Metrics and causality on Moyal planes
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 causal structure similar to the one of the usual Minkowski space, up to the notion of locality.
 Publication:

arXiv eprints
 Pub Date:
 July 2015
 DOI:
 10.48550/arXiv.1507.06559
 arXiv:
 arXiv:1507.06559
 Bibcode:
 2015arXiv150706559F
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 58B34;
 54E35;
 53C50;
 54F05
 EPrint:
 33 pages. Improved version