Temporal Lorentzian spectral triples

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

We present the notion of temporal Lorentzian spectral triple which is an extension of the notion of pseudo-Riemannian spectral triple with a way to ensure that the signature of the metric is Lorentzian. A temporal Lorentzian spectral triple corresponds to a specific 3 + 1 decomposition of a possibly noncommutative Lorentzian space. This structure introduces a notion of global time in noncommutative geometry. As an example, we construct a temporal Lorentzian spectral triple over a Moyal-Minkowski spacetime. We show that, when time is commutative, the algebra can be extended to unbounded elements. Using such an extension, it is possible to define a Lorentzian distance formula between pure states with a well-defined noncommutative formulation.

langue originaleAnglais
Numéro d'article1430007
Nombre de pages23
journalReviews in Mathematical Physics
Volume26
Numéro de publication8
Les DOIs
étatPublié - 22 sept. 2014

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Spectral Triples
algebra
Distance formula
signatures
decomposition
formulations
Noncommutative Geometry
Pure State
geometry
Well-defined
Signature
Space-time
Decompose
Metric
Algebra
Formulation

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Temporal Lorentzian spectral triples. / Franco, Nicolas.

Dans: Reviews in Mathematical Physics, Vol 26, Numéro 8, 1430007, 22.09.2014.

Résultats de recherche: Contribution à un journal/une revueArticle

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