Quantum Symmetries For Quantum Spaces
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Quantum Symmetries For Quantum Spaces
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Author : Roberto Hernandez Palomares
language : en
Publisher:
Release Date : 2021
Quantum Symmetries For Quantum Spaces written by Roberto Hernandez Palomares and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Categories (Mathematics) categories.
This thesis consists of three self-contained papers from my graduate work at The Ohio State University. In Chapter 2, we introduce most of the necessary results, notation, techniques, and examples used in the reminder of this document, involving unitary tensor categories (UTC) and C*-2-categories. In Chapter 3 we introduce Q-Systems in a $\dag$-2-category and their bimodules, and define the Q-System completion of a $\dag$-2-category. We later prove $\rCorr,$ the C*-2-category of right C*-correspondences, is Q-System complete by constructing an inverse to the canonical embedding of $\rCorr$ into its Q-System completion $\QSys(\rCorr)$. In Chapter 4 we introduce generalized Temperley-Lieb-Jones ($\TLJ$) $\dag$-2-categories associated to weighted bidirected graphs, meant to represent lattices of inclusions of finite-index subfactors. We formally define unitary modules for these generalized $\TLJ$ $\dag$-2-categories as strong $\dag$-2-functors into $\BigHilb,$ the $\dag$-2-category of row-finite separable bigraded Hilbert spaces. We then classify these modules up to $\dag$-2-equivalence in terms of weighted bi-directed $\Gamma$-fair and balanced graphs, in the spirit of Yamagami's classification of fiber functors on $\TLJ(\delta)$ categories [Yam04], and De Commer and Yamashita's classification of unitary modules for ${\rm Rep(SU}_q(2))$ [DCY15]. In Chapter 5 we show that every UTC acts on some separable simple and monotracial C*-algebra, using diagrammatic, functional analytic and free probabilistic techniques. We construct a fully-faithful bi-involutive strong tensor functor onto a full subcategory of fgp bimodules over a simple exact separable unital monotracial C*-algebra. This C*-algebra is built solely from the category using the Guionnet-Jones-Shlyakhtenko construction introduced in [GJS11]. Proving the aforementioned properties of this functor involves a certain Hilbertification tensor functor, whose source is the UTC of finitely generated projective Hilbert C*-bimodules with certain tracial compatibilities, into the category of bi-finite spherical bimodules over an interpolated free group factor. The composite of these two functors recovers the UTC-action constructed in {BHP12].
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.
Symmetries Of Quantum Spaces
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Author : Piotr Podleś
language : en
Publisher:
Release Date : 1992
Symmetries Of Quantum Spaces written by Piotr Podleś and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Quantum Theory And Symmetries
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Author : Heinz Dietrich Doebner
language : en
Publisher: World Scientific
Release Date : 2000
Quantum Theory And Symmetries written by Heinz Dietrich Doebner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.
This volume gives an overview of the recent representative developments in relativistic and non-relativistic quantum theory, which are related to the application of various mathematical notions of various symmetries. These notions are centered upon groups, algebras and their generalizations, and are applied in interaction with topology, differential geometry, functional analysis and related fields. The emphasis is on results in the following areas: foundation of quantum physics, quantization methods, nonlinear quantum mechanics, algebraic quantum field theory, gauge and string theories, discrete spaces, quantum groups and generalized symmetries.
Construction Of Quantum Symmetries For Realistic Field Theories On Noncommutative Spaces
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Author : Florian Koch
language : en
Publisher:
Release Date : 2006
Construction Of Quantum Symmetries For Realistic Field Theories On Noncommutative Spaces written by Florian Koch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
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.
Quantum Groups And Noncommutative Spaces
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Author : Matilde Marcolli
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-02
Quantum Groups And Noncommutative Spaces written by Matilde Marcolli 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 2010-11-02 with Mathematics categories.
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.
Quantum Symmetries Proceedings Of The International Workshop On Mathematical Physics
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Author : Doebner Heinz-dietrich
language : en
Publisher: World Scientific
Release Date : 1993-10-29
Quantum Symmetries Proceedings Of The International Workshop On Mathematical Physics written by Doebner Heinz-dietrich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-29 with categories.
Quantum symmetry modelled through quantum group or its dual, quantum algebra, is a very active field of relevant physical and mathematical research stimulated often by physical intuition and with promising physical applications. This volume gives some information on the progress of this field during the years after the quantum group workshop in Clausthal 1989. Quantum symmetry is connected with very different approaches and views. The field is not yet coherent; there are different notions of quantum groups and of quantum algebras through algebraic deformations of groups and algebras. Hence its development has various directions following more special mathematical and physical interests.
Quantum Theory And Symmetries Procs Of The Second Intl Symp
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Author : Andrzej Horzela
language : en
Publisher: World Scientific
Release Date : 2002-06-26
Quantum Theory And Symmetries Procs Of The Second Intl Symp written by Andrzej Horzela and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-06-26 with Science categories.
This book presents the up-to-date status of quantum theory and the outlook for its development in the 21st century. The covered topics include basic problems of quantum physics, with emphasis on the foundations of quantum theory, quantum computing and control, quantum optics, coherent states and Wigner functions, as well as on methods of quantum physics based on Lie groups and algebras, quantum groups and noncommutative geometry.
Reflections On Quanta Symmetries And Supersymmetries
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Author : V.S. Varadarajan
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-20
Reflections On Quanta Symmetries And Supersymmetries written by V.S. Varadarajan 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 2011-05-20 with Mathematics categories.
This is a collection of essays based on lectures that author has given on various occasions on foundation of quantum theory, symmetries and representation theory, and the quantum theory of the superworld created by physicists. The lectures are linked by a unifying theme: how the quantum world and superworld appear under the lens of symmetry and supersymmetry. In the world of ultra-small times and distances such as the Planck length and Planck time, physicists believe no measurements are possible and so the structure of spacetime itself is an unknown that has to be first understood. There have been suggestions (Volovich hypothesis) that world geometry at such energy regimes is non-archimedian and some of the lectures explore the consequences of such a hypothesis. Ultimately, symmetries and supersymmetries are described by the representation of groups and supergroups. The author's interest in representation is a lifelong one and evolved slowly, and owes a great deal to conversations and discussions he had with George Mackey and Harish-Chandra. The book concludes with a retrospective look at these conversations.