Connes distance function on fuzzy sphere and the connection between geometry and statistics
Abstract
An algorithm to compute Connes spectral distance, adaptable to the Hilbert-Schmidt operatorial formulation of non-commutative quantum mechanics, was developed earlier by introducing the appropriate spectral triple and used to compute infinitesimal distances in the Moyal plane, revealing a deep connection between geometry and statistics. In this paper, using the same algorithm, the Connes spectral distance has been calculated in the Hilbert-Schmidt operatorial formulation for the fuzzy sphere whose spatial coordinates satisfy the algebra. This has been computed for both the discrete, as well as for the Perelemov's coherent state. Here also, we get a connection between geometry and statistics which is shown by computing the infinitesimal distance between mixed states on the quantum Hilbert space of a particular fuzzy sphere, indexed by .
Cite
@article{arxiv.1406.6782,
title = {Connes distance function on fuzzy sphere and the connection between geometry and statistics},
author = {Shivraj Prajapat and Yendrembam Chaoba Devi and Aritra K Mukhopadhyay and Biswajit Chakraborty and Frederik G Scholtz},
journal= {arXiv preprint arXiv:1406.6782},
year = {2014}
}