Measuring finite quantum geometries via quasi-coherent states
Measuring finite quantum geometries via quasi-coherent states
复制标题
通过准相干态测量有限量子几何
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
H. Steinacker
中科院分区：
文献类型：
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作者：
Lukas Schneiderbauer;H. Steinacker
我们开发了一种系统的方法来确定和测量由一组有限维厄米特矩阵实现的一般量子几何或模糊几何的几何。该方法被设计用来恢复嵌入在RD中的量子化辛空间的半经典极限，包括著名的模糊空间的例子，但它适用得更广泛。中心工具由准相干态提供，准相干态被定义为目标空间中对应于局域点膜的拉普拉斯-或狄拉克算符的基态。这些准相干态的位移能被用来提取半经典几何的局域维度和切线空间，并为半经典近似的质量和自洽提供了一个度量。通过不同的实例对该方法进行了讨论和测试，并在一个开源的数学软件包中实现了该方法。
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 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.