Connes distance by examples: Homothetic spectral metric spaces

Details Connes distance by examples: Homothetic spectral metric spaces Connes distance by examples: Homothetic spectral metric spaces

2011-12-14

arxiv.org/abs/1112.3285v1

Physics

Mathematical Physics

23 pages

Scientific paper

We study metric properties stemming from the Connes spectral distance on three types of non compact noncommutative spaces which have received attention recently from various viewpoints in the physics litterature. These are the noncommutative Moyal plane, a family of harmonic Moyal spectral triples for which the Dirac operator squares to the harmonic oscillator hamiltonian and a family of spectral triples with Dirac operator related to the Landau operator. We show that these triples are homothetic spectral metric spaces, having an infinite number of distinct pathwise connected components. The homothetic factors linking the distances are related to determinants of effective Clifford metrics. We obtain as a by product new exemples of explicit spectral distance formulas. The results are discussed.

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