论文标题
$κ$ -Minkowski的动量空间非交换时空
The Momentum Spaces of $κ$-Minkowski noncommutative spacetime
论文作者
论文摘要
在$κ$ -Minkowski非共同时空开发物理模型中的一个有用概念是弯曲的动量空间。这种结构不是唯一的：已经确定了几种不等的动量空间几何形状。有些与时空特征的假设不同（即洛伦兹和欧几里得人），但是有不等于的动量空间可以与相同的特征，甚至相同的对称性相关。此外，在文献中，有两种方法来定义这些动量空间，一种基于$κ$ -Minkowski代数产生的谎言组的右（或左）不变指标。另一个基于$κ$ -Minkowski协调代数的$ 5 $维矩阵表示。两种方法都会导致独特的结构。在这里，我们找到了这两种方法之间的关系，并引入了一种统一的方法，能够描述所有动量空间，并确定时空对称的相应量子组。我们复制已知结果并获得了一些新结果。特别是，我们描述了与$κ$-Poincaré群体相关的三个动量空间，该空间是De Sitter，Anti-DE保姆或Minkowski空间的一半，我们确定了区分它们的区别。此外，我们发现了一个新的动量空间，该空间具有光锥的几何形状，与Carroll组的$κ$变形有关。
A useful concept in the development of physical models on the $κ$-Minkowski noncommutative spacetime is that of a curved momentum space. This structure is not unique: several inequivalent momentum space geometries have been identified. Some are associated to a different assumption regarding the signature of spacetime (i.e. Lorentzian vs. Euclidean), but there are inequivalent momentum spaces that can be associated to the same signature and even the same group of symmetries. Moreover, in the literature there are two approaches to the definition of these momentum spaces, one based on the right- (or left-)invariant metrics on the Lie group generated by the $κ$-Minkowski algebra. The other is based on the construction of $5$-dimensional matrix representation of the $κ$-Minkowski coordinate algebra. Neither approach leads to a unique construction. Here, we find the relation between these two approaches and introduce a unified approach, capable of describing all momentum spaces, and identify the corresponding quantum group of spacetime symmetries. We reproduce known results and get a few new ones. In particular, we describe the three momentum spaces associated to the $κ$-Poincaré group, which are half of a de Sitter, anti-de Sitter or Minkowski space, and we identify what distinguishes them. Moreover, we find a new momentum space with the geometry of a light cone, associated to a $κ$-deformation of the Carroll group.
