Disctances in finite spaces from noncommutative geometry

DOI10.1016/S0393-0440(00)00044-9zbMath0983.46053arXivhep-th/9912217OpenAlexW3099473158WikidataQ125800303 ScholiaQ125800303MaRDI QIDQ5927608

Pierre Martinetti, Bruno Iochum, Thomas Krajewski

Publication date: 20 March 2001

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9912217

zbMATH Keywords

noncommutative geometryDirac operators\(n\)-point commutative spacesdistance formulaGelfand constructionpure state spaceRiemannian geodesic distance

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87)

Related Items (26)

Carnot-Carathéodory metric and gauge fluctuation in noncommutative geometry ⋮ On Pythagoras theorem for products of spectral triples ⋮ Discrete Kaluza–Klein from scalar fluctuations in noncommutative geometry ⋮ Type-II two-Higgs-doublet model in noncommutative geometry ⋮ Noncommutative geometry of the Moyal plane: translation isometries, Connes' distance on coherent states, Pythagoras equality ⋮ Metric properties of the fuzzy sphere ⋮ On isometries of spectral triples associated to AF-algebras and crossed products ⋮ Quantum causality in κ-Minkowski and related constraints ⋮ Spectral metric spaces for Gibbs measures ⋮ From Monge to Higgs: a survey of distance computations in noncommutative geometry ⋮ Pythagoras Theorem in noncommutative geometry ⋮ Revisiting Connes’ finite spectral distance on noncommutative spaces: Moyal plane and fuzzy sphere ⋮ A dual formula for the spectral distance in noncommutative geometry ⋮ Reconstructing manifolds from truncations of spectral triples ⋮ Spectral geometry with a cut-off: topological and metric aspects ⋮ The geometry of physical observables ⋮ WHAT KIND OF NONCOMMUTATIVE GEOMETRY FOR QUANTUM GRAVITY? ⋮ Spectral distance on the circle ⋮ CONNES DISTANCE BY EXAMPLES: HOMOTHETIC SPECTRAL METRIC SPACES ⋮ The spectral distance in the Moyal plane ⋮ Single extra dimension from \(\kappa\)-Poincaré and gauge invariance ⋮ Canonical quantization and the spectral action: a nice example ⋮ Towards a Monge-Kantorovich metric in noncommutative geometry ⋮ Connes distance function on fuzzy sphere and the connection between geometry and statistics ⋮ Connes' spectral triple and \(U\)(1) gauge theory on finite sets ⋮ Quantum causality constraints on kappa-Minkowski space-time

Cites Work

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• Metrics on state spaces
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• Noncommutative differential geometry of matrix algebras
• Shadow of noncommutativity
• On the universal Chamseddine–Connes action. I. Details of the action computation
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• Spectral Noncommutative Geometry and Quantization
• NONCOMMUTATIVE GEOMETRY AND GRADED ALGEBRAS IN ELECTROWEAK INTERACTIONS
• Noncommutative differential calculus and lattice gauge theory
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