### Résumé

langue originale | Anglais |
---|---|

Pages (de - à) | 147-173 |

journal | Contemporary Mathematics |

Volume | 676 |

Les DOIs | |

état | Publié - oct. 2016 |

### Empreinte digitale

### Citer ceci

*Contemporary Mathematics*,

*676*, 147-173. https://doi.org/10.1090/conm/676/13610

}

*Contemporary Mathematics*, VOL. 676, p. 147-173. https://doi.org/10.1090/conm/676/13610

**Metrics and causality on Moyal planes.** / Franco, Nicolas; Wallet, Jean-Christophe.

Résultats de recherche: Contribution à un journal/une revue › Article

TY - JOUR

T1 - Metrics and causality on Moyal planes

AU - Franco, Nicolas

AU - Wallet, Jean-Christophe

PY - 2016/10

Y1 - 2016/10

N2 - 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.

AB - 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.

KW - Noncommutative geometry,

KW - spectral distance

KW - causal structures

KW - Moyal spaces

KW - quantum locally compact spaces.

U2 - http://dx.doi.org/10.1090/conm/676/13610

DO - http://dx.doi.org/10.1090/conm/676/13610

M3 - Article

VL - 676

SP - 147

EP - 173

JO - Contemporary Mathematics

JF - Contemporary Mathematics

SN - 0271-4132

ER -