Download or read book Measures and Hilbert Lattices written by Gudrun Kalmbach and published by World Scientific Publishing Company Incorporated. This book was released on 1986 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has two parts. In section 1 to 6 classical measure theory is extended to the theory of measures and states on orthomodular lattices. In section 7 to 12 of this book special properties of complete orthomodular lattices are investigated and characterizations of factors and Hilbert lattices are given

Download or read book Measures And Hilbert Lattices written by Gudrun Kalmbach and published by World Scientific. This book was released on 1986-10-01 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: IntroductionOrthomodular MeasuresGleason's TheoremJordan-Hahn DecompositionOrthofacial Sets of StatesEquational Classes Related to StatesDecomposition of Complete Orthomodular LatticesCharacterization of Dimension LatticesBirkhoff-Von Neumann TheoremCoordinatizationsKakutani-Mackey TheoremKeller's Non-Classical Hilbert Spaces Readership: Mathematician and Physicist who are interested in Hilbert Lattices.

Download or read book Infinite Dimensional Hilbert Lattices written by Ronald Paul Morash and published by . This book was released on 1971 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Gleason s Theorem and Its Applications written by Anatolij Dvurecenskij and published by Springer Science & Business Media. This book was released on 1993-01-31 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with Gleason's theorem and Gleason's measures and indicates the many ways in which they can be applied. The book comprises five chapters. Chapter 1 is devoted to elements of Hilbert space theory. Chapter 2 is devoted to quantum logic theory. Gleason's theorem is described and proved in Chapter 3, together with proofs for measures that can attain infinite values. In Chapter 4 the possibility of applying Gleason's theorem to the completeness criteria of inner product spaces is addressed. Chapter 5 discusses orthogonal measures and the unexpected possibility of describing states on Keller spaces, as well as other applications. Throughout the book, important facts and concepts are illustrated exercises. For mathematicians and physicists interested in the mathematical foundations of quantum mechanics, and those whose work involves noncommutative measure theory, orthomodular lattices. Hilbert space theory and probability theory.

Download or read book Handbook of Quantum Logic and Quantum Structures written by Kurt Engesser and published by Elsevier. This book was released on 2011-08-11 with total page 821 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 Orthomodular Lattices written by L. Beran and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. Bowever, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programmi ng profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-s.cale order", which are almost impossible to fit into the existing classifica tion schemes. They draw upon widely different sections of mathe matics.

Download or read book Quantum Measure Theory written by J. Hamhalter and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first systematic treatment of measures on projection lattices of von Neumann algebras. It presents significant recent results in this field. One part is inspired by the Generalized Gleason Theorem on extending measures on the projection lattices of von Neumann algebras to linear functionals. Applications of this principle to various problems in quantum physics are considered (hidden variable problem, Wigner type theorems, decoherence functional, etc.). Another part of the monograph deals with a fascinating interplay of algebraic properties of the projection lattice with the continuity of measures (the analysis of Jauch-Piron states, independence conditions in quantum field theory, etc.). These results have no direct analogy in the standard measure and probability theory. On the theoretical physics side, they are instrumental in recovering technical assumptions of the axiomatics of quantum theories only by considering algebraic properties of finitely additive measures (states) on quantum propositions.

Download or read book Complementarity Problems written by George Isac and published by Springer. This book was released on 2006-11-15 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of complementarity problems is now an interesting mathematical subject with many applications in optimization, game theory, stochastic optimal control, engineering, economics etc. This subject has deep relations with important domains of fundamental mathematics such as fixed point theory, ordered spaces, nonlinear analysis, topological degree, the study of variational inequalities and also with mathematical modeling and numerical analysis. Researchers and graduate students interested in mathematical modeling or nonlinear analysis will find here interesting and fascinating results.

Download or read book Quantum Measures and Spaces written by G. Kalmbach and published by Springer. This book was released on 2013-01-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has evolved from lectures and seminars of the author, held at different academic institutions during the years 1983-1998. It has four parts. In the first part orthomodular measure theory, generalizing classical measure theory for the purpose of quantum mechanics, is developed. Quantum structures are investigated and inner products are constructed in rich supply for measurements. This part has grown out of Hilbert space and operator theory and the quantum mechanical measurement process. In the second part a new finite-dimensional geometrical model is presented for the four basic interactions, for bags and particle series. Symmetry transfor mation groups, such as U(1), SU(2), SU(3), together with a new group D , are 3 here the guides for the geometric constructions. Infinite dimensional spaces are the theme of the third part of the book: Hilbert lattices are special dimension lattices. Complete spaces, archimedean and non-archimedean orthomodular spaces are studied or characterized, and coordinates and dimension functions for such spaces are constructed. In the last part of the book, brief reviews are found on topics, diversely spread in the literature. They are intended as reference for an interested reader, which want to know some more details, concerning the material of this book. The book can be used for future research, for seminars and lectures on quantum structures. It is a continuation of the author's book on orthomodular lattices.

Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-11-11 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Banach hilbert Spaces Vector Measures And Group Representations written by Tsoy-wo Ma and published by World Scientific Publishing Company. This book was released on 2002-06-13 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an elementary introduction to classical analysis on normed spaces, with special attention paid to fixed points, calculus, and ordinary differential equations. It contains a full treatment of vector measures on delta rings without assuming any scalar measure theory and hence should fit well into existing courses. The relation between group representations and almost periodic functions is presented. The mean values offer an infinitedimensional analogue of measure theory on finitedimensional Euclidean spaces. This book is ideal for beginners who want to get through the basic material as soon as possible and then do their own research immediately.

Download or read book Convergence Theorems for Lattice Group Valued Measures written by Antonio Boccuto and published by Bentham Science Publishers. This book was released on 2015-04-06 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convergence Theorems for Lattice Group-valued Measures explains limit and boundedness theorems for measures taking values in abstract structures. The book begins with a historical survey about these topics since the beginning of the last century, moving on to basic notions and preliminaries on filters/ideals, lattice groups, measures and tools which are featured in the rest of this text. Readers will also find a survey on recent classical results about limit, boundedness and extension theorems for lattice group-valued measures followed by information about recent developments on these kinds of theorems and several results in the setting of filter/ideal convergence. In addition, each chapter has a general description of the topics and an appendix on random variables, concepts and lattices is also provided. Thus readers will benefit from this book through an easy-to-read historical survey about all the problems on convergence and boundedness theorems, and the techniques and tools which are used to prove the main results. The book serves as a primer for undergraduate, postgraduate and Ph. D. students on mathematical lattice and topological groups and filters, and a treatise for expert researchers who aim to extend their knowledge base.

Download or read book The Statistical Mechanics of Quantum Lattice Systems written by and published by European Mathematical Society. This book was released on 2009 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum statistical mechanics plays a major role in many fields such as thermodynamics, plasma physics, solid-state physics, and the study of stellar structure. While the theory of quantum harmonic oscillators is relatively simple, the case of anharmonic oscillators, a mathematical model of a localized quantum particle, is more complex and challenging. Moreover, infinite systems of interacting quantum anharmonic oscillators possess interesting ordering properties with respect to quantum stabilization. This book presents a rigorous approach to the statistical mechanics of such systems, in particular with respect to their actions on a crystal lattice. The text is addressed to both mathematicians and physicists, especially those who are concerned with the rigorous mathematical background of their results and the kind of problems that arise in quantum statistical mechanics. The reader will find here a concise collection of facts, concepts, and tools relevant for the application of path integrals and other methods based on measure and integration theory to problems of quantum physics, in particular the latest results in the mathematical theory of quantum anharmonic crystals. The methods developed in the book are also applicable to other problems involving infinitely many variables, for example, in biology and economics.

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 Kurt G del and the Foundations of Mathematics written by Matthias Baaz and published by Cambridge University Press. This book was released on 2011-06-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

Download or read book Randomness And Undecidability In Physics written by Karl Svozil and published by World Scientific. This book was released on 1993-10-05 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent findings in the computer sciences, discrete mathematics, formal logics and metamathematics have opened up a royal road for the investigation of undecidability and randomness in physics. A translation of these formal concepts yields a fresh look into diverse features of physical modelling such as quantum complementarity and the measurement problem, but also stipulates questions related to the necessity of the assumption of continua.Conversely, any computer may be perceived as a physical system: not only in the immediate sense of the physical properties of its hardware. Computers are a medium to virtual realities. The foreseeable importance of such virtual realities stimulates the investigation of an “inner description”, a “virtual physics” of these universes of computation. Indeed, one may consider our own universe as just one particular realisation of an enormous number of virtual realities, most of them awaiting discovery.One motive of this book is the recognition that what is often referred to as “randomness” in physics might actually be a signature of undecidability for systems whose evolution is computable on a step-by-step basis. To give a flavour of the type of questions envisaged: Consider an arbitrary algorithmic system which is computable on a step-by-step basis. Then it is in general impossible to specify a second algorithmic procedure, including itself, which, by experimental input-output analysis, is capable of finding the deterministic law of the first system. But even if such a law is specified beforehand, it is in general impossible to predict the system behaviour in the “distant future”. In other words: no “speedup” or “computational shortcut” is available. In this approach, classical paradoxes can be formally translated into no-go theorems concerning intrinsic physical perception.It is suggested that complementarity can be modelled by experiments on finite automata, where measurements of one observable of the automaton destroys the possibility to measure another observable of the same automaton and it vice versa.Besides undecidability, a great part of the book is dedicated to a formal definition of randomness and entropy measures based on algorithmic information theory.

Download or read book Real Functions Measures Integration and Quantum Structures written by and published by . This book was released on 1993 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: