Noncommutative Geometry and Optimal Transport
Pierre Martinetti · Jean-Christophe Wallet
loka 2016 · American Mathematical Soc.
E-kirja
223
sivuja
reportArvioita ja arvosteluja ei ole vahvistettu Lue lisää
Tietoa tästä e-kirjasta
The distance formula in noncommutative geometry was introduced by Connes at the end of the 1980s. It is a generalization of Riemannian geodesic distance that makes sense in a noncommutative setting, and provides an original tool to study the geometry of the space of states on an algebra. It also has an intriguing echo in physics, for it yields a metric interpretation for the Higgs field. In the 1990s, Rieffel noticed that this distance is a noncommutative version of the Wasserstein distance of order 1 in the theory of optimal transport. More exactly, this is a noncommutative generalization of Kantorovich dual formula of the Wasserstein distance. Connes distance thus offers an unexpected connection between an ancient mathematical problem and the most recent discovery in high energy physics. The meaning of this connection is far from clear. Yet, Rieffel's observation suggests that Connes distance may provide an interesting starting point for a theory of optimal transport in noncommutative geometry.
This volume contains several review papers that will give the reader an extensive introduction to the metric aspect of noncommutative geometry and its possible interpretation as a Wasserstein distance on a quantum space, as well as several topic papers.
This volume contains several review papers that will give the reader an extensive introduction to the metric aspect of noncommutative geometry and its possible interpretation as a Wasserstein distance on a quantum space, as well as several topic papers.
Tietoja kirjoittajasta
Edited by Pierre Martinetti: Università di Genova, Genova, Italy,
Jean-Christophe Wallet: CNRS, Université Paris-Sud 11, Orsay, France
Arvioi tämä e-kirja
Kerro meille mielipiteesi.
Tietoa lukemisesta
Älypuhelimet ja tabletit
Asenna Google Play Kirjat ‑sovellus Androidille tai iPadille/iPhonelle. Se synkronoituu automaattisesti tilisi kanssa, jolloin voit lukea online- tai offline-tilassa missä tahansa oletkin.
Kannettavat ja pöytätietokoneet
Voit kuunnella Google Playsta ostettuja äänikirjoja tietokoneesi selaimella.
Lukulaitteet ja muut laitteet
Jos haluat lukea kirjoja sähköisellä lukulaitteella, esim. Kobo-lukulaitteella, sinun täytyy ladata tiedosto ja siirtää se laitteellesi. Siirrä tiedostoja tuettuihin lukulaitteisiin seuraamalla ohjekeskuksen ohjeita.
