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

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 and 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 ∈ ℤ/2.
Authors:
;  [1] ;  [2] ;  [3] ;  [4]
  1. S. N. Bose National Centre For Basic Sciences, Salt Lake, Kolkata 700098 (India)
  2. Technical Physics Division, Bhabha Atomic Research Centre (BARC), Mumbai 400085 (India)
  3. Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)
  4. National Institute for Theoretical Physics (NITheP), Stellenbosch 7602 (South Africa)
Publication Date:
OSTI Identifier:
22403127
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; ANNIHILATION OPERATORS; FUZZY LOGIC; GEOMETRY; HILBERT SPACE; QUANTUM MECHANICS; SPHERES; SU-2 GROUPS