Gromov-Hausdorff convergence of state spaces for spectral truncations
Quantum Algebra
2021-01-13 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We study the convergence aspects of the metric on spectral truncations of geometry. We find general conditions on sequences of operator system spectral triples that allows one to prove a result on Gromov-Hausdorff convergence of the corresponding state spaces when equipped with Connes' distance formula. We exemplify this result for spectral truncations of the circle, Fourier series on the circle with a finite number of Fourier modes, and matrix algebras that converge to the sphere.
Keywords
Cite
@article{arxiv.2005.08544,
title = {Gromov-Hausdorff convergence of state spaces for spectral truncations},
author = {Walter D. van Suijlekom},
journal= {arXiv preprint arXiv:2005.08544},
year = {2021}
}
Comments
15 pages, 3 figures (published version)