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arXiv · 1406.6782

Connes distance function on fuzzy sphere and the connection between geometry and statistics

Shivraj Prajapat·Yendrembam Chaoba Devi·Aritra K Mukhopadhyay·Biswajit Chakraborty·Frederik G Scholtz
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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 $su(2)$ algebra. This has been computed for both the discrete, as well as for the Perelemov's $SU(2)$ 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 $n\in\mathbb{Z}/2$.

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Shivraj Prajapat, Yendrembam Chaoba Devi, Aritra K Mukhopadhyay, Biswajit Chakraborty, Frederik G Scholtz. 2014-06-26. Connes distance function on fuzzy sphere and the connection between geometry and statistics. https://arxiv.org/abs/1406.6782

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