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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