Computational explorations of a deformed fuzzy sphere

Autor(en)

L. Glaser

Abstrakt

This work examines the deformed fuzzy sphere, as an example of a fuzzy space that can be described through a spectral triple, using computer visualizations. We first explore this geometry using an analytic expression for the eigenvalues to examine the spectral dimension and volume of the geometry. In the second part of the paper we extend the code from Glaser and Stern [J. Geom. Phys. 159, 103921 (2021)], in which the truncated sphere was visualized through localized states. This generalization allows us to examine finite spectral triples. In particular, we apply this code to the deformed fuzzy sphere as a first step in the more ambitious program of using it to examine arbitrary finite spectral triples, like those generated from random fuzzy spaces, as show in Barrett and Glaser [J. Phys. A: Math. Theor. 49, 245001 (2016)].

Organisation(en)

Mathematische Physik

Journal

Journal of Mathematical Physics

Band

64

Anzahl der Seiten

16

ISSN

0022-2488

DOI

https://doi.org/10.48550/arXiv.2304.13002

Publikationsdatum

12-2023

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik, 103029 Statistische Physik

ASJC Scopus Sachgebiete

Statistical and Nonlinear Physics, Mathematical Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/af2d4cc9-122f-419e-a22d-24226e3d7fbd