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Inequivalent Representations Of Canonical Commutation And Anti Commutation Relations
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Book Synopsis Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations by : Asao Arai
Download or read book Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations written by Asao Arai and published by Springer Nature. This book was released on 2020-02-04 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Canonical commutation relations (CCR) and canonical anti-commutation relations (CAR) are basic principles in quantum physics including both quantum mechanics with finite degrees of freedom and quantum field theory. From a structural viewpoint, quantum physics can be primarily understood as Hilbert space representations of CCR or CAR. There are many interesting physical phenomena which can be more clearly understood from a representation–theoretical viewpoint with CCR or CAR. This book provides an introduction to representation theories of CCR and CAR in view of quantum physics. Particular emphases are put on the importance of inequivalent representations of CCR or CAR, which may be related to characteristic physical phenomena. The topics presented include general theories of representations of CCR and CAR with finite and infinite degrees of freedom, the Aharonov–Bohm effect, time operators, quantum field theories based on Fock spaces, Bogoliubov transformations, and relations of infinite renormalizations with inequivalent representations of CCR. This book can be used as a text for an advanced topics course in mathematical physics or mathematics.
Book Synopsis Chemistry, Quantum Mechanics and Reductionism by : H. Primas
Download or read book Chemistry, Quantum Mechanics and Reductionism written by H. Primas and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide a deeper insight into the modern theories of molecular matter. It incorporates the most important developments which have taken place during the last decades and reflects the modern trend to abstraction. At the present state of the art we have acquired a fairly good knowledge of "how to. compute" small molecules us ing the methods of quantum chemistry. Yet, in spite of many statements to the contrary and many superficial discussions, the theoretical basis of chemistry and biology is not safely in our hands. It is all but impossible to summarize the modern developments of the theory of matter in nontechnical language. But I hope that I can give some feeling for the problems, the intellectual excitements and the wor ries of some theoreticians. I know very well that such an enterprise is a dangerous adventure and that one says that a clever scientist should take care of his reputation by barricading himself behind the safe wall of his speciality. This volume is not meant to be a textbook; in many respects it has complementary goals. For good and bad reasons, most textbooks ignore the historical and philosophical aspects and go ahead on the basis of crude simplifications; many even lie like the devil and do not shrink from naive indoctrination. Some sections of this book can be read as commentaries on our standard texts, they are intended to stir the waters with controversy.
Book Synopsis Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields: An Introduction To Mathematical Analysis Of Quantum Fields (Second Edition) by : Asao Arai
Download or read book Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields: An Introduction To Mathematical Analysis Of Quantum Fields (Second Edition) written by Asao Arai and published by World Scientific. This book was released on 2024-09-03 with total page 1115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation and anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove-Miyatake model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and an introductory description to each model is given. In this second edition, a new chapter (Chapter 15) is added to describe a mathematical theory of spontaneous symmetry breaking which is an important subject in modern quantum physics.This book is a good introductory text for graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory. It is also well-suited for self-study, providing readers a firm foundation of knowledge and mathematical techniques for more advanced books and current research articles in the field of mathematical analysis on quantum fields. Numerous problems are added to aid readers in developing a deeper understanding of the field.
Book Synopsis Quantum Field Theory And Its Macroscopic Manifestations: Boson Condensation, Ordered Patterns And Topological Defects by : Massimo Blasone
Download or read book Quantum Field Theory And Its Macroscopic Manifestations: Boson Condensation, Ordered Patterns And Topological Defects written by Massimo Blasone and published by World Scientific. This book was released on 2011-02-21 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum dynamics underlies macroscopic systems exhibiting some kind of ordering, such as superconductors, ferromagnets and crystals. Even large scale structures in the Universe and ordering in biological systems appear to be the manifestation of microscopic dynamics ruling their elementary components. The scope of this book is to answer questions such as: how it happens that the mesoscopic/macroscopic scale and stability characterizing those systems are dynamically generated out of the microscopic scale of fluctuating quantum components; how quantum particles coexist and interact with classically behaving macroscopic objects, e.g. vortices, magnetic domains and other topological defects. The quantum origin of topological defects and their interaction with quanta is a crucial issue for the understanding of symmetry breaking phase transitions and structure formation in a wide range of systems from condensed matter to cosmology. Deliberately not discussing other important problems, primarily renormalization problems, this book provides answers to such questions in a unitary, self-consistent physical and mathematical framework, which makes it unique in the panorama of existing texts on a similar subject. Crystals, ferromagnets and superconductors appear to be macroscopic quantum systems, i.e. their macroscopic properties cannot be explained without recourse to the underlying quantum dynamics. Recognizing that quantum field dynamics is not confined to the microscopic world is one of the achievements of this book, also marking its difference from other texts. The combined use of algebraic methods, and operator and functional formalism constitutes another distinctive, valuable feature./a
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1975-12 with total page 886 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Epistemology and Transformation of Knowledge in Global Age by : Zlatan Delic
Download or read book Epistemology and Transformation of Knowledge in Global Age written by Zlatan Delic and published by BoD – Books on Demand. This book was released on 2017-07-26 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of seven chapters containing multiple questions of the global socially epistemological situation in science and higher education. Despite the progress of techno-sciences, we are facing blind flaws in leading systems of knowledge and perception. The global era, in a paradox way, connects the new knowledge of economics, postpolitics, postdemocracy, and biopolitical regulation of live and unpresentable forms of the global geo-located violence. Techno-optimism and techno-dictatorship in the twenty-first century coincide with the ideology of market, biopolitics of mandatory satisfaction, religious revivalism, and collapse of higher education. In order for sciences to recover, it is necessary to make a globally epistemological and moral turn toward the truth. The book shows that, when joint desires of the new economics of knowledge and technology erase epistemology (in a way to assign definitions of knowledge and rules and practices of the public usage of the mind), then the time for epistemology is on its way.
Book Synopsis Powers, Time and Free Will by : Christopher J. Austin
Download or read book Powers, Time and Free Will written by Christopher J. Austin and published by Springer Nature. This book was released on 2022-03-28 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together twelve original contributions by leading scholars on the much-debated issues of what is free will and how can we exercise it in a world governed by laws of nature. Which conception of laws of nature best fits with how we conceive of free will? And which constraints does our conception of the laws of nature place on how we think of free will? The metaphysics of causation and the metaphysics of dispositions are also explored in this edited volume, in relation to whether they may or may not be game-changers in how we think about both free will and the laws of nature. The volume presents the views of a range of international experts on these issues, and aims at providing the reader with novel approaches to a core problem in philosophy. The target audience is composed by academics and scholars who are interested in an original and contemporary approach to these long-debated issues. Chapters [2] and [4] are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Book Synopsis Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields by : Asao Arai
Download or read book Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields written by Asao Arai and published by Springer Nature. This book was released on 2022-10-18 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains the mathematical structures of supersymmetric quantum field theory (SQFT) from the viewpoints of functional and infinite-dimensional analysis. The main mathematical objects are infinite-dimensional Dirac operators on the abstract Boson–Fermion Fock space. The target audience consists of graduate students and researchers who are interested in mathematical analysis of quantum fields, including supersymmetric ones, and infinite-dimensional analysis. The major topics are the clarification of general mathematical structures that some models in the SQFT have in common, and the mathematically rigorous analysis of them. The importance and the relevance of the subject are that in physics literature, supersymmetric quantum field models are only formally (heuristically) considered and hence may be ill-defined mathematically. From a mathematical point of view, however, they suggest new aspects related to infinite-dimensional geometry and analysis. Therefore, it is important to show the mathematical existence of such models first and then study them in detail. The book shows that the theory of the abstract Boson–Fermion Fock space serves this purpose. The analysis developed in the book also provides a good example of infinite-dimensional analysis from the functional analysis point of view, including a theory of infinite-dimensional Dirac operators and Laplacians.
Book Synopsis Gauging What's Real by : Richard Healey
Download or read book Gauging What's Real written by Richard Healey and published by Oxford University Press on Demand. This book was released on 2007-09-27 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauge theories have provided our most successful representations of the fundamental forces of nature. But how do such representations work? Healey aims to answer this question, and defends a distinctive thesis which proves that loops rather than points are the locations of fundamental properties.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1973 with total page 1162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quanta and Mind by : J. Acacio de Barros
Download or read book Quanta and Mind written by J. Acacio de Barros and published by Springer Nature. This book was released on 2019-09-19 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume examines aspects of the mind/consciousness that are relevant to the interpretations of quantum mechanics. In it, an international group of contributors focus on the possible connections between quantum mechanics and consciousness. They look at how consciousness can help us with quantum mechanics as well as how quantum mechanics can contribute to our understanding of consciousness. For example, what do different interpretations aimed at solving the measurement problem in quantum mechanics tell us about the nature of consciousness, such as von Neumann's interpretation? Each interpretation has, associated to it, a corresponding metaphysical framework that helps us think about possible “models” of consciousness. Alternatively, what does the nature of consciousness tell us about the role of the observer and time reversibility in the measurement process? The book features 20 papers on contemporary approaches to quanta and mind. It brings together the work of scholars from different disciplines with diverse views on the connections between quanta and mind, ranging from those who are supportive of a link between consciousness and quantum physics to those who are very skeptical of such link. Coverage includes such topics as free will in a quantum world, contextuality and causality, mind and matter interaction, quantum panpsychism, the quantum and quantum-like brain, and the role of time in brain-mind dynamics.
Book Synopsis Models, Simulations, and Representations by : Paul Humphreys
Download or read book Models, Simulations, and Representations written by Paul Humphreys and published by Routledge. This book was released on 2013-03-01 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although scientific models and simulations differ in numerous ways, they are similar in so far as they are posing essentially philosophical problems about the nature of representation. This collection is designed to bring together some of the best work on the nature of representation being done by both established senior philosophers of science and younger researchers. Most of the pieces, while appealing to existing traditions of scientific representation, explore new types of questions, such as: how understanding can be developed within computational science; how the format of representations matters for their use, be it for the purpose of research or education; how the concepts of emergence and supervenience can be further analyzed by taking into account computational science; or how the emphasis upon tractability--a particularly important issue in computational science--sheds new light on the philosophical analysis of scientific reasoning.
Book Synopsis Nonperturbative Quantum Field Theory by : G. Hooft
Download or read book Nonperturbative Quantum Field Theory written by G. Hooft and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of index-t. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail.
Book Synopsis Representation and Reality in Humans, Other Living Organisms and Intelligent Machines by : Gordana Dodig-Crnkovic
Download or read book Representation and Reality in Humans, Other Living Organisms and Intelligent Machines written by Gordana Dodig-Crnkovic and published by Springer. This book was released on 2017-08-29 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book enriches our views on representation and deepens our understanding of its different aspects. It arises out of several years of dialog between the editors and the authors, an interdisciplinary team of highly experienced researchers, and it reflects the best contemporary view of representation and reality in humans, other living beings, and intelligent machines. Structured into parts on the cognitive, computational, natural sciences, philosophical, logical, and machine perspectives, a theme of the field and the book is building and presenting networks, and the editors hope that the contributed chapters will spur understanding and collaboration between researchers in domains such as computer science, philosophy, logic, systems theory, engineering, psychology, sociology, anthropology, neuroscience, linguistics, and synthetic biology.
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 1979-05-31 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twentieth century has witnessed a striking transformation in the understanding 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 orrter 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 structure, 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 manoeuvers under Bohr, through a formative stage in which the mathematical framework was bifurcated (between Schrodinger and Heisenberg) to an elegant culmination in von Neumann's Hilbert space formulation, the elementary theory moved, flanked even at this later stage by the ill-understood formalisms for the relativistic version and for the field-theoretic alternative; after that we have a gradual, but constant, elaboration of all these quantal theories as abstract mathematical structures (their point of departure being von Neumann's formalism) until at the present time theoretical work is heavily preoccupied with the manipulation of purely abstract structures.
Book Synopsis Algebraic Methods in Statistical Mechanics and Quantum Field Theory by : Dr. Gérard G. Emch
Download or read book Algebraic Methods in Statistical Mechanics and Quantum Field Theory written by Dr. Gérard G. Emch and published by Courier Corporation. This book was released on 2014-08-04 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematic algebraic approach offers a careful formulation of the problems' physical motivations as well as self-contained descriptions of the mathematical methods for arriving at solutions. 1972 edition.
Book Synopsis Space, Time, and Spacetime by : Vesselin Petkov
Download or read book Space, Time, and Spacetime written by Vesselin Petkov and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to the centennial anniversary of Minkowski's discovery of spacetime, this volume contains papers, most presented at the Third International Conference on the Nature and Ontology of Spacetime, that address some of the deepest questions in physics.
