论文标题
从小组理论角度来看，特殊相对论及其牛顿限制
Special Relativity and its Newtonian Limit from a Group Theoretical Perspective
论文作者
论文摘要
在这篇教学文章中，我们探索了一种强大的语言，用于描述给定基本物理理论固有的时空和粒子动力学概念，重点是特殊相对论及其牛顿限制。公式的起点是相对性对称性的表示。此外，通过对称收缩的概念，这是一种自然的方式，可以理解牛顿理论是如何成为爱因斯坦理论的近似值的一种自然方式。我们从庞加莱对称性的特殊相对论和Minkowski Spacetime作为代数和群体的固定代表空间的性质开始。然后，我们进入平行于自旋零粒子的相空间，与之相关的是，我们在汉密尔顿公式下的动力学呈现了完整的方案，这说明了基本上是相位空间几何形状的对称特征。最后，提出了将所有这些减少到牛顿理论中，作为其时空，相空间和动力学在适当的相对性对称收缩下的近似值。尽管所涉及的所有概念都已确定，但由于一个连贯的图片填补了关于主题的文献的差距，因此该故事的系统呈现。
In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting point of the formulation is the representations of the relativity symmetries. Moreover, that seriously furnishes -- via the notion of symmetry contractions -- a natural way in which one can understand how the Newtonian theory arises as an approximation to Einstein's theory. We begin with the Poincaré symmetry underlying special relativity and the nature of Minkowski spacetime as a coset representation space of the algebra and the group. Then, we proceed to the parallel for the phase space of a spin zero particle, in relation to which we present the full scheme for its dynamics under the Hamiltonian formulation, illustrating that as essentially the symmetry feature of the phase space geometry. Lastly, the reduction of all that to the Newtonian theory as an approximation with its space-time, phase space, and dynamics under the appropriate relativity symmetry contraction is presented. While all notions involved are well established, the systematic presentation of that story as one coherent picture fills a gap in the literature on the subject matter.
