Noncommutative Geometry and Optimal Transport is popular PDF and ePub book, written by Pierre Martinetti in 2016-10-26, it is a fantastic choice for those who relish reading online the Mathematical optimization genre. Let's immerse ourselves in this engaging Mathematical optimization book by exploring the summary and details provided below. Remember, Noncommutative Geometry and Optimal Transport can be Read Online from any device for your convenience.
Noncommutative Geometry and Optimal Transport Book PDF Summary
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.
Detail Book of Noncommutative Geometry and Optimal Transport PDF
- Author : Pierre Martinetti
- Release : 26 October 2016
- Publisher : American Mathematical Soc.
- ISBN : 9781470422974
- Genre : Mathematical optimization
- Total Page : 223 pages
- Language : English
- PDF File Size : 11,5 Mb
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