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Author: Chris Heunen
Publisher: Oxford University Press
ISBN: 0191060062
Category : Mathematics
Languages : en
Pages : 320
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Book Description
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.
Author: Chris Heunen
Publisher: Oxford University Press
ISBN: 0191060062
Category : Mathematics
Languages : en
Pages : 320
Get Book Here
Book Description
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.
Author: Jürg Fröhlich
Publisher: Springer
ISBN: 3540476113
Category : Mathematics
Languages : en
Pages : 438
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Book Description
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.
Author: Peter Woit
Publisher: Springer
ISBN: 3319646125
Category : Science
Languages : en
Pages : 659
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Book Description
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.
Author: Tim Maudlin
Publisher: Princeton University Press
ISBN: 069118352X
Category : Philosophy
Languages : en
Pages : 249
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Book Description
A sophisticated and original introduction to the philosophy of quantum mechanics from one of the world’s leading philosophers of physics In this book, Tim Maudlin, one of the world’s leading philosophers of physics, offers a sophisticated, original introduction to the philosophy of quantum mechanics. The briefest, clearest, and most refined account of his influential approach to the subject, the book will be invaluable to all students of philosophy and physics. Quantum mechanics holds a unique place in the history of physics. It has produced the most accurate predictions of any scientific theory, but, more astonishing, there has never been any agreement about what the theory implies about physical reality. Maudlin argues that the very term “quantum theory” is a misnomer. A proper physical theory should clearly describe what is there and what it does—yet standard textbooks present quantum mechanics as a predictive recipe in search of a physical theory. In contrast, Maudlin explores three proper theories that recover the quantum predictions: the indeterministic wavefunction collapse theory of Ghirardi, Rimini, and Weber; the deterministic particle theory of deBroglie and Bohm; and the conceptually challenging Many Worlds theory of Everett. Each offers a radically different proposal for the nature of physical reality, but Maudlin shows that none of them are what they are generally taken to be.
Author: Bob Coecke
Publisher: Cambridge University Press
ISBN: 1108107710
Category : Science
Languages : en
Pages : 847
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Book Description
The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. Requiring only basic mathematical literacy, this book employs a unique formalism that builds an intuitive understanding of quantum features while eliminating the need for complex calculations. This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations. Written in an entertaining and user-friendly style and including more than one hundred exercises, this book is an ideal first course in quantum theory, foundations, and computation for students from undergraduate to PhD level, as well as an opportunity for researchers from a broad range of fields, from physics to biology, linguistics, and cognitive science, to discover a new set of tools for studying processes and interaction.
Author: J.M. Jauch
Publisher: Indiana University Press
ISBN: 9780253205452
Category : Science
Languages : en
Pages : 140
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Book Description
**** A reprint of the 1974 Indiana edition with a new foreword by Douglas R. Hofstadter. It is a non-mathematical book, engagingly written, and intended to lead the lay reader to an understanding of quantum theory. Also available in paper binding at $7.95. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Marek Kuś
Publisher: Springer Nature
ISBN: 3030308960
Category : Science
Languages : en
Pages : 139
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Book Description
The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations. Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science.
Author: Steven Holzner
Publisher: John Wiley & Sons
ISBN: 111846088X
Category : Science
Languages : en
Pages : 339
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Book Description
Your plain-English guide to understanding and working with the micro world Quantum Physics For Dummies, Revised Edition helps make quantum physics understandable and accessible. From what quantum physics can do for the world to understanding hydrogen atoms, readers will get complete coverage of the subject, along with numerous examples to help them tackle the tough equations. Compatible with classroom text books and courses, Quantum Physics For Dummies, Revised Edition lets students study at their own paces and helps them prepare for graduate or professional exams. Coverage includes: The Schrodinger Equation and its Applications The Foundations of Quantum Physics Vector Notation Spin Scattering Theory, Angular Momentum, and more Quantum physics — also called quantum mechanics or quantum field theory — can be daunting for even the most dedicated student or enthusiast of science, math, or physics. This friendly, concise guide makes this challenging subject understandable and accessible, from atoms to particles to gases and beyond. Plus, it's packed with fully explained examples to help you tackle the tricky equations like a pro! Compatible with any classroom course — study at your own pace and prepare for graduate or professional exams Your journey begins here — understand what quantum physics is and what kinds of problems it can solve Know the basic math — from state vectors to quantum matrix manipulations, get the foundation you need to proceed Put quantum physics to work — make sense of Schrödinger's equation and handle particles bound in square wells and harmonic oscillators Solve problems in three dimensions — use the full operators to handle wave functions and eigenvectors to find the natural wave functions of a system Discover the latest research — learn the cutting-edge quantum physics theories that aim to explain the universe itself
Author: Anatoli Klimyk
Publisher: Springer Science & Business Media
ISBN: 3642608965
Category : Science
Languages : en
Pages : 568
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Book Description
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.
Author: Volker Liermann
Publisher: Springer Nature
ISBN: 3030788296
Category : Business & Economics
Languages : en
Pages : 362
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Book Description
This book, the second one of three volumes, gives practical examples by a number of use cases showing how to take first steps in the digital journey of banks and insurance companies. The angle shifts over the volumes from a business-driven approach in “Disruption and DNA” to a strong technical focus in “Data Storage, Processing and Analysis”, leaving “Digitalization and Machine Learning Applications” with the business and technical aspects in-between. This second volume mainly emphasizes use cases as well as the methods and technologies applied to drive digital transformation (such as processes, leveraging computational power and machine learning models).
