The Podleś Spheres Converge to the Sphere

We prove that the Podleś spheres S q 2 converge in quantum Gromov–Hausdorff distance to the classical 2-sphere as the deformation parameter q tends to 1. Moreover, we construct a q -deformed analogue of the fuzzy spheres, and prove that they converge to S q 2 as their linear dimension tends to infin...

Full description

Saved in:
Bibliographic Details
Published in:Communications in mathematical physics 2022-06, Vol.392 (3), p.1029-1061
Main Authors: Aguilar, Konrad, Kaad, Jens, Kyed, David
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Convergence
Deformation
Mathematical and Computational Physics
Mathematical Physics
Metric space
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Spheres
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that the Podleś spheres S q 2 converge in quantum Gromov–Hausdorff distance to the classical 2-sphere as the deformation parameter q tends to 1. Moreover, we construct a q -deformed analogue of the fuzzy spheres, and prove that they converge to S q 2 as their linear dimension tends to infinity, thus providing a quantum counterpart to a classical result of Rieffel.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-022-04363-4