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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 Quantum Analogues: From Phase Transitions to Black Holes and Cosmology by : William Unruh
Download or read book Quantum Analogues: From Phase Transitions to Black Holes and Cosmology written by William Unruh and published by Springer. This book was released on 2007-04-14 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, analogies between laboratory physics (e.g. quantum optics and condensed matter) and gravitational/cosmological phenomena such as black holes have attracted an increasing interest. This book contains a series of selected lectures devoted to this new and rapidly developing field. Various analogies connecting (apparently) different areas in physics are presented in order to bridge the gap between them and to provide an alternative point of view.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976 with total page 1118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Mathematics of Quantization and Quantum Fields by : Jan Dereziński
Download or read book Mathematics of Quantization and Quantum Fields written by Jan Dereziński and published by Cambridge University Press. This book was released on 2023-01-31 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2013 book, now OA, offers a definitive review of mathematical aspects of quantization and quantum field theory.
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 Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathematics. It is a translation with updates and editorial comments of the Soviet Mathematical En cyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977 - 1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivision has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathe matics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, engineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis An Introduction to Non-Perturbative Foundations of Quantum Field Theory by : Franco Strocchi
Download or read book An Introduction to Non-Perturbative Foundations of Quantum Field Theory written by Franco Strocchi and published by Oxford University Press, USA. This book was released on 2013-02-14 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses fundamental aspects of Quantum Field Theory and of Gauge theories, with attention to mathematical consistency. Basic issues of the standard model of elementary particles (Higgs mechanism and chiral symmetry breaking in quantum Chromodynamics) are treated without relying on the perturbative expansion and on instanton calculus.
Book Synopsis Causality, Measurement Theory and the Differentiable Structure of Space-Time by : R. N. Sen
Download or read book Causality, Measurement Theory and the Differentiable Structure of Space-Time written by R. N. Sen and published by Cambridge University Press. This book was released on 2010-02-11 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments: the demonstration that causality can be defined on discrete space-times; and Sewell's measurement theory, in which the wave packet is reduced without recourse to the observer's conscious ego, nonlinearities or interaction with the rest of the universe. The definition of causality on a discrete space-time assumes that space-time is made up of geometrical points. Using Sewell's measurement theory, the author concludes that the notion of geometrical points is as meaningful in quantum mechanics as it is in classical mechanics, and that it is impossible to tell whether the differential calculus is a discovery or an invention. Providing a mathematical discourse on the relation between theoretical and experimental physics, the book gives detailed accounts of the mathematically difficult measurement theories of von Neumann and Sewell.
Book Synopsis Symmetry Breaking in the Standard Model by : Franco Strocchi
Download or read book Symmetry Breaking in the Standard Model written by Franco Strocchi and published by Springer. This book was released on 2019-07-03 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a non-perturbative approach to the symmetry breaking in the standard model, in this way avoiding the critical issues which affect the standard presentations. The debated empirical meaning of global and local gauge symmetries is clarified. The absence of Goldstone bosons in the Higgs mechanism is non-perturbatively explained by the validity of Gauss laws obeyed by the currents which generate the relatedglobal gauge symmetry. The solution of the U(1) problem and the vacuum structure in quantum chromodynamics (QCD) are obtained without recourse to the problematic semiclassical instanton approximation, by rather exploiting the topology of the gauge group.
Book Synopsis The Philosophy of Ernst Cassirer by : J Tyler Friedman
Download or read book The Philosophy of Ernst Cassirer written by J Tyler Friedman and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-06-16 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings Cassirer’s work into the arena of contemporary debates both within and outside of philosophy. All articles offer a fresh and contemporary look at one of the most prolific and important philosophers of the 20th century. The papers are authored by a wide array of scholars working in different areas, such as epistemology, philosophy of culture, sociology, psychopathology, philosophy of science and aesthetics.
Book Synopsis Symmetries in Science III by : Bruno Gruber
Download or read book Symmetries in Science III written by Bruno Gruber and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nicely printed and bound proceedings of a major symposium contain 29 reviews of highly diverse developments in the world of symmetry, plus 14 rather briefer research papers. The variety of the topics treated and the authority of the contributors suggest that most physical theorists will find here so
Book Synopsis Integrable And Superintegrable Systems by : Boris A Kuperschmidt
Download or read book Integrable And Superintegrable Systems written by Boris A Kuperschmidt and published by World Scientific. This book was released on 1990-10-25 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.
Book Synopsis Statistical Mechanics at the Turn of the Decade by : E. G. D. Cohen
Download or read book Statistical Mechanics at the Turn of the Decade written by E. G. D. Cohen and published by Marcel Dekker. This book was released on 1971 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
Book Synopsis Topological Geometrodynamics by : Matti Pitkanen
Download or read book Topological Geometrodynamics written by Matti Pitkanen and published by Luniver Press. This book was released on 2006 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological GeometroDynamics is a modification of general relativity inspired by the conceptual problems related to the definitions of inertial and gravitational energy in general relativity. Topological geometrodynamics can be also seen as a generalization of super string models. Physical space-times are seen as four-dimensional surfaces in certain eight-dimensional space. The choice of this space is fixed by symmetries of the standard model so that geometrization of known classical fields and elementary particle quantum numbers results. The notion of many-sheeted space-time allows re-interpretation of the structures of perceived world in terms of macroscopic space-time topology. The generalization of the number concept based on fusion of real numbers and p-adic number fields implies a further generalization of the space-time concept allowing to identify space-time correlates of cognition and intentionality. Quantum measurement theory extended to a quantum theory of consciousness becomes an organic part of theory. A highly non-trivial prediction is the existence of a fractal hierarchy of copies of standard model physics with dark matter identified in terms of macroscopic quantum phases characterized by dynamical and quantized Planck constant. The book is a comprehensive overview and analysis of topological geometrodynamics as a mathematical and physical theory.
Book Synopsis Quantum Probability Communications by : S Attal
Download or read book Quantum Probability Communications written by S Attal and published by World Scientific. This book was released on 2003 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture notes from a Summer School on Quantum Probability held at the University of Grenoble are collected in these two volumes of the QP-PQ series. The articles have been refereed and extensively revised for publication. It is hoped that both current and future students of quantum probability will be engaged, informed and inspired by the contents of these two volumes. An extensive bibliography containing the references from all the lectures is included in Volume 12.
