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We study the noncommutative geometry of the Moyal plane from a metric point of view.
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J.E. Moyal, Quantum mechanics as a statistical theory
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P. Martinetti, R. Wulkenhaar, Discrete Kaluza Klein from scalar fluctuations in non-commutative geometry
2002
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V. Gayral, J.M. Gracia-Bondía, B. Iochum, T. Schücker, J.C. Várilly, Moyal planes are spectral triples
2004
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B. Iochum, T. Schücker, C. Stephan, On a Classification of Irreducible Almost Commutative Geometries
2004
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M.A. Rieffel, Compact quantum metric spaces
2004
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M.A. Rieffel, Gromov-Hausdorff distance for quantum metric spaces. Matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance
2004
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V. Gayral, B. Iochum, The spectral action for Moyal planes
2005
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G. Amelino-Camelia, G. Gubitosi, F. Mercati, Discreteness of area in noncommutative space
2009
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2009
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2009
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J.C. Wallet, Derivations of the Moyal algebra and Noncommutative gauge theories
2009
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F. D’Andrea, P. Martinetti, A view on optimal transport from noncommutative geometry
2010
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A. Connes, On the spectral characterization of manifolds
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