论文标题
再审查的共形组
The Conformal Group Revisited
论文作者
论文摘要
从100年左右的时间开始，通常已经接受了“共形组”可以在任意维n中定义为保留非退化平坦度量的一组转换，直至非零可逆点，依赖于称为“共形因子”。但是，当n> 2时，它是一个有限的尺寸谎言组，具有n翻译，n（n-1）/2旋转，1扩张和n个称为“兴高采烈”的非线性变换的变换，总计（n+1）（n+2）/2转换。由于进行了米歇尔森 - 莫利实验，即使在真空中，具有15个参数的时空组是众所周知的电磁构法（EM）的最大群体，即使通过任何可局部的可逆变换，两组磁场和感应的麦克斯韦方程都是不变的。由于该最后一个通用数字也被很好地定义，并且在n = 2的n = 1或6中等于3，因此本文的目的是使用现代的数学工具，例如Spencer操作员在OD或PD方程系统上使用Spencer操作员，这既限制了它们的符号，从而限制了Spencer -tose to Spencer -ocolomology，以便为任何n n n n n n n n n n n n n n = 2。 “有限类型”系统的概念对于这种新定义至关重要。
Since 100 years or so, it has been usually accepted that the " conformal group " could be defined in an arbitrary dimension n as the group of transformations preserving a non degenerate flat metric up to a nonzero invertible point depending factor called " conformal factor ". However, when n > 2, it is a finite dimensional Lie group of transformations with n translations, n(n-1)/2 rotations, 1 dilatation and n nonlinear transformations called " elations " , that is a total of (n+1)(n+2)/2 transformations. Because of the Michelson-Morley experiment, the conformal group of space-time with 15 parameters is well known as the biggest group of invariance of the constitutive law of electromagnetism (EM) in vacuum, even though the two sets of field and induction Maxwell equations are respectively invariant by any local invertible transformation. As this last generic number is also well defined and becomes equal to 3 for n=1 or 6 for n=2, the purpose of this paper is to use modern mathematical tools such as the Spencer operator on systems of OD or PD equations, both with its restriction to their symbols leading to the Spencer -cohomology, in order to provide a unique striking definition that could be valid for any n. The concept of a " finite type " system is crucial for such a new definition.
