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