Overview
- Gives an accessible introduction to current research
- Provides a common point of view on several interconnected, but originally independently developed areas of mathematics
- Open problems suggest directions for future research
- Provides a survey of current research topics in functional analysis and its applications to quantum physics
- Offers a unique blend of uses of quantum symmetries (in quantum groups, non-commutative probability and quantum physics)
- Covers a variety of different facets of the modern concept of quantum symmetries
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2189)
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Table of contents (4 chapters)
Keywords
About this book
Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems.
A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions.
The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory ofBanach spaces to quantum information. The latter applications will also be of interest to theoretical and mathematical physicists working in quantum theory.
Authors, Editors and Affiliations
Bibliographic Information
Book Title: Quantum Symmetries
Book Subtitle: Metabief, France 2014
Authors: Guillaume Aubrun, Adam Skalski, Roland Speicher
Editors: Uwe Franz
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-63206-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-63205-6Published: 14 October 2017
eBook ISBN: 978-3-319-63206-3Published: 11 October 2017
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IX, 119
Number of Illustrations: 15 b/w illustrations, 3 illustrations in colour
Topics: Functional Analysis, Quantum Physics, Probability Theory and Stochastic Processes, Convex and Discrete Geometry