论文标题
轻型世界的非共同空间
The noncommutative space of light-like worldlines
论文作者
论文摘要
像光（或无效的平面）$κ$ - （3+1）Poincaré群体的相互变量的轻型世界线的非共同空间完全构建为量化Null GeoDesics的相应Poisson均质均质空间。这个新的非共同空间是五维的，事实证明是定义为二次代数，可以映射到两个Heisenberg-weyl代数的直接总和的非中心延伸，其非共同参数只是Planck scale参数$κ^{-1} $。此外，据表明，庞加莱集团通常的时间般的$κ$ - 不允许构建像光明世界的泊松同质空间。因此，为了模拟量子斑点时空上无质量颗粒的传播的最自然选择似乎是由光明的$κ$ defformation提供的。
The noncommutative space of light-like worldlines that is covariant under the light-like (or null-plane) $κ$-deformation of the (3+1) Poincaré group is fully constructed as the quantization of the corresponding Poisson homogeneous space of null geodesics. This new noncommutative space of geodesics is five-dimensional, and turns out to be defined as a quadratic algebra that can be mapped to a non-central extension of the direct sum of two Heisenberg-Weyl algebras whose noncommutative parameter is just the Planck scale parameter $κ^{-1}$. Moreover, it is shown that the usual time-like $κ$-deformation of the Poincaré group does not allow the construction of the Poisson homogeneous space of light-like worldlines. Therefore, the most natural choice in order to model the propagation of massless particles on a quantum Minkowski spacetime seems to be provided by the light-like $κ$-deformation.
