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.
Download or read book A Guide to Quantum Groups written by Vyjayanthi Chari and published by . This book was released on 1995 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Quantum Groups written by George Lusztig and published by Springer Science & Business Media. This book was released on 2010-10-27 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.
Download or read book Quantum Groups written by Christian Kassel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.
Download or read book Foundations of Quantum Group Theory written by Shahn Majid and published by Cambridge University Press. This book was released on 2000 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate level text which systematically lays out the foundations of Quantum Groups.
Download or read book Lectures on Quantum Groups written by Pavel I. Etingof and published by . This book was released on 2010 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Download or read book Quantum Groups written by Ross Street and published by Cambridge University Press. This book was released on 2007-01-18 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.
Download or read book Quantum Theory for Mathematicians written by Brian C. Hall and published by Springer Science & Business Media. This book was released on 2013-06-19 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.
Download or read book Quantum Theory Groups and Representations written by Peter Woit and published by Springer. This book was released on 2017-11-01 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
Download or read book Quantum Steampunk written by Nicole Yunger Halpern and published by JHU Press. This book was released on 2022-04-12 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The science-fiction genre known as steampunk juxtaposes futuristic technologies with Victorian settings. This fantasy is becoming reality at the intersection of two scientific fields-twenty-first-century quantum physics and nineteenth-century thermodynamics, or the study of energy-in a discipline known as quantum steampunk"--
Download or read book Advanced Quantum Mechanics written by Yuli V. Nazarov and published by Cambridge University Press. This book was released on 2013-01-03 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to advanced quantum theory, this textbook focuses on its practical applications and is ideal for graduate students in physics.
Download or read book Ultimate Zero and One written by Colin P. Williams and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: As miniaturisation deepens, and nanotechnology and its machines become more prevalent in the real world, the need to consider using quantum mechanical concepts to perform various tasks in computation increases. Such tasks include: the teleporting of information, breaking heretofore "unbreakable" codes, communicating with messages that betray eavesdropping, and the generation of random numbers. This is the first book to apply quantum physics to the basic operations of a computer, representing the ideal vehicle for explaining the complexities of quantum mechanics to students, researchers and computer engineers, alike, as they prepare to design and create the computing and information delivery systems for the future. Both authors have solid backgrounds in the subject matter at the theoretical and more practical level. While serving as a text for senior/grad level students in computer science/physics/engineering, this book has its primary use as an up-to-date reference work in the emerging interdisciplinary field of quantum computing - the only prerequisite being knowledge of calculus and familiarity with the concept of the Turing machine.
Download or read book Assimilated Cuban s Guide to Quantum Santeria written by Carlos Hernandez and published by Rosarium Publishing. This book was released on 2016-01-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: A quirky collection of short sci-fi stories for fans of Kij Johnson and Kelly Link Assimilation is founded on surrender and being broken; this collection of short stories features people who have assimilated, but are actively trying to reclaim their lives. There is a concert pianist who defies death by uploading his soul into his piano. There is the person who draws his mother's ghost out of the bullet hole in the wall near where she was executed. Another character has a horn growing out of the center of his forehead—punishment for an affair. But he is too weak to end it, too much in love to be moral. Another story recounts a panda breeder looking for tips. And then there's a border patrol agent trying to figure out how to process undocumented visitors from another galaxy. Poignant by way of funny, and philosophical by way of grotesque, Hernandez's stories are prayers for self-sovereignty.
Download or read book Quantum Groups and Their Representations written by Anatoli Klimyk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
Download or read book A Group Theoretical Approach to Quantum Optics written by Andrei B. Klimov and published by John Wiley & Sons. This book was released on 2009-08-04 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by major contributors to the field who are well known within the community, this is the first comprehensive summary of the many results generated by this approach to quantum optics to date. As such, the book analyses selected topics of quantum optics, focusing on atom-field interactions from a group-theoretical perspective, while discussing the principal quantum optics models using algebraic language. The overall result is a clear demonstration of the advantages of applying algebraic methods to quantum optics problems, illustrated by a number of end-of-chapter problems. An invaluable source for atomic physicists, graduates and students in physics.
Download or read book Three Roads To Quantum Gravity written by Lee Smolin and published by Basic Books. This book was released on 2008-03-18 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: "It would be hard to imagine a better guide to this difficult subject." -- Scientific American In Three Roads to Quantum Gravity, Lee Smolin provides an accessible overview of the attempts to build a final "theory of everything." He explains in simple terms what scientists are talking about when they say the world is made from exotic entities such as loops, strings, and black holes and tells the fascinating stories behind these discoveries: the rivalries, epiphanies, and intrigues he witnessed firsthand. "Provocative, original, and unsettling." -- The New York Review of Books "An excellent writer, a creative thinker." -- Nature
