Quantum Groups Formalism And Applications

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Quantum Groups and Their Applications in Physics

Author : Leonardo Castellani
Publisher : IOS Press
ISBN 13 : 9789051992472
Total Pages : 950 pages
Book Rating : 4.9/5 (924 download)

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Book Synopsis Quantum Groups and Their Applications in Physics by : Leonardo Castellani

Download or read book Quantum Groups and Their Applications in Physics written by Leonardo Castellani and published by IOS Press. This book was released on 1996 with total page 950 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on quantum groups, i.e., continuous deformations of Lie groups, and their applications in physics. These algebraic structures have been studied in the last decade by a growing number of mathematicians and physicists, and are found to underlie many physical systems of interest. They do provide, in fact, a sort of common algebraic ground for seemingly very different physical problems. As it has happened for supersymmetry, the q-group symmetries are bound to play a vital role in physics, even in fundamental theories like gauge theory or gravity. In fact q-symmetry can be considered itself as a generalization of supersymmetry, evident in the q-commutator formulation. The hope that field theories on q-groups are naturally reguralized begins to appear founded, and opens new perspectives for quantum gravity. The topics covered in this book include: conformal field theories and quantum groups, gauge theories of quantum groups, anyons, differential calculus on quantum groups and non-commutative geometry, poisson algebras, 2-dimensional statistical models, (2+1) quantum gravity, quantum groups and lattice physics, inhomogeneous q-groups, q-Poincaregroup and deformed gravity and gauging of W-algebras.

Quantum Groups

Author : Vladimir K. Dobrev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110427788
Total Pages : 450 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Quantum Groups by : Vladimir K. Dobrev

Download or read book Quantum Groups written by Vladimir K. Dobrev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-07-10 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies

From Field Theory to Quantum Groups

Author : Bernard Jancewicz
Publisher : World Scientific
ISBN 13 : 981022544X
Total Pages : 351 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis From Field Theory to Quantum Groups by : Bernard Jancewicz

Download or read book From Field Theory to Quantum Groups written by Bernard Jancewicz and published by World Scientific. This book was released on 1996 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Jerzy Lukierski, an outstanding specialist in the domain of quantum groups, will reach on May 21, 1995 the age of sixty. This is a birthday volume dedicated to him. It assumes the form of a collection of papers on a wide range of topics in modern research area from theoretical high energy physics to mathematical physics. Various topics of quantum groups will be treated with a special emphasis. Quantum groups is nowadays a very fashionable subject both in mathematics and high energy physics.

Quantum Groups in Two-Dimensional Physics

Author : Cisar Gómez
Publisher : Cambridge University Press
ISBN 13 : 0521460654
Total Pages : 477 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Quantum Groups in Two-Dimensional Physics by : Cisar Gómez

Download or read book Quantum Groups in Two-Dimensional Physics written by Cisar Gómez and published by Cambridge University Press. This book was released on 1996-04-18 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 1996 introduction to integrability and conformal field theory in two dimensions using quantum groups.

Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups

Author : Ludwig Pittner
Publisher : Springer Science & Business Media
ISBN 13 : 3540478019
Total Pages : 476 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups by : Ludwig Pittner

Download or read book Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups written by Ludwig Pittner and published by Springer Science & Business Media. This book was released on 2009-01-29 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum groups and quantum algebras as well as non-commutative differential geometry are important in mathematics and considered to be useful tools for model building in statistical and quantum physics. This book, addressing scientists and postgraduates, contains a detailed and rather complete presentation of the algebraic framework. Introductory chapters deal with background material such as Lie and Hopf superalgebras, Lie super-bialgebras, or formal power series. Great care was taken to present a reliable collection of formulae and to unify the notation, making this volume a useful work of reference for mathematicians and mathematical physicists.

Proceedings of the Second International Symposium on Quantum Theory and Symmetries

Author : Edward Kapuścik
Publisher : World Scientific
ISBN 13 : 9789812777850
Total Pages : 656 pages
Book Rating : 4.7/5 (778 download)

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Book Synopsis Proceedings of the Second International Symposium on Quantum Theory and Symmetries by : Edward Kapuścik

Download or read book Proceedings of the Second International Symposium on Quantum Theory and Symmetries written by Edward Kapuścik and published by World Scientific. This book was released on 2002 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Theory and Applications of the Poincaré Group

Author : Young Suh Kim
Publisher : Springer Science & Business Media
ISBN 13 : 9400945582
Total Pages : 346 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Theory and Applications of the Poincaré Group by : Young Suh Kim

Download or read book Theory and Applications of the Poincaré Group written by Young Suh Kim and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special relativity and quantum mechanics, formulated early in the twentieth century, are the two most important scientific languages and are likely to remain so for many years to come. In the 1920's, when quantum mechanics was developed, the most pressing theoretical problem was how to make it consistent with special relativity. In the 1980's, this is still the most pressing problem. The only difference is that the situation is more urgent now than before, because of the significant quantity of experimental data which need to be explained in terms of both quantum mechanics and special relativity. In unifying the concepts and algorithms of quantum mechanics and special relativity, it is important to realize that the underlying scientific language for both disciplines is that of group theory. The role of group theory in quantum mechanics is well known. The same is true for special relativity. Therefore, the most effective approach to the problem of unifying these two important theories is to develop a group theory which can accommodate both special relativity and quantum mechanics. As is well known, Eugene P. Wigner is one of the pioneers in developing group theoretical approaches to relativistic quantum mechanics. His 1939 paper on the inhomogeneous Lorentz group laid the foundation for this important research line. It is generally agreed that this paper was somewhat ahead of its time in 1939, and that contemporary physicists must continue to make real efforts to appreciate fully the content of this classic work.

Contextual Approach to Quantum Formalism

Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
ISBN 13 : 1402095937
Total Pages : 354 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Contextual Approach to Quantum Formalism by : Andrei Y. Khrennikov

Download or read book Contextual Approach to Quantum Formalism written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell’s theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed.

Introduction to Quantum Groups

Author : Masud Chaichian
Publisher : World Scientific
ISBN 13 : 9789810226237
Total Pages : 362 pages
Book Rating : 4.2/5 (262 download)

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Book Synopsis Introduction to Quantum Groups by : Masud Chaichian

Download or read book Introduction to Quantum Groups written by Masud Chaichian and published by World Scientific. This book was released on 1996 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade there has been an extemely rapid growth in the interest and development of quantum group theory.This book provides students and researchers with a practical introduction to the principal ideas of quantum groups theory and its applications to quantum mechanical and modern field theory problems. It begins with a review of, and introduction to, the mathematical aspects of quantum deformation of classical groups, Lie algebras and related objects (algebras of functions on spaces, differential and integral calculi). In the subsequent chapters the richness of mathematical structure and power of the quantum deformation methods and non-commutative geometry is illustrated on the different examples starting from the simplest quantum mechanical system — harmonic oscillator and ending with actual problems of modern field theory, such as the attempts to construct lattice-like regularization consistent with space-time Poincaré symmetry and to incorporate Higgs fields in the general geometrical frame of gauge theories. Graduate students and researchers studying the problems of quantum field theory, particle physics and mathematical aspects of quantum symmetries will find the book of interest.

Quantum Groups and Quantum Spaces

Author : Robert Budzyński
Publisher :
ISBN 13 :
Total Pages : 452 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Quantum Groups and Quantum Spaces by : Robert Budzyński

Download or read book Quantum Groups and Quantum Spaces written by Robert Budzyński and published by . This book was released on 1997 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Quantum Groups

Author : Teo Banica
Publisher : Springer Nature
ISBN 13 : 3031238176
Total Pages : 428 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Introduction to Quantum Groups by : Teo Banica

Download or read book Introduction to Quantum Groups written by Teo Banica and published by Springer Nature. This book was released on 2023-01-01 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Generalized Coherent States and Their Applications

Author : Askold Perelomov
Publisher : Springer Science & Business Media
ISBN 13 : 3642616291
Total Pages : 323 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Generalized Coherent States and Their Applications by : Askold Perelomov

Download or read book Generalized Coherent States and Their Applications written by Askold Perelomov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph treats an extensively developed field in modern mathematical physics - the theory of generalized coherent states and their applications to various physical problems. Coherent states, introduced originally by Schrodinger and von Neumann, were later employed by Glauber for a quantal description of laser light beams. The concept was generalized by the author for an arbitrary Lie group. In the last decade the formalism has been widely applied to various domains of theoretical physics and mathematics. The area of applications of generalized coherent states is very wide, and a comprehensive exposition of the results in the field would be helpful. This monograph is the first attempt toward this aim. My purpose was to compile and expound systematically the vast amount of material dealing with the coherent states and available through numerous journal articles. The book is based on a number of undergraduate and postgraduate courses I delivered at the Moscow Physico-Technical Institute. In its present form it is intended for professional mathematicians and theoretical physicists; it may also be useful for university students of mathematics and physics. In Part I the formalism is elaborated and explained for some of the simplest typical groups. Part II contains more sophisticated material; arbitrary Lie groups and symmetrical spaces are considered. A number of examples from various areas of theoretical and mathematical physics illustrate advantages of this approach, in Part III. It is a pleasure for me to thank Dr. Yu. Danilov for many useful remarks.

Quantum Groups and Lie Theory

Author : Andrew Pressley
Publisher : Cambridge University Press
ISBN 13 : 9781139437028
Total Pages : 246 pages
Book Rating : 4.4/5 (37 download)

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Book Synopsis Quantum Groups and Lie Theory by : Andrew Pressley

Download or read book Quantum Groups and Lie Theory written by Andrew Pressley and published by Cambridge University Press. This book was released on 2002-01-17 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises an overview of the material presented at the 1999 Durham Symposium on Quantum Groups and includes contributions from many of the world's leading figures in this area. It will be of interest to researchers and will also be useful as a reference text for graduate courses.

Proceedings of XIV Max Born Symposium, New Symmetries and Integrable Models

Author : Andrzej Frydryszak
Publisher : World Scientific
ISBN 13 : 9789810242701
Total Pages : 264 pages
Book Rating : 4.2/5 (427 download)

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Book Synopsis Proceedings of XIV Max Born Symposium, New Symmetries and Integrable Models by : Andrzej Frydryszak

Download or read book Proceedings of XIV Max Born Symposium, New Symmetries and Integrable Models written by Andrzej Frydryszak and published by World Scientific. This book was released on 2000 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Max Born Symposia started in 1991 and have been held once or twice a year in different places in Lower Silesia. The scientific topics of the Symposia are closely related with front-line research subjects in theoretical physics. This volume deals with new concepts of symmetries in the theory of fundamental intersections as well as integrable dynamical systems.

A Guide to Quantum Groups

Author : Vyjayanthi Chari
Publisher : Cambridge University Press
ISBN 13 : 9780521558846
Total Pages : 672 pages
Book Rating : 4.5/5 (588 download)

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Book Synopsis A Guide to Quantum Groups by : Vyjayanthi Chari

Download or read book A Guide to Quantum Groups written by Vyjayanthi Chari and published by Cambridge University Press. This book was released on 1995-07-27 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory, and has thrown new light on many different topics, notably low-dimensional topology and conformal field theory. The goal of this book is to give a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Thus this book can serve both as an introduction for the newcomer, and as a guide for the more experienced reader. All who have an interest in the subject will welcome this unique treatment of quantum groups.

Journal of Physics A

Author :
Publisher :
ISBN 13 :
Total Pages : 472 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Journal of Physics A by :

Download or read book Journal of Physics A written by and published by . This book was released on 1999 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on fundamental mathematical and computational methods underpinning physics. Relevant to statistical physics, chaotic and complex systems, classical and quantum mechanics, classical and quantum integrable systems and classical and quantum field theory.

Symmetry And Structural Properties Of Condensed Matter - Proceedings Of The 5th International School On Theoretical Physics

Author : Tadeusz Lulek
Publisher : World Scientific
ISBN 13 : 9814543632
Total Pages : 494 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Symmetry And Structural Properties Of Condensed Matter - Proceedings Of The 5th International School On Theoretical Physics by : Tadeusz Lulek

Download or read book Symmetry And Structural Properties Of Condensed Matter - Proceedings Of The 5th International School On Theoretical Physics written by Tadeusz Lulek and published by World Scientific. This book was released on 1999-10-15 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume continues the series of proceedings of summer schools on theoretical physics which aim at an adequate description of the structure of condensed matter in terms of sophisticated, advanced mathematical tools. This time, the main emphasis is put on the question of whether (and when) the energy bands in solids are continuous. Profs. L Michel, J Zak and others consider the origin, existence and continuity of band structure. Also, some previously discussed problems (magnetic symmetry, flux quantization, statistics, quasicrystals, the Bethe ansatz) are pursued further, and appropriate mathematical tools, rooted in “actions of groups on sets”, are developed.