Quantum Isometry Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Isometry Groups write by Debashish Goswami. This book was released on 2017-01-05. Quantum Isometry Groups available in PDF, EPUB and Kindle. This book offers an up-to-date overview of the recently proposed theory of quantum isometry groups. Written by the founders, it is the first book to present the research on the “quantum isometry group”, highlighting the interaction of noncommutative geometry and quantum groups, which is a noncommutative generalization of the notion of group of isometry of a classical Riemannian manifold. The motivation for this generalization is the importance of isometry groups in both mathematics and physics. The framework consists of Alain Connes’ “noncommutative geometry” and the operator-algebraic theory of “quantum groups”. The authors prove the existence of quantum isometry group for noncommutative manifolds given by spectral triples under mild conditions and discuss a number of methods for computing them. One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitly describe quantum isometry groups of most of the noncommutative manifolds studied in the literature. Some physical motivations and possible applications are also discussed.
Quantum Groups and Noncommutative Spaces
Quantum Groups and Noncommutative Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Groups and Noncommutative Spaces write by Matilde Marcolli. This book was released on 2010-11-02. Quantum Groups and Noncommutative Spaces available in PDF, EPUB and Kindle. This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.
Physical and Mathematical Aspects of Symmetries
Physical and Mathematical Aspects of Symmetries - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Physical and Mathematical Aspects of Symmetries write by Sergio Duarte. This book was released on 2018-01-09. Physical and Mathematical Aspects of Symmetries available in PDF, EPUB and Kindle. This proceedings records the 31st International Colloquium on Group Theoretical Methods in Physics (“Group 31”). Plenary-invited articles propose new approaches to the moduli spaces in gauge theories (V. Pestun, 2016 Weyl Prize Awardee), the phenomenology of neutrinos in non-commutative space-time, the use of Hardy spaces in quantum physics, contradictions in the use of statistical methods on complex systems, and alternative models of supersymmetry. This volume’s survey articles broaden the colloquia’s scope out into Majorana neutrino behavior, the dynamics of radiating charges, statistical pattern recognition of amino acids, and a variety of applications of gauge theory, among others. This year’s proceedings further honors Bertram Kostant (2016 Wigner Medalist), as well as S.T. Ali and L. Boyle, for their life-long contributions to the math and physics communities. The aim of the ICGTMP is to provide a forum for physicists, mathematicians, and scientists of related disciplines who develop or apply methods in group theory to share their research. The 31st ICGTMP was held in Rio de Janeiro, Brazil, from June 19th to June 25th, 2016. This was the first time that a colloquium of the prestigious and traditional ICGTMP series (which started in 1972 in Marseille, France) took place in South America. (The history of the colloquia can be found at http://icgtmp.blogs.uva.es/)
Quantum Symmetries
Quantum Symmetries - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Symmetries write by Guillaume Aubrun. This book was released on 2017-10-11. Quantum Symmetries available in PDF, EPUB and Kindle. 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 of Banach spaces to quantum information. The latter applications will also be of interest to theoretical and mathematical physicists working in quantum theory.
Introduction to Quantum Groups
Introduction to Quantum Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Quantum Groups write by Teo Banica. This book was released on 2023-01-01. Introduction to Quantum Groups available in PDF, EPUB and Kindle. This book introduces the reader to quantum groups, focusing on the simplest ones, namely the closed subgroups of the free unitary group. Although such quantum groups are quite easy to understand mathematically, interesting examples abound, including all classical Lie groups, their free versions, half-liberations, other intermediate liberations, anticommutation twists, the duals of finitely generated discrete groups, quantum permutation groups, quantum reflection groups, quantum symmetry groups of finite graphs, and more. The book is written in textbook style, with its contents roughly covering a one-year graduate course. Besides exercises, the author has included many remarks, comments and pieces of advice with the lone reader in mind. The prerequisites are basic algebra, analysis and probability, and a certain familiarity with complex analysis and measure theory. Organized in four parts, the book begins with the foundations of the theory, due to Woronowicz, comprising axioms, Haar measure, Peter–Weyl theory, Tannakian duality and basic Brauer theorems. The core of the book, its second and third parts, focus on the main examples, first in the continuous case, and then in the discrete case. The fourth and last part is an introduction to selected research topics, such as toral subgroups, homogeneous spaces and matrix models. Introduction to Quantum Groups offers a compelling introduction to quantum groups, from the simplest examples to research level topics.
