利用准相干态测量有限量子几何
Measuring finite Quantum Geometries via Quasi-Coherent States
摘要：
我们开发了一个系统的方法来确定和测量数字的几何通用量子或“模糊”的几何实现了一组有限维厄米矩阵。该方法的目的是恢复嵌入在$\mathbb{R}^d$的量化辛空间的半经典极限，包括著名的模糊空间的例子，但它适用于更普遍。中心工具是准相干态，它被定义为拉普拉斯或狄拉克算符的基态，对应于目标空间中的定域点膜。这些准相干态的位移能被用来提取半经典几何的局部维数和切空间，并提供了半经典近似的质量和自洽性的度量。该方法进行了讨论和测试的各种例子，并在一个开源的Mathematica软件包中实现。
英文摘要：
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical limit of quantized symplectic spaces embedded in $\mathbb{R}^d$ including the well-known examples of fuzzy spaces, but it applies much more generally. The central tool is provided by quasi-coherent states, which are defined as ground states of Laplace- or Dirac operators corresponding to localized point branes in target space. The displacement energy of these quasi-coherent states is used to extract the local dimension and tangent space of the semi-classical geometry, and provides a measure for the quality and self-consistency of the semi-classical approximation. The method is discussed and tested with various examples, and implemented in an open-source Mathematica package.
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