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Measuring finite Quantum Geometries via Quasi-Coherent States
- Autor(en)
- Lukas Schneiderbauer, Harold C. Steinacker
- Abstrakt
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.
- Organisation(en)
- Mathematische Physik
- Journal
- Journal of Physics A: Mathematical and Theoretical
- Band
- 49
- Anzahl der Seiten
- 44
- ISSN
- 1751-8113
- DOI
- https://doi.org/10.1088/1751-8113/49/28/285301
- Publikationsdatum
- 05-2016
- Peer-reviewed
- Ja
- ÖFOS 2012
- 103036 Theoretische Physik, 103019 Mathematische Physik
- Schlagwörter
- ASJC Scopus Sachgebiete
- Allgemeine Physik und Astronomie, Statistical and Nonlinear Physics, Statistics and Probability, Mathematical Physics, Modelling and Simulation
- Link zum Portal
- https://ucrisportal.univie.ac.at/de/publications/b79a7ed6-f5c7-4cf1-abaf-0ae56670ae52