论文标题
$κ$ - 加利利人和$κ$ -Carrollian的非交通空间
$κ$-Galilean and $κ$-Carrollian noncommutative spaces of worldlines
论文作者
论文摘要
与$κ$-POINCARé相对论对称性及其“非权利主义”（Galilei）和“超相关”（Carroll）限制相关的非共同空间是无法区分的，因为它们的协调能够满足相同的代数。在这项工作中，我们表明，在观察类似时间的世界线的相关空间时，可以区分三个量子运动模型。具体而言，我们以$κ$ -Galilei和$κ$ -Carroll对称的$κ$ -Galilei和$κ$ -Carroll对称的构建非交通型空间，作为相应$κ$-PoinCincaré空间的收缩，我们表明这三个空间由不同的代数定义。特别是，$κ$ -Galilei世界的空间类似于所谓的Euclidean Snyder型号，而$κ$ -Carroll Space证明是合理的。此外，我们确定了地球学量子空间与相应的非共同空间之间的映射，该空间需要通过添加非共同的时间坐标来扩展大地测量空间。
The noncommutative spacetimes associated to the $κ$-Poincaré relativistic symmetries and their "non-relativistic" (Galilei) and "ultra-relativistic" (Carroll) limits are indistinguishable, since their coordinates satisfy the same algebra. In this work, we show that the three quantum kinematical models can be differentiated when looking at the associated spaces of time-like worldlines. Specifically, we construct the noncommutative spaces of time-like geodesics with $κ$-Galilei and $κ$-Carroll symmetries as contractions of the corresponding $κ$-Poincaré space and we show that these three spaces are defined by different algebras. In particular, the $κ$-Galilei space of worldlines resembles the so-called Euclidean Snyder model, while the $κ$-Carroll space turns out to be commutative. Furthermore, we identify the map between quantum spaces of geodesics and the corresponding noncommutative spacetimes, which requires to extend the space of geodesics by adding the noncommutative time coordinate.
