论文标题
在时空描述和相对性的一些几何方面
On Some Geometrical Aspects of Space-Time Description and Relativity
论文作者
论文摘要
为了要求未来的相对论概念，必须基于原始概念而不是如今的常见形式主义，因此回忆并重新考虑了其几何形状的一些根源。因此，为了讨论三个空间和动态，我们回想起了Minkowski在1910年的方法，以实施如今常用的4矢量计算和相关的紧张表示形式以及Klein关于Lorentz Group几何形状的1910年论文。要包括微观表示，我们讨论了Wigner's和Weinberg的“增强”方法，以描述其还原性的谎言代数和coset理论，并根据$ p^{5} $中的对象将物理识别与基于Case $（1,0）\ oplus（1,0）\ oplus（1,1,1,1）$ of Electect的对象联系起来。因此，我们没有遵循某些方面的特殊和误导性的“旧表示理论，基于4矢量的微积分和张量，我们提供和使用基于线条几何形状的替代表示，除了包括已知代表理论之外，还能够描述3个空间的（经典）投影几何形状，并且可以产生旋转的层次和旋转式的层次。此外，这种几何形状能够提供更一般的途径，尤其是su（2）$ \ oplus $ i〜su（2）的特殊相对论代数，以及它包括量规理论和仿射几何学。因此，它是对基于相对论的更通用表示理论的未来理解的基础，但是，基于经典投射几何形状和$ p^{5} $所知的根。作为一个应用程序，我们讨论了Lorentz在线路和复杂几何形状方面的转换，我们可以将它们识别为...
In order to ask for future concepts of relativity, one has to build upon the original concepts instead of the nowadays common formalism only, and as such recall and reconsider some of its roots in geometry. So in order to discuss 3-space and dynamics, we recall briefly Minkowski's approach in 1910 implementing the nowadays commonly used 4-vector calculus and related tensorial representations as well as Klein's 1910 paper on the geometry of the Lorentz group. To include microscopic representations, we discuss few aspects of Wigner's and Weinberg's 'boost' approach to describe 'any spin' with respect to its reductive Lie algebra and coset theory, and we relate the physical identification to objects in $P^{5}$ based on the case $(1,0)\oplus(0,1)$ of the electromagnetic field. So instead of following this -- in some aspects -- special and misleading 'old' representation theory, based on 4-vector calculus and tensors, we provide and use an alternative representation based on line geometry which -- besides comprising known representation theory -- is capable of both describing (classical) projective geometry of 3-space as well as it yields spin matrices and the classical Lie transfer. In addition, this geometry is capable of providing a more general route to known Lie symmetries, especially of the su(2)$\oplus$i~su(2) Lie algebra of special relativity, as well as it comprises gauge theories and affine geometry. Thus it serves as foundation for a future understanding of more general representation theory of relativity based, however, on roots known from classical projective geometry and $P^{5}$. As an application, we discuss Lorentz transformations in point space in terms of line and Complex geometry, where we can identify them as...
