Quantum Symmetries On Operator Algebras
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Quantum Symmetries On Operator Algebras
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Author : David Emrys Evans
language : en
Publisher:
Release Date : 1998
Quantum Symmetries On Operator Algebras written by David Emrys Evans and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In the last 20 years, the study of operator algebras has developed from a branch of functional analysis to a central field of mathematics with applications and connections with different areas in both pure mathematics (foliations, index theory, K-theory, cyclic homology, affine Kac--Moody algebras, quantum groups, low dimensional topology) and mathematical physics (integrable theories, statistical mechanics, conformal field theories and the string theories of elementary particles). The theory of operator algebras was initiated by von Neumann and Murray as a tool for studying group representations and as a framework for quantum mechanics, and has since kept in touch with its roots in physics as a framework for quantum statistical mechanics and the formalism of algebraic quantum field theory. However, in 1981, the study of operator algebras took a new turn with the introduction by Vaughan Jones of subfactor theory and remarkable connections were found with knot theory, 3-manifolds, quantum groups and integrable systems in statistical mechanics and conformal field theory. The purpose of this book, one of the first in the area, is to look at these combinatorial-algebraic developments from the perspective of operator algebras; to bring the reader to the frontline of research with the minimum of prerequisites from classical theory.
Quantum Symmetries On Operator Algebras
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Author : David E. Evans
language : en
Publisher:
Release Date : 1998
Quantum Symmetries On Operator Algebras written by David E. Evans and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Quantum groups categories.
Operator Algebras And Quantum Statistical Mechanics 1
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Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 1987
Operator Algebras And Quantum Statistical Mechanics 1 written by Ola Bratteli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
This is the first of two volumes presenting the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications. The book is self-contained and most proofs are presented in detail, which makes it a useful text for students with a knowledge of basic functional analysis. The introductory chapter surveys the history and justification of algebraic techniques in statistical physics and outlines the applications that have been made. The second edition contains new and improved results. The principal changes include: A more comprehensive discussion of dissipative operators and analytic elements; the positive resolution of the question of whether maximal orthogonal probability measure on the state space of C-algebra were automatically maximal along all the probability measures on the space.
Quantum Symmetries In Theoretical Physics And Mathematics
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Author : Robert Coquereaux
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Quantum Symmetries In Theoretical Physics And Mathematics written by Robert Coquereaux and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This volume presents articles from several lectures presented at the school on ``Quantum Symmetries in Theoretical Physics and Mathematics'' held in Bariloche, Argentina. The various lecturers provided significantly different points of view on several aspects of Hopf algebras, quantum group theory, and noncommutative differential geometry, ranging from analysis, geometry, and algebra to physical models, especially in connection with integrable systems and conformal field theories.Primary topics discussed in the text include subgroups of quantum $SU(N)$, quantum ADE classifications and generalized Coxeter systems, modular invariance, defects and boundaries in conformal field theory, finite dimensional Hopf algebras, Lie bialgebras and Belavin-Drinfeld triples, real forms ofquantum spaces, perturbative and non-perturbative Yang-Baxter operators, braided subfactors in operator algebras and conformal field theory, and generalized ($d$) cohomologies.
Operator Algebras And Quantum Statistical Mechanics 1
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Author : Ola Bratteli
language : en
Publisher:
Release Date : 2014-01-15
Operator Algebras And Quantum Statistical Mechanics 1 written by Ola Bratteli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Quantum Symmetries
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Author : Guillaume Aubrun
language : en
Publisher: Springer
Release Date : 2017-10-11
Quantum Symmetries written by Guillaume Aubrun and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-11 with Mathematics categories.
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.
Quantum Group Symmetry And Q Tensor Algebras
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Author : L. C. Biedenharn
language : en
Publisher: World Scientific
Release Date : 1995
Quantum Group Symmetry And Q Tensor Algebras written by L. C. Biedenharn and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations of the q-deformed angular momentum group are discussed, including the case where q is a root of unity, and general results are obtained for all unitary quantum groups using the method of algebraic induction. Tensor operators are defined and discussed with examples, and a systematic treatment of the important (3j) series of operators is developed in detail. This book is a good reference for graduate students in physics and mathematics.
Operator Algebras And Quantum Statistical Mechanics
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Author : Ola Bratteli
language : en
Publisher:
Release Date : 1987
Operator Algebras And Quantum Statistical Mechanics written by Ola Bratteli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Operator Algebras And Quantum Statistical Mechanics
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Author : Ola Bratteli
language : en
Publisher:
Release Date : 1979
Operator Algebras And Quantum Statistical Mechanics written by Ola Bratteli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.
Operator Algebras And Quantum Statistical Mechanics
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Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-09
Operator Algebras And Quantum Statistical Mechanics written by Ola Bratteli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-09 with Science categories.
For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.
