Inequivalent Representations Of Canonical Commutation And Anti Commutation Relations
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| Author | : Asao Arai |
| Publisher | : Springer Nature |
| Total Pages | : 505 |
| Release | : 2020-02-04 |
| Genre | : Science |
| ISBN | : 9811521808 |
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.
| Author | : Massimo Blasone |
| Publisher | : World Scientific |
| Total Pages | : 545 |
| Release | : 2011 |
| Genre | : Science |
| ISBN | : 1848162804 |
This book is a self-contained presentation of the quantum field theory of topological defects created during spontaneous symmetry breakdown phase transitions, with a particular emphasis on phenomenological issues of current interest.
| Author | : J. Acacio de Barros |
| Publisher | : Springer Nature |
| Total Pages | : 261 |
| Release | : 2019-09-19 |
| Genre | : Philosophy |
| ISBN | : 3030219089 |
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.
| Author | : |
| Publisher | : |
| Total Pages | : 1118 |
| Release | : 1976 |
| Genre | : Nuclear energy |
| ISBN | : |
| Author | : Paul Humphreys |
| Publisher | : Routledge |
| Total Pages | : 330 |
| Release | : 2013-03-01 |
| Genre | : Philosophy |
| ISBN | : 1136668497 |
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.
| Author | : G. Hooft |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 603 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461307295 |
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.
| Author | : Gordana Dodig-Crnkovic |
| Publisher | : Springer |
| Total Pages | : 379 |
| Release | : 2017-08-29 |
| Genre | : Computers |
| ISBN | : 3319437844 |
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.
| Author | : C.A. Hooker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 498 |
| Release | : 1979-05-31 |
| Genre | : Philosophy |
| ISBN | : 9789027707079 |
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.
| Author | : Dr. Gérard G. Emch |
| Publisher | : Courier Corporation |
| Total Pages | : 336 |
| Release | : 2014-08-04 |
| Genre | : Science |
| ISBN | : 0486151719 |
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.
| Author | : Vesselin Petkov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 316 |
| Release | : 2010-09-02 |
| Genre | : Science |
| ISBN | : 3642135382 |
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.
