nonlinear transformations that have been called "elations" by E. Cartan in 1922. Using the fact that dimension $n=4$ has very specific properties for the computation of the Spencer cohomology, we prove that there is no conceptual difference between the Cosserat EL field or induction equations and the Maxwell EM field or induction equations. As a byproduct, the well known field/matter couplings (piezzoelectricity, photoelasticity, ...) can be described abstractly, with the only experimental need to measure the corresponding coupling constants. In the sudy of gravitation, the dimension $n=4$ also allows to have a conformal factor defined everywhere but at the central attractive mass and the inversion law of the subgroupoid made by strict second order jets transforms attraction into repulsion.
