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Quantum Theory And Sets
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Book Synopsis Quantum Theory & Sets by : Alexander P. M. van den Bosch
Download or read book Quantum Theory & Sets written by Alexander P. M. van den Bosch and published by Lulu.com. This book was released on 2017-12-16 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: In dit bereik van deze zaken zien we dit, een q.mech met geen quantum flux, maar heel normaal een tuple set in een strech.. een aantal var.'s van alle Dirac functies & Schrodinger. en een BOOM van alternatieve routes door over die tuple strech gezet.. als een modale logica Kripke structuur. Quantum theory & Sets
Book Synopsis Linear Algebra for Quantum Theory by : Per-Olov Löwdin
Download or read book Linear Algebra for Quantum Theory written by Per-Olov Löwdin and published by Wiley-Interscience. This book was released on 1998-04-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essential mathematical tools for the study of modern quantumtheory. Linear Algebra for Quantum Theory offers an excellent survey ofthose aspects of set theory and the theory of linear spaces andtheir mappings that are indispensable to the study of quantumtheory. Unlike more conventional treatments, this text postponesits discussion of the binary product concept until later chapters,thus allowing many important properties of the mappings to bederived without it. The book begins with a thorough exploration of set theoryfundamentals, including mappings, cardinalities of sets, andarithmetic and theory of complex numbers. Next is an introductionto linear spaces, with coverage of linear operators, eigenvalue andthe stability problem of linear operators, and matrices withspecial properties. Material on binary product spaces features self-adjoint operatorsin a space of indefinite metric, binary product spaces with apositive definite metric, properties of the Hilbert space, andmore. The final section is devoted to axioms of quantum theoryformulated as trace algebra. Throughout, chapter-end problem setshelp reinforce absorption of the material while letting readerstest their problem-solving skills. Ideal for advanced undergraduate and graduate students intheoretical and computational chemistry and physics, Linear Algebrafor Quantum Theory provides the mathematical means necessary toaccess and understand the complex world of quantum theory.
Book Synopsis Categories for Quantum Theory by : Chris Heunen
Download or read book Categories for Quantum Theory written by Chris Heunen and published by Oxford University Press, USA. This book was released on 2019-09-30 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory by : Felix Lev
Download or read book Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory written by Felix Lev and published by Springer Nature. This book was released on 2020-11-03 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book delves into finite mathematics and its application in physics, particularly quantum theory. It is shown that quantum theory based on finite mathematics is more general than standard quantum theory, whilst finite mathematics is itself more general than standard mathematics.As a consequence, the mathematics describing nature at the most fundamental level involves only a finite number of numbers while the notions of limit, infinite/infinitesimal and continuity are needed only in calculations that describe nature approximately. It is also shown that the concepts of particle and antiparticle are likewise approximate notions, valid only in special situations, and that the electric charge and baryon- and lepton quantum numbers can be only approximately conserved.
Book Synopsis Hilbert Space Operators in Quantum Physics by : Jirí Blank
Download or read book Hilbert Space Operators in Quantum Physics written by Jirí Blank and published by Springer Science & Business Media. This book was released on 2008-09-24 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.
Book Synopsis Mathematical Foundations of Quantum Theory by : A.R. Marlow
Download or read book Mathematical Foundations of Quantum Theory written by A.R. Marlow and published by Elsevier. This book was released on 2012-12-02 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fundamental quantum theory must deal, and then some unsolved problems in the quantum logic approach to the foundations of quantum mechanics are considered. Considerable chapters cover topics on manuals and logics for quantum mechanics. This book also examines the problems in quantum logic, and then presents examples of their interpretation and relevance to nonclassical logic and statistics. The accommodation of conventional Fermi-Dirac and Bose-Einstein statistics in quantum mechanics or quantum field theory is illustrated. The final chapters of the book present a system of axioms for nonrelativistic quantum mechanics, with particular emphasis on the role of density operators as states. Specific connections of this theory with other formulations of quantum theory are also considered. These chapters also deal with the determination of the state of an elementary quantum mechanical system by the associated position and momentum distribution. This book is of value to physicists, mathematicians, and researchers who are interested in quantum theory.
Book Synopsis Probability and Finance by : Glenn Shafer
Download or read book Probability and Finance written by Glenn Shafer and published by John Wiley & Sons. This book was released on 2005-02-25 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a foundation for probability based on game theory rather than measure theory. A strong philosophical approach with practical applications. Presents in-depth coverage of classical probability theory as well as new theory.
Book Synopsis Quantum Theory, Groups and Representations by : Peter Woit
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 659 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.
Book Synopsis Quantum Mechanics for Mathematicians by : Leon Armenovich Takhtadzhi͡an
Download or read book Quantum Mechanics for Mathematicians written by Leon Armenovich Takhtadzhi͡an and published by American Mathematical Soc.. This book was released on 2008 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.
Book Synopsis Quantum Structures and the Nature of Reality by : Diederik Aerts
Download or read book Quantum Structures and the Nature of Reality written by Diederik Aerts and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Structures and the Nature of Reality is a collection of papers written for an interdisciplinary audience about the quantum structure research within the International Quantum Structures Association. The advent of quantum mechanics has changed our scientific worldview in a fundamental way. Many popular and semi-popular books have been published about the paradoxical aspects of quantum mechanics. Usually, however, these reflections find their origin in the standard views on quantum mechanics, most of all the wave-particle duality picture. Contrary to relativity theory, where the meaning of its revolutionary ideas was linked from the start with deep structural changes in the geometrical nature of our world, the deep structural changes about the nature of our reality that are indicated by quantum mechanics cannot be traced within the standard formulation. The study of the structure of quantum theory, its logical content, its axiomatic foundation, has been motivated primarily by the search for their structural changes. Due to the high mathematical sophistication of this quantum structure research, no books have been published which try to explain the recent results for an interdisciplinary audience. This book tries to fill this gap by collecting contributions from some of the main researchers in the field. They reveal the steps that have been taken towards a deeper structural understanding of quantum theory.
Book Synopsis Quantum Theory and Sets by : Alexander P. M. van den Bosch
Download or read book Quantum Theory and Sets written by Alexander P. M. van den Bosch and published by . This book was released on 2017-07-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We find here a compilation of the authors recent up following books on his enactment of how to refresh representation of Quant. Mech. and FT/Q.Flux with a surprise. With many many examples. This bundle contains the earlier books: The Super Station, So Far no Good, Rain Weaver, The Dark Window, The Real Deal, QFST, Strangeness in QFT, Quantum State Theory, The Quantum Space Realigned, The river runs dry, The Sandman, Game, The Show, The Thing, So Long & Thanks for all the Fish, Going Outside. Full of examples from diff. computer implementations. For this second Edition: The Steering in Clearing, a prayer doc to round this investigation to a new start in industrial research. The upside: the new content in the introduction about the involvement of consciousness as a bit-string of act & observation choices of the organism / drugs and larger molecules / Turing Machines, as a basis of collapsers of the wave, the state tuple. Consciousness as a wave that collapses a wave, that's different and new. Fundamentally.
Book Synopsis Quantum Theory for Mathematicians by : Brian C. Hall
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.
Book Synopsis The General Principles of Quantum Theory by : George Temple
Download or read book The General Principles of Quantum Theory written by George Temple and published by Routledge. This book was released on 2014-04-29 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published in 1934, this monograph was one of the first introductory accounts of the principles which form the physical basis of the Quantum Theory, considered as a branch of mathematics. The exposition is restricted to a discussion of general principles and does not attempt detailed application to the wide domain of atomic physics, although a number of special problems are considered in elucidation of the principles. The necessary fundamental mathematical methods – the theory of linear operators and of matrics – are developed in the first chapter so this could introduce anyone to the new theory. This is an interesting snapshot of scientific history.
Book Synopsis A First Course in Topos Quantum Theory by : Cecilia Flori
Download or read book A First Course in Topos Quantum Theory written by Cecilia Flori and published by Springer. This book was released on 2013-03-27 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory’s unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity. The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory? A possible way to overcome critical issues in present-day quantum physics – such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility of talking about systems without reference to an external observer – is through a reformulation of quantum theory in terms of a different mathematical framework called topos theory. This course-tested primer sets out to explain to graduate students and newcomers to the field alike, the reasons for choosing topos theory to resolve the above-mentioned issues and how it brings quantum physics back to looking more like a “neo-realist” classical physics theory again.
Book Synopsis The Logico-Algebraic Approach to Quantum Mechanics by : C.A. Hooker
Download or read book The Logico-Algebraic Approach to Quantum Mechanics written by C.A. Hooker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twentieth century has witnessed a striking transformation in the un derstanding of the theories of mathematical physics. There has emerged clearly the idea that physical theories are significantly characterized by their abstract mathematical structure. This is in opposition to the tradi tional opinion that one should look to the specific applications of a theory in order to understand it. One might with reason now espouse the view that to understand the deeper character of a theory one must know its abstract structure and understand the significance of that struc ture, while to understand how a theory might be modified in light of its experimental inadequacies one must be intimately acquainted with how it is applied. Quantum theory itself has gone through a development this century which illustrates strikingly the shifting perspective. From a collection of intuitive physical maneuvers under Bohr, through a formative stage in which the mathematical framework was bifurcated (between Schrödinger and Heisenberg) to an elegant culmination in von Neumann's Hilbert space formulation the elementary theory moved, flanked even at the later stage by the ill-understood formalisms for the relativistic version and for the field-theoretic altemative; after that we have a gradual, but constant, elaboration of all these quantal theories as abstract mathematical struc tures (their point of departure being von Neumann's formalism) until at the present time theoretical work is heavily preoccupied with the manip ulation of purely abstract structures.
Book Synopsis Quantum Theory of Collective Phenomena by : G. L. Sewell
Download or read book Quantum Theory of Collective Phenomena written by G. L. Sewell and published by Oxford University Press, USA. This book was released on 1986 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study provides a systematic approach to the quantum theory of collective phenomena, based principally on the model of infinite systems. The author sets the theory within the framework of modern statistical mechanics, formulating it in rigorous, though relatively simple, mathematical terms. This approach leads to a generalized form of statistical thermodynamics, and to useful characterizations of such collective phenomena as phase transitions, irreversibility, and metastability, going beyond the scope of traditional statistical mechanics of finite systems.
Book Synopsis Quantum Paradoxes by : Yakir Aharonov
Download or read book Quantum Paradoxes written by Yakir Aharonov and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Guide through the Mysteries of Quantum Physics! Yakir Aharonov is one of the pioneers in measuring theory, the nature of quantum correlations, superselection rules, and geometric phases and has been awarded numerous scientific honors. The author has contributed monumental concepts to theoretical physics, especially the Aharonov-Bohm effect and the Aharonov-Casher effect. Together with Daniel Rohrlich, Israel, he has written a pioneering work on the remaining mysteries of quantum mechanics. From the perspective of a preeminent researcher in the fundamental aspects of quantum mechanics, the text combines mathematical rigor with penetrating and concise language. More than 200 exercises introduce readers to the concepts and implications of quantum mechanics that have arisen from the experimental results of the recent two decades. With students as well as researchers in mind, the authors give an insight into that part of the field, which led Feynman to declare that "nobody understands quantum mechanics". * Free solutions manual available for lecturers at www.wiley-vch.de/supplements/
