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arXiv · 1601.08007

Measuring finite Quantum Geometries via Quasi-Coherent States

Lukas Schneiderbauer·Harold C. Steinacker
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Abstract

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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Lukas Schneiderbauer, Harold C. Steinacker. 2016-05-23. Measuring finite Quantum Geometries via Quasi-Coherent States. https://doi.org/10.1088/1751-8113%2F49%2F28%2F285301

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