Categories For Quantum Theory
DOWNLOAD
Download Categories For Quantum Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Categories For Quantum Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Categories For Quantum Theory
DOWNLOAD
Author : Chris Heunen
language : en
Publisher: Oxford University Press
Release Date : 2019-11-14
Categories For Quantum Theory written by Chris Heunen and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-14 with Mathematics categories.
Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition, and a conceptual way to understand many high-level quantum phenomena. This text lays the foundation for this categorical quantum mechanics, with an emphasis on the graphical calculus which makes computation intuitive. Biproducts and dual objects are introduced and used to model superposition and entanglement, with quantum teleportation studied abstractly using these structures. Monoids, Frobenius structures and Hopf algebras are described, and it is shown how they can be used to model classical information and complementary observables. The CP construction, a categorical tool to describe probabilistic quantum systems, is also investigated. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Prior knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text links with many other areas are highlighted, such as representation theory, topology, quantum algebra, knot theory, and probability theory, and nonstandard models are presented, such as sets and relations. All results are stated rigorously, and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.
Quantum Groups Quantum Categories And Quantum Field Theory
DOWNLOAD
Author : Jürg Fröhlich
language : en
Publisher: Springer
Release Date : 2006-11-15
Quantum Groups Quantum Categories And Quantum Field Theory written by Jürg Fröhlich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.
Quantum Theory Groups And Representations
DOWNLOAD
Author : Peter Woit
language : en
Publisher: Springer
Release Date : 2017-11-01
Quantum Theory Groups And Representations written by Peter Woit and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-01 with Science categories.
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.
Quantum Theory For Mathematicians
DOWNLOAD
Author : Brian C. Hall
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-19
Quantum Theory For Mathematicians written by Brian C. Hall 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 2013-06-19 with Science categories.
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.
A Guide To Quantum Groups
DOWNLOAD
Author : Vyjayanthi Chari
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-27
A Guide To Quantum Groups written by Vyjayanthi Chari and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-27 with Mathematics categories.
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.
Quantum Groups And Their Representations
DOWNLOAD
Author : Anatoli Klimyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantum Groups And Their Representations written by Anatoli Klimyk 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 2012-12-06 with Science categories.
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.
Introducing Quantum Theory
DOWNLOAD
Author : J.P. McEvoy
language : en
Publisher: Icon Books Ltd
Release Date : 2014-06-05
Introducing Quantum Theory written by J.P. McEvoy and has been published by Icon Books Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-05 with Science categories.
Quantum theory confronts us with bizarre paradoxes which contradict the logic of classical physics. At the subatomic level, one particle seems to know what the others are doing, and according to Heisenberg's "uncertainty principle", there is a limit on how accurately nature can be observed. And yet the theory is amazingly accurate and widely applied, explaining all of chemistry and most of physics. Introducing Quantum Theory takes us on a step-by-step tour with the key figures, including Planck, Einstein, Bohr, Heisenberg and Schrodinger. Each contributed at least one crucial concept to the theory. The puzzle of the wave-particle duality is here, along with descriptions of the two questions raised against Bohr's "Copenhagen Interpretation" - the famous "dead and alive cat" and the EPR paradox. Both remain unresolved.
Group Theory And Quantum Mechanics
DOWNLOAD
Author : Bartel L. van der Waerden
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Group Theory And Quantum Mechanics written by Bartel L. van der Waerden 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 2012-12-06 with Mathematics categories.
The German edition of this book appeared in 1932 under the title "Die gruppentheoretische Methode in der Quantenmechanik". Its aim was, to explain the fundamental notions of the Theory of Groups and their Representations, and the application of this theory to the Quantum Mechanics of Atoms and Molecules. The book was mainly written for the benefit of physicists who were supposed to be familiar with Quantum Mechanics. However, it turned out that it was also used by. mathematicians who wanted to learn Quantum Mechanics from it. Naturally, the physical parts were too difficult for mathematicians, whereas the mathematical parts were sometimes too difficult for physicists. The German language created an additional difficulty for many readers. In order to make the book more readable for physicists and mathe maticians alike, I have rewritten the whole volume. The changes are most notable in Chapters 1 and 6. In Chapter t, I have tried to give a mathematically rigorous exposition of the principles of Quantum Mechanics. This was possible because recent investigations in the theory of self-adjoint linear operators have made the mathematical foundation of Quantum Mechanics much clearer than it was in t 932. Chapter 6, on Molecule Spectra, was too much condensed in the German edition. I hope it is now easier to understand. In Chapter 2-5 too, numerous changes were made in order to make the book more readable and more useful.
Picturing Quantum Processes
DOWNLOAD
Author : Bob Coecke
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-16
Picturing Quantum Processes written by Bob Coecke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-16 with Computers categories.
Quantum phenomena are explained through the language of diagrams, setting out an innovative visual method of presenting complex scientific theories. Focusing on physical intuition over mathematical formalism, and packed with exercises, this unique book is accessible to students and researchers across scientific disciplines, from undergraduate to Ph.D. level.
Representation Theory Of Algebraic Groups And Quantum Groups
DOWNLOAD
Author : Toshiaki Shoji
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2004
Representation Theory Of Algebraic Groups And Quantum Groups written by Toshiaki Shoji and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.
A collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. This title presents an overview of developments in representation theory of algebraic groups and quantum groups. It includes papers containing results concerning Lusztig's conjecture on cells in affine Weyl groups.