Metrics and causality on Moyal planes. (English) Zbl 1365.58005
Martinetti, Pierre (ed.) et al., Noncommutative geometry and optimal transport. Workshop on noncommutative geometry and optimal transport, Besançon, France, November 27, 2014. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2297-4/pbk; 978-1-4704-3560-8/ebook). Contemporary Mathematics 676, 147-173 (2016).
From the paper’s abstract: Metrics structures stemming from the Connes distance promote Moyal planes to the status of quantum metric spaces. We discuss this aspect in the light of recent developments, emphasizing the role of Moyal planes as representative examples of a recently introduced notion of quantum (noncommutative) locally compact space. We move then to the framework of Lorentzian noncommutative geometry and we examine the possibility of defining a notion of causality on Moyal plane, which is somewhat controversial in the area of mathematical physics. We show the actual existence of causal relations between the elements of a particular class of pure (coherent) states on Moyal plane with related structure similar to the one of the usual Minkowski space, up to the notion of locality.
For the entire collection see [Zbl 1353.46001].
For the entire collection see [Zbl 1353.46001].
Reviewer: Iakovos Androulidakis (Athína)
MSC:
| 58B34 | Noncommutative geometry (à la Connes) |
| 54E35 | Metric spaces, metrizability |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
| 54F05 | Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces |
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