论文标题
量子（矩阵）几何形状和准共晶态
Quantum (Matrix) Geometry and Quasi-Coherent States
论文作者
论文摘要
描述了一个通用框架，该框架将几何结构与任何一组$ d $有限的二维遗传学矩阵$ x^a，\ a = 1，...，d $相关联。该框架将模糊空间的众所周知示例概括并系统化，并允许提取基本的经典空间，而无需大型矩阵或表示理论的限制。该方法基于先前介绍的准共产状态概念。特别是，自然出现了量子kähler几何形状的概念，其中包括众所周知的量化coadhexhexhexhexhexhexhexhexhexhechechect Orbits，例如Fuzzy Sphere $ S^2_n $和模糊$ \ Mathbb {c} p^n_n $。建立了量子kähler几何形状的量化图。确定了不是Kähler的量子几何形状的一些例子，包括最小的模糊圆环。
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and allows to extract the underlying classical space without requiring the limit of large matrices or representation theory. The approach is based on the previously introduced concept of quasi-coherent states. In particular, a concept of quantum Kähler geometry arises naturally, which includes the well-known quantized coadjoint orbits such as the fuzzy sphere $S^2_N$ and fuzzy $\mathbb{C} P^n_N$. A quantization map for quantum Kähler geometries is established. Some examples of quantum geometries which are not Kähler are identified, including the minimal fuzzy torus.
