论文标题
$κ$ -NEWTONIAN和$κ$ -Carrollian代数及其非共同空间
The $κ$-Newtonian and $κ$-Carrollian algebras and their noncommutative spacetimes
论文作者
论文摘要
我们得出了非相关性$ c \ to \ infty $和超相关的$ c \至0 $限制的$κ$限制的对称性和（3+1）维度的时空，并且具有宇宙学常数。我们将Bialgebra收缩的理论应用于$κ$ - （a）ds量子代数的泊松版本，并量化由此产生的合同的Poisson-Hopf代数代数，从而产生了$κ$ $κ$ - 牛顿（Newton-Hooke and parlilei and para and para and para and para and para and para and para，对称性，包括其变形的二次Casimir操作员。相应的$κ$ -Newtonian和$κ$ -Carrollian非交易空间也是$κ$ - （a）ds非交换时空的非偏见和超偏见的极限。这些构造使我们能够分析量子变形参数$κ$，曲率参数$η$和光速度参数$ c $之间的非平凡相互作用。
We derive the non-relativistic $c\to\infty$ and ultra-relativistic $c\to 0$ limits of the $κ$-deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the $κ$-(A)dS quantum algebra, and quantize the resulting contracted Poisson-Hopf algebras, thus giving rise to the $κ$-deformation of the Newtonian (Newton-Hooke and Galilei) and Carrollian (Para-Poincaré, Para-Euclidean and Carroll) quantum symmetries, including their deformed quadratic Casimir operators. The corresponding $κ$-Newtonian and $κ$-Carrollian noncommutative spacetimes are also obtained as the non-relativistic and ultra-relativistic limits of the $κ$-(A)dS noncommutative spacetime. These constructions allow us to analyze the non-trivial interplay between the quantum deformation parameter $κ$, the curvature parameter $η$ and the speed of light parameter $c$.
