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The momentum spaces of κ-Minkowski noncommutative spacetime
Nuclear Physics B ( IF 2.8 ) Pub Date : 2020-07-23 , DOI: 10.1016/j.nuclphysb.2020.115117
Fedele Lizzi , Mattia Manfredonia , Flavio Mercati

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.



中文翻译:

κ- Minkowski非交换时空的动量空间

κ- Minkowski非交换时空上建立物理模型的一个有用概念是弯曲动量空间。这种结构不是唯一的:已经确定了几种不等价的动量空间几何形状。有些与关于时空签名的假设(洛伦兹对欧几里得)的假设不同,但是存在不相等的动量空间,它们可以与相同的签名甚至同一组对称相关。此外,在文献中,有两种方法来定义这些动量空间,一种是基于由κ- Minkowski代数生成的Lie群的右(或左)不变度量。另一种是基于5维矩阵表示的构造κ- Minkowski坐标代数。两种方法都不会导致独特的构造。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,该方法能够描述所有动量空间,并确定相应的时空对称性量子组。我们重现已知结果并获得一些新结果。特别是,我们描述了与κ-庞加莱群相关的三个动量空间,它们是de Sitter,anti-de Sitter或Minkowski空间的一半,并确定它们的区别。此外,我们发现了一个具有光锥几何形状的新动量空间,与卡洛尔群的κ变形有关。

更新日期:2020-07-28
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