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Field Quantization
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Book Synopsis Field Quantization by : Walter Greiner
Download or read book Field Quantization written by Walter Greiner and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theoretical physics has become a many-faceted science. For the young stu dent it is difficult enough to cope with the overwhelming amount of new scientific material that has to be learned, let alone obtain an overview of the entire field, which ranges from mechanics through electrodynamics, quantum mechanics, field theory, nuclear and heavy-ion science, statistical mechanics, thermodynamics, and solid-state theory to elementary-particle physics. And this knowledge should be acquired in just 8-10 semesters, during which, in addition, a Diploma or Master's thesis has to be worked on or examinations prepared for. All this can be achieved only if the university teachers help to introduce the student to the new disciplines as early on as possible, in order to create interest and excitement that in turn set free essential new energy. At the Johann Wolfgang Goethe University in Frankfurt we therefore con front the student with theoretical physics immediately, in the first semester. Theoretical Mechanics I and II, Electrodynamics, and Quantum Mechanics I - An Introduction are the basic courses during the first two years. These lectures are supplemented with many mathematical explanations and much support material. After the fourth semester of studies, graduate work begins, and Quantum Mechanics II - Symmetries, Statistical Mechanics and Ther modynamics, Relativistic Quantum Mechanics, Quantum Electrodynamics, the Gauge Theory of Weak Interactions, and Quantum Chromo dynamics are obligatory.
Book Synopsis Quantization of Fields with Constraints by : Dmitri Gitman
Download or read book Quantization of Fields with Constraints written by Dmitri Gitman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauge field theories underlie all models now used in elementary particle physics. These theories refer to the class of singular theories which are also theories with constraints. The quantization of singular theories remains one of the key problems of quantum field theory and is being intensively discussed in the literature. This book is an attempt to fill the need for a comprehensive analysis of this problem, which has not heretofore been met by the available monographs and reviews. The main topics are canonical quantization and the path integral method. In addition, the Lagrangian BRST quantization is completely described, for the first time in a monograph. The book also presents a number of original results obtained by the authors, in particular, a complete description of the physical sector of an arbitrary gauge theory, quantization of singular theories with higher theories with time-dependent constraints, and correct derivatives, quantization of canonical quantization of theories of a relativistic point-like particle. As a general illustration we present quantization of field theories such as electrodynamics, Yang-Mills theory, and gravity. It should be noted that this monograph is aimed not only at giving the reader the rules of quantization according to the principle "if you do it this way, it will be good", but also at presenting strong arguments based on the modem interpretation of the classical and quantum theories which show that these methods· are the natural, if not the only possible ones.
Book Synopsis An Introduction to Field Quantization by : Y. Takahashi
Download or read book An Introduction to Field Quantization written by Y. Takahashi and published by Elsevier. This book was released on 2016-09-20 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Field Quantization is an introductory discussion of field quantization and problems closely related to it. Field quantization establishes a commutation relation of the field and finds an operator in such a manner that the Heisenberg equation of motion is satisfied. This book contains eight chapters and begins with a review of the quantization of the Schroedinger field and the close relation between quantized field theory and the many-body theory in quantum mechanics. These topics are followed by discussions of the quantization of the radiation field and the field of lattice vibrations in a solid. The succeeding chapter deals with the familiar linear equations in relativistic field theory and the deduction of certain spin independent theories, which these fields have in common. Other chapter explores the derivation technique of the conservation laws for fields with arbitrary spin directly from the field equations without explicit recourse to Noether's theorem using a configuration space version of the generalized Ward identity. The discussion then shifts to the relativistic quantization method applicable to any field with arbitrary spin; the transformation of various fields under the Lorentz transformation; and a general method for constructing wave functions explicitly, as well as the application of this method to several examples. The concluding chapter focuses on the quantization of interacting fields. This book will prove useful to physicists and researchers.
Book Synopsis Selected Topics in Field Quantization by : Wolfgang Pauli
Download or read book Selected Topics in Field Quantization written by Wolfgang Pauli and published by Courier Corporation. This book was released on 2000-01-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1950s the distinguished theoretical physicist Wolfgang Pauli delivered a landmark series of lectures at the Swiss Federal Institute of Technology in Zurich. His comprehensive coverage of the fundamentals of classical and modern physics was painstakingly recorded not only by his students, but also by a number of collaborators whose carefully edited transcriptions resulted in a remarkable six-volume work. This volume, the sixth in the series, focuses on selected topics in field quantization and considers such subjects as quantization of the electron-positron field, response to an external field, quantization of free fields, quantum electrodynamics, interacting fields, the Heisenberg representation, the S-matrix, and Feynman's approach to quantum electrodynamics. As does each book in the series, Volume 6 includes an index and a wealth of helpful figures. Originally published in 1973, the text remains entirely relevant thanks to Pauli's manner of presentation. As Victor F. Weisskopf notes in the Foreword to the series, Pauli's style is "commensurate to the greatness of its subject in its clarity and impact…. Pauli's lectures show how physical ideas can be presented clearly
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 Field Theory, Quantization and Statistical Physics by : E. Tirapegui
Download or read book Field Theory, Quantization and Statistical Physics written by E. Tirapegui and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is with great emotion that we present here this volume dedicated to the memory of Bernard Jouvet, Docteur es Sciences, Directeur des Recher ches at the Centre National pour la Recherche Scientifique. The life and the career as a physicist of Professor Jouvet are evoked in the following pages by Professor F. Cerulus, a friend of long standing of Professor Jouvet. The contributions have been written by physicists who were friends, collaborators or former students of Professor Jouvet. I express here my gratitude for their contributions. I wish also to thank Mrs. France Jouvet for her kind help in the realiza tion of this book. Without her support this would have been impossible. I am also especially indebted to Professor M. Flato for his constant encouragement and kind cooperation, and to F. Langouche and D. Roekaerts for their generous help in the preparation of this volume. E. TIRAPEGUI TABLE OF CONTENTS FOREWORD VII BIOGRAPHICAL SKETCH XI XIX LIST OF SELECTED SCIENTIFIC PUBLICA TIONS PART ONE: FIELD THEORY AND QUANTIZATION C. BECCHI, A. ROUET and R. sToRA/Renormalizable Theories with Symmetry Breaking 3 J. CALMET and A. VISCONTI/Computing Methods in Quantum Electrodynamics 33 GERARD CLEMENT/Classical Mechanics of Autocomposite Particles 59 s. DEsER/Exclusion of Static Solutions in Gravity-Matter Coupling 77 D. ARNAL, J.C. COR TET, M. FLATO and D. STERNHEIMER/ Star-Products: Quantization and Representations without Operators 85 R. GASTMANs/High Energy Tests of Quantum Electrodynamics 113 L. GOMBEROFF and E.K.
Book Synopsis Quantization of Fields by : Andrey Nikolaevich Volobuev
Download or read book Quantization of Fields written by Andrey Nikolaevich Volobuev and published by . This book was released on 2018-09-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the book Quantization of Fields, the problems of electromagnetic and gravitational fields quantization are examined. Quantization of an electromagnetic field is carried out in photon space, i.e., in the reference system moving with a light velocity. This reference system accompanies a photon, therefore, it is possible to carry out the display of a photon to receive representation about its form and to investigate its parameters and properties. In photon space, the Schrodinger's nonlinear equation with logarithmic nonlinearity (which the wave function of a photon obeys) is found. On the basis of this equation, the problem of a material particle and photon interaction in photon space is investigated. It is shown that the interaction of a photon and material particle can be calculated in the closed form in photon space. Such calculations can be carried out only approximately by a method of the perturbations theory in Euclidian spaces. It is shown that during interaction of a photon and electron on the electron surface, there are waves propagating with a light velocity. The problem of a vacuum in the photon space and also multiphoton system in this space is investigated.During the quantization of a gravitational field, Einstein's equation for a field of gravitation as a basis is used. It is assumed that curved space-time (Riemann's space) is not quantized. Quantization is subjected to an energy-impulse tensor. It is supposed that the curvature of space-time due to the presence of the massive bodies does not create a strength condition in space. The part of corresponding components of an energy-impulse tensor is replaced with quantum sizes by a principle of formation for the quantum mechanics matrix form. On the basis of the quantum form of the gravitational field equation, the solution as a graviton-quantum of a gravitational field is received. It is shown that during the propagation of a graviton near a massive body, there is a pumping of the gravitation field energy in the graviton. Therefore, in the field of a massive body, the graviton is possible to register. When there is distance between the graviton and a massive body, its energy is pumped over back in a gravitation field of a massive body. Therefore, to registering the graviton far from a massive body is problematic. In the book, some standard questions of general relativity - the classical theory of gravitational radiation, the theory of gravitational waves, the Schwarzschild's theory of the solitary mass field, etc. - are submitted also.
Book Synopsis Quantization of Gauge Systems by : Marc Henneaux
Download or read book Quantization of Gauge Systems written by Marc Henneaux and published by Princeton University Press. This book was released on 1992 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail. The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.
Book Synopsis Enhanced Quantization by : John R Klauder
Download or read book Enhanced Quantization written by John R Klauder and published by World Scientific. This book was released on 2015-02-04 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This pioneering book addresses the question: Are the standard procedures of canonical quantization fully satisfactory, or is there more to learn about assigning a proper quantum system to a given classical system? As shown in this book, the answer to this question is: The standard procedures of canonical quantization are not the whole story! This book offers alternative quantization procedures that complete the story of quantization. The initial chapters are designed to present the new procedures in a clear and simple manner for general readers. As is necessary, systems that exhibit acceptable results with conventional quantization lead to the same results when the new procedures are used for them. However, later chapters examine selected models that lead to unacceptable results when quantized conventionally. Fortunately, these same models lead to acceptable results when the new quantization procedures are used. Contents:Introduction and OverviewSelected Topics in Classical and Quantum Mechanics:Selected Topics in Classical MechanicsSelected Topics in Quantum MechanicsEnhanced Quantization of Simple Systems:Essentials of Enhanced QuantizationEnhanced Affine Quantization and the Initial Cosmological SingularityEnhanced Quantization of Some Complex Systems:Examples of Enhanced Quantization: Bosons, Fermions, and AnyonsEnhanced Quantization of Rotationally Invariant ModelsEnhanced Quantization of Ultralocal Field Theories:Enhanced Quantization of Ultralocal ModelsEnhanced Quantization of Covariant Scalars and Gravity:Enhanced Quantization of Covariant Scalar Field ModelsEnhanced Quantization of Gravity Readership: Graduate students and researchers in quantum mechanics. Key Features:Solutions for previously insoluble problemsNontrivial behavior for scalar fieldsNovel quantization proceduresKeywords:Affine Quantization;Weak Correspondence Principle;Triviality of Scalar Fields;Affine Quantum Gravity;Coherent States
Book Synopsis Path Integral Quantization and Stochastic Quantization by : Michio Masujima
Download or read book Path Integral Quantization and Stochastic Quantization written by Michio Masujima and published by Springer Science & Business Media. This book was released on 2008-11-21 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we discuss the path integral quantization and the stochastic quantization of classical mechanics and classical field theory. Forthe description ofthe classical theory, we have two methods, one based on the Lagrangian formalism and the other based on the Hamiltonian formal ism. The Hamiltonian formalism is derived from the Lagrangian·formalism. In the standard formalism ofquantum mechanics, we usually make use ofthe Hamiltonian formalism. This fact originates from the following circumstance which dates back to the birth of quantum mechanics. The first formalism ofquantum mechanics is Schrodinger's wave mechan ics. In this approach, we regard the Hamilton-Jacobi equation of analytical mechanics as the Eikonal equation of "geometrical mechanics". Based on the optical analogy, we obtain the Schrodinger equation as a result ofthe inverse of the Eikonal approximation to the Hamilton-Jacobi equation, and thus we arrive at "wave mechanics". The second formalism ofquantum mechanics is Heisenberg's "matrix me chanics". In this approach, we arrive at the Heisenberg equation of motion from consideration of the consistency of the Ritz combination principle, the Bohr quantization condition and the Fourier analysis of a physical quantity. These two formalisms make up the Hamiltonian.formalism of quantum me chanics.
Book Synopsis The Quantization of Gravity by : Claus Gerhardt
Download or read book The Quantization of Gravity written by Claus Gerhardt and published by Springer. This book was released on 2018-04-14 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint operators where the temporal operator has a pure point spectrum with eigenvalues $\lambda_i$ and related eigenfunctions, while, for the spatial operator, it is possible to find corresponding eigendistributions for each of the eigenvalues $\lambda_i$, if the Cauchy hypersurface is asymptotically Euclidean or if the quantized spacetime is a black hole with a negative cosmological constant. The hyperbolic equation then has a sequence of smooth solutions which are products of temporal eigenfunctions and spatial eigendistributions. Due to this "spectral resolution" of the wave equation quantum statistics can also be applied to the quantized systems. These quantum statistical results could help to explain the nature of dark matter and dark energy.
Book Synopsis New Symmetry Principles in Quantum Field Theory by : J. Frölich
Download or read book New Symmetry Principles in Quantum Field Theory written by J. Frölich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.
Book Synopsis An Interpretive Introduction to Quantum Field Theory by : Paul Teller
Download or read book An Interpretive Introduction to Quantum Field Theory written by Paul Teller and published by Princeton University Press. This book was released on 2020-07-21 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is a subject that has captured the imagination of a surprisingly broad range of thinkers, including many philosophers of science. Quantum field theory, however, is a subject that has been discussed mostly by physicists. This is the first book to present quantum field theory in a manner that makes it accessible to philosophers. Because it presents a lucid view of the theory and debates that surround the theory, An Interpretive Introduction to Quantum Field Theory will interest students of physics as well as students of philosophy. Paul Teller presents the basic ideas of quantum field theory in a way that is understandable to readers who are familiar with non-relativistic quantum mechanics. He provides information about the physics of the theory without calculational detail, and he enlightens readers on how to think about the theory physically. Along the way, he dismantles some popular myths and clarifies the novel ways in which quantum field theory is both a theory about fields and about particles. His goal is to raise questions about the philosophical implications of the theory and to offer some tentative interpretive views of his own. This provocative and thoughtful book challenges philosophers to extend their thinking beyond the realm of quantum mechanics and it challenges physicists to consider the philosophical issues that their explorations have encouraged.
Book Synopsis Relativistic Quantum Physics by : Tommy Ohlsson
Download or read book Relativistic Quantum Physics written by Tommy Ohlsson and published by Cambridge University Press. This book was released on 2011-09-22 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum physics and special relativity theory were two of the greatest breakthroughs in physics during the twentieth century and contributed to paradigm shifts in physics. This book combines these two discoveries to provide a complete description of the fundamentals of relativistic quantum physics, guiding the reader effortlessly from relativistic quantum mechanics to basic quantum field theory. The book gives a thorough and detailed treatment of the subject, beginning with the classification of particles, the Klein–Gordon equation and the Dirac equation. It then moves on to the canonical quantization procedure of the Klein–Gordon, Dirac and electromagnetic fields. Classical Yang–Mills theory, the LSZ formalism, perturbation theory, elementary processes in QED are introduced, and regularization, renormalization and radiative corrections are explored. With exercises scattered through the text and problems at the end of most chapters, the book is ideal for advanced undergraduate and graduate students in theoretical physics.
Book Synopsis Geometric Quantization and Quantum Mechanics by : Jedrzej Sniatycki
Download or read book Geometric Quantization and Quantum Mechanics written by Jedrzej Sniatycki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a revised and expanded version of the lecture notes of two seminar series given during the academic year 1976/77 at the Department of Mathematics and Statistics of the University of Calgary, and in the summer of 1978 at the Institute of Theoretical Physics of the Technical University Clausthal. The aim of the seminars was to present geometric quantization from the point of view· of its applica tions to quantum mechanics, and to introduce the quantum dynamics of various physical systems as the result of the geometric quantization of the classical dynamics of these systems. The group representation aspects of geometric quantiza tion as well as proofs of the existence and the uniqueness of the introduced structures can be found in the expository papers of Blattner, Kostant, Sternberg and Wolf, and also in the references quoted in these papers. The books of Souriau (1970) and Simms and Woodhouse (1976) present the theory of geometric quantization and its relationship to quantum mech anics. The purpose of the present book is to complement the preceding ones by including new developments of the theory and emphasizing the computations leading to results in quantum mechanics.
Book Synopsis Problem Book in Quantum Field Theory by : Voja Radovanovic
Download or read book Problem Book in Quantum Field Theory written by Voja Radovanovic and published by Springer Science & Business Media. This book was released on 2008-01-24 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Problem Book in Quantum Field Theory contains about 200 problems with solutions or hints that help students to improve their understanding and develop skills necessary for pursuing the subject. It deals with the Klein-Gordon and Dirac equations, classical field theory, canonical quantization of scalar, Dirac and electromagnetic fields, the processes in the lowest order of perturbation theory, renormalization and regularization. The solutions are presented in a systematic and complete manner. The material covered and the level of exposition make the book appropriate for graduate and undergraduate students in physics, as well as for teachers and researchers.
Book Synopsis Stochastic Quantization by : Mikio Namiki
Download or read book Stochastic Quantization written by Mikio Namiki and published by Springer Science & Business Media. This book was released on 2008-10-04 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on stochastic quantization which was originally proposed by G. Parisi and Y. S. Wu in 1981 and then developed by many workers. I assume that the reader has finished a standard course in quantum field theory. The Parisi-Wu stochastic quantization method gives quantum mechanics as the thermal-equilibrium limit of a hypothetical stochastic process with respect to some fictitious time other than ordinary time. We can consider this to be a third method of quantization; remarkably different from the conventional theories, i. e, the canonical and path-integral ones. Over the past ten years, we have seen the technical merits of this method in quantizing gauge fields and in performing large numerical simulations, which have never been obtained by the other methods. I believe that the stochastic quantization method has the potential to extend the territory of quantum mechanics and of quantum field theory. However, I should remark that stochastic quantization is still under development through many mathematical improvements and physical applications, and also that the fictitious time of the theory is only a mathematical tool, for which we do not yet know its origin in the physical background. For these reasons, in this book, I attempt to describe its theoretical formulation in detail as well as practical achievements.
