Download or read book The Logic of Quantum Mechanics Volume 15 written by Enrico G. Beltrametti and published by Cambridge University Press. This book was released on 2010-12-09 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the logic, theory and mathematics of quantum mechanics in a clear and thorough way.
Download or read book An Introduction to Hilbert Space and Quantum Logic written by David W. Cohen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.
Download or read book The Logic of Quantum Mechanics Volume 15 written by Enrico G. Beltrametti and published by Cambridge University Press. This book was released on 2014-05-14 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the logic, theory and mathematics of quantum mechanics in a clear and thorough way.
Download or read book Quantum Mechanics written by Leonard Susskind and published by Basic Books (AZ). This book was released on 2014-02-25 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the bestselling author of The Theoretical Minimum, a DIY introduction to the math and science of quantum physics First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics. In this follow-up to The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics’ weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like The Theoretical Minimum, this volume runs parallel to Susskind’s eponymous Stanford University-hosted continuing education course. An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.
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 John von Neumann and the Foundations of Quantum Physics written by Miklós Rédei and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: John von Neumann (1903-1957) was undoubtedly one of the scientific geniuses of the 20th century. The main fields to which he contributed include various disciplines of pure and applied mathematics, mathematical and theoretical physics, logic, theoretical computer science, and computer architecture. Von Neumann was also actively involved in politics and science management and he had a major impact on US government decisions during, and especially after, the Second World War. There exist several popular books on his personality and various collections focusing on his achievements in mathematics, computer science, and economy. Strangely enough, to date no detailed appraisal of his seminal contributions to the mathematical foundations of quantum physics has appeared. Von Neumann's theory of measurement and his critique of hidden variables became the touchstone of most debates in the foundations of quantum mechanics. Today, his name also figures most prominently in the mathematically rigorous branches of contemporary quantum mechanics of large systems and quantum field theory. And finally - as one of his last lectures, published in this volume for the first time, shows - he considered the relation of quantum logic and quantum mechanical probability as his most important problem for the second half of the twentieth century. The present volume embraces both historical and systematic analyses of his methodology of mathematical physics, and of the various aspects of his work in the foundations of quantum physics, such as theory of measurement, quantum logic, and quantum mechanical entropy. The volume is rounded off by previously unpublished letters and lectures documenting von Neumann's thinking about quantum theory after his 1932 Mathematical Foundations of Quantum Mechanics. The general part of the Yearbook contains papers emerging from the Institute's annual lecture series and reviews of important publications of philosophy of science and its history.
Download or read book Quantum Probability Logic written by Meir Hemmo and published by Springer Nature. This book was released on 2020-04-07 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a broad perspective on the state of the art in the philosophy and conceptual foundations of quantum mechanics. Its essays take their starting point in the work and influence of Itamar Pitowsky, who has greatly influenced our understanding of what is characteristically non-classical about quantum probabilities and quantum logic, and this serves as a vantage point from which they reflect on key ongoing debates in the field. Readers will find a definitive and multi-faceted description of the major open questions in the foundations of quantum mechanics today, including: Is quantum mechanics a new theory of (contextual) probability? Should the quantum state be interpreted objectively or subjectively? How should probability be understood in the Everett interpretation of quantum mechanics? What are the limits of the physical implementation of computation? The impact of this volume goes beyond the exposition of Pitowsky’s influence: it provides a unique collection of essays by leading thinkers containing profound reflections on the field. Chapter 1. Classical logic, classical probability, and quantum mechanics (Samson Abramsky) Chapter 2. Why Scientific Realists Should Reject the Second Dogma of Quantum Mechanic (Valia Allori) Chapter 3. Unscrambling Subjective and Epistemic Probabilities (Guido Bacciagaluppi) Chapter 4. Wigner’s Friend as a Rational Agent (Veronika Baumann, Časlav Brukner) Chapter 5. Pitowsky's Epistemic Interpretation of Quantum Mechanics and the PBR Theorem (Yemima Ben-Menahem) Chapter 6. On the Mathematical Constitution and Explanation of Physical Facts (Joseph Berkovitz) Chapter 7. Everettian probabilities, the Deutsch-Wallace theorem and the Principal Principle (Harvey R. Brown, Gal Ben Porath) Chapter 8. ‘Two Dogmas’ Redu (Jeffrey Bub) Chapter 9. Physical Computability Theses (B. Jack Copeland, Oron Shagrir) Chapter 10. Agents in Healey’s Pragmatist Quantum Theory: A Comparison with Pitowsky’s Approach to Quantum Mechanics (Mauro Dorato) Chapter 11. Quantum Mechanics As a Theory of Observables and States and, Thereby, As a Theory of Probability (John Earman, Laura Ruetsche) Chapter 12. The Measurement Problem and two Dogmas about Quantum Mechanic (Laura Felline) Chapter 13. There Is More Than One Way to Skin a Cat: Quantum Information Principles In a Finite World(Amit Hagar) Chapter 14. Is Quantum Mechanics a New Theory of Probability? (Richard Healey) Chapter 15. Quantum Mechanics as a Theory of Probability (Meir Hemmo, Orly Shenker) Chapter 16. On the Three Types of Bell's Inequalities (Gábor Hofer-Szabó) Chapter 17. On the Descriptive Power of Probability Logic (Ehud Hrushovski) Chapter 18. The Argument against Quantum Computers (Gil Kalai) Chapter 19. Why a Relativistic Quantum Mechanical World Must be Indeterministic (Avi Levy, Meir Hemmo) Chapter 20. Subjectivists about Quantum Probabilities Should be Realists about Quantum States (Wayne C. Myrvold) Chapter 21. The Relativistic Einstein-Podolsky-Rosen Argument (Michael Redhead) Chapter 22. What price statistical independence? How Einstein missed the photon.(Simon Saunders) Chapter 23. How (Maximally) Contextual is Quantum Mechanics? (Andrew W. Simmons) Chapter 24. Roots and (Re)Sources of Value (In)Definiteness Versus Contextuality (Karl Svozil) Chapter 25: Schrödinger’s Reaction to the EPR Paper (Jos Uffink) Chapter 26. Derivations of the Born Rule (Lev Vaidman) Chapter 27. Dynamical States and the Conventionality of (Non-) Classicality (Alexander Wilce).
Download or read book Particles and Paradoxes written by Peter Gibbins and published by Cambridge University Press. This book was released on 1987-09-25 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum theory is our deepest theory of the nature of matter. It is a theory that, notoriously, produces results which challenge the laws of classical logic and suggests that the physical world is illogical. This book gives a critical review of work on the foundations of quantum mechanics at a level accessible to non-experts. Assuming his readers have some background in mathematics and physics, Peter Gibbins focuses on the questions of whether the results of quantum theory require us to abandon classical logic and whether quantum logic can resolve the paradoxes produced by quantum mechanics. He argues that quantum logic does not dispose of the problems faced by classical logic, that no reasonable interpretation of quantum mechanics in terms of 'hidden variables' can be found, and that after all these years quantum mechanics remains a mystery to us. Particles and Paradoxes provides a much-needed and valuable introduction to the philosophy of quantum mechanics and, at the same time, an example of just what it is to do the philosophy of physics.
Download or read book Handbook of Quantum Logic and Quantum Structures Quantum Logic written by and published by . This book was released on 2009 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 1975-09-30 with total page 638 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.
Download or read book Quantum Mechanics on Phase Space written by Franklin E. Schroeck Jr. and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, we shall present a new mathematical formulation of quantum theory, clarify a number of discrepancies within the prior formulation of quantum theory, give new applications to experiments in physics, and extend the realm of application of quantum theory well beyond physics. Here, we motivate this new formulation and sketch how it developed. Since the publication of Dirac's famous book on quantum mechanics [Dirac, 1930] and von Neumann's classic text on the mathematical foundations of quantum mechanics two years later [von Neumann, 1932], there have appeared a number of lines of development, the intent of each being to enrich quantum theory by extra polating or even modifying the original basic structure. These lines of development have seemed to go in different directions, the major directions of which are identified here: First is the introduction of group theoretical methods [Weyl, 1928; Wigner, 1931] with the natural extension to coherent state theory [Klauder and Sudarshan, 1968; Peremolov, 1971]. The call for an axiomatic approach to physics [Hilbert, 1900; Sixth Problem] led to the development of quantum logic [Mackey, 1963; Jauch, 1968; Varadarajan, 1968, 1970; Piron, 1976; Beltrametti & Cassinelli, 1981], to the creation of the operational approach [Ludwig, 1983-85, 1985; Davies, 1976] with its application to quantum communication theory [Helstrom, 1976; Holevo, 1982), and to the development of the C* approach [Emch, 1972]. An approach through stochastic differential equations ("stochastic mechanics") was developed [Nelson, 1964, 1966, 1967].
Download or read book Quantum Logic in Algebraic Approach written by Miklós Rédei and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic. The seminars were delivered during the first semester of the 1993/1994 academic year in the Unit for Foundations of Science of the Department of History and Foundations of Mathematics and Science, Faculty of Physics, Utrecht University, The Netherlands, while I was staying in that Unit on a European Community Research Grant, and in the Center for Philosophy of Science, University of Pittsburgh, U. S. A. , where I was staying during the 1994/1995 academic year as a Visiting Fellow on a Fulbright Research Grant, and where I also was supported by the Istvan Szechenyi Scholarship Foundation. The financial support provided by these foundations, by the Center for Philosophy of Science and by the European Community is greatly acknowledged, and I wish to thank D. Dieks, the professor of the Foundations Group in Utrecht and G. Massey, the director of the Center for Philosophy of Science in Pittsburgh for making my stay at the respective institutions possible. I also wish to thank both the members of the Foundations Group in Utrecht, especially D. Dieks, C. Lutz, F. Muller, J. Uffink and P. Vermaas and the participants in the seminars at the Center for Philosophy of Science in Pittsburgh, especially N. Belnap, J. Earman, A. Janis, J. Norton, and J.
Download or read book Linear Operators for Quantum Mechanics written by Thomas F. Jordan and published by Courier Corporation. This book was released on 2012-09-20 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this compact treatment examines linear space, functionals, and operators; diagonalizing operators; operator algebras; and equations of motion. 1969 edition.
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.
Download or read book Handbook of Quantum Logic and written by Kurt Engesser and published by Elsevier Science Limited. This book was released on 2007 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled “The logic of quantum mechanics? quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results. Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate. The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability. - Written by eminent scholars in the field of logic - A comprehensive presentation of the theory, approaches and results in the field of quantum logic - Volume focuses on quantum structures
Download or read book From Classical Mechanics To Quantum Field Theory A Tutorial written by Manuel Asorey and published by World Scientific. This book was released on 2020-01-14 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects an extended version of the lectures delivered by the authors at the Fall Workshop on Geometry and Physics in the years 2014, 2015, 2016.It aims at introducing advanced graduate and PhD students, as well as young researchers, to current research in mathematics and physics. In particular, it fills the gap between the more physical-oriented and the more mathematical-oriented literature on quantum theory. It introduces various approaches to methods of quantization, along with their impact on modern mathematical methods.
Download or read book Unconventional Models of Computation written by Christian Calude and published by Springer Science & Business Media. This book was released on 1998-02-01 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering recent research into unconventional methods of computing for disciplines in computer science, mathematics, biology, physics and philosophy, the subjects include: nonconventional computational methods, DNA computation, quantum computation, and beyong Turing computability; new methods of discrete computation; theoretical and conceptual new computational paradigms; practical knowledge on new computing technologies.
