论文标题
量化空间的渐近通勤：$ \ mathbb {cp}^{p，q} $的情况
Asymptotic commutativity of quantized spaces: the case of $\mathbb{CP}^{p,q}$
论文作者
论文摘要
我们提出了一个程序，用于量化复杂的投影空间$ \ mathbb {cp}^{p，q} $，$ q \ ge 1 $，并在这些空间上构造相关的星级产品。该量化是独一无二的，要求它保留了公制的整个等轴测代数。尽管量化代数，即$ su（p+1，q）$，通过量化保留，但生成这些异构体的杀伤向量会选择量子校正。量化程序是最近应用于欧几里得$ ads_2 $的扩展程序，在此发现，除了恒星产物在极限中尖锐的乘积将杀伤量量的所有量子校正都消失在渐近极限中。换句话说，该空间是渐进的反DE保姆，使其成为$ ADS/CFT $对应原理的候选者。在本文中，我们发现量化的典型欧几里得$ ads_2 $可以扩展到量化$ \ m athbb {cp}^{p，q} $，即，非交换性仅限于有限的原点社区，这些量子空间接近$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ mathbb {cp} cp {cp}^p，
We present a procedure for quantizing complex projective spaces $\mathbb{CP}^{p,q}$, $q\ge 1$, as well as construct relevant star products on these spaces. The quantization is made unique with the demand that it preserves the full isometry algebra of the metric. Although the isometry algebra, namely $su(p+1,q)$, is preserved by the quantization, the Killing vectors generating these isometries pick up quantum corrections. The quantization procedure is an extension of one applied recently to Euclidean $AdS_2$, where it was found that all quantum corrections to the Killing vectors vanish in the asymptotic limit, in addition to the result that the star product trivializes to pointwise product in the limit. In other words, the space is asymptotically anti-de Sitter making it a possible candidate for the $AdS/CFT$ correspondence principle. In this article, we find indications that the results for quantized Euclidean $AdS_2$ can be extended to quantized $\mathbb{CP}^{p,q}$, i.e., noncommutativity is restricted to a limited neighborhood of some origin, and these quantum spaces approach $\mathbb{CP}^{p,q}$ in the asymptotic limit.
