Metrics and causality on Moyal planes
| Autor: | Jean-Christophe Wallet, Nicolas Franco |
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| Rok vydání: | 2016 |
| Předmět: |
High Energy Physics - Theory
Pure mathematics Plane (geometry) Noncommutative geometry quantum locally compact spaces FOS: Physical sciences spectral distance Mathematical Physics (math-ph) Causal structure 58B34 54E35 53C50 54F05 Causality (physics) Metric space High Energy Physics - Theory (hep-th) causal structures Minkowski space Locally compact space Moyal spaces Mathematical Physics Moyal bracket Mathematics |
| Zdroj: | Noncommutative Geometry and Optimal Transport. :147-173 |
| ISSN: | 1098-3627 0271-4132 |
| DOI: | 10.1090/conm/676/13610 |
| Popis: | 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 causal structure similar to the one of the usual Minkowski space, up to the notion of locality. 33 pages. Improved version; a summary added at the end of the introduction, misprints corrected. Version to appear in Contemporary Mathematics |
| Databáze: | OpenAIRE |
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