Download or read book Quantization Methods in the Theory of Differential Equations written by Vladimir E. Nazaikinskii and published by CRC Press. This book was released on 2002-05-16 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a systematic and mathematically rigorous exposition of methods for studying linear partial differential equations. It focuses on quantization of the corresponding objects (states, observables and canonical transformations) in the phase space. The quantization of all three types of classical objects is carried out in a unified w

Download or read book Methods of Quantization written by Heimo Latal and published by Springer. This book was released on 2008-01-11 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of our present understanding of the elementary building blocks of matter and the forces between them is based on the quantized version of the field theories which are locally symmetric under gauge transformations. The present set of lecture notes gives both a status report and a survey of recent advances for the most important quantization methods in the field theories for elementary particle physics. The first part of the book introduces light-cone quantization as an interesting alternative to the commonly used covariant perturbation theory and functional-integral methods. Next, a general formalism for quantizing systems with constraints, the projection-operator approach, is presented and structural aspects of the renormalization problem for gauge invariant field theories are discussed. Finally, the mathematics underlying the functional-integral quantization is reviewed. Suitable as a reference for researchers in the field, the book will prove particularly useful for lecturers and graduate students in search of additional reading beyond the standard texts on quantum field theory.

Download or read book The Method of Second Quantization written by F.A. Berazin and published by Elsevier. This book was released on 2012-12-02 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Method of Second Quantization deals with the method of second quantization and its use to solve problems of quantum mechanics involving an indefinite number of particles, mainly in field theory and quantum statistics. Topics covered include operations on generating functionals; linear canonical transformations; quadratic operators; and Thirring's four-fermion model. State spaces and the simplest operators are also described. This book is comprised of four chapters and begins with an overview of the method of second quantization and the relevant notations. The first chapter focuses on the connections between vectors and functionals and between operators and functionals, together with fundamental rules for operating on functionals. The reader is then introduced to the so-called quadratic operators and the linear canonical transformations closely connected with them. Quadratic operators reduced and not reduced to normal form are considered. The final chapter discusses the Thirring model, the simplest relativistically invariant model in quantum field theory, and explains why it includes infinities. This monograph will be of value to students and practitioners of mathematical physics.

Download or read book Second Quantization Based Methods in Quantum Chemistry written by Poul Joergensen and published by Elsevier. This book was released on 2012-12-02 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second Quantization-Based Methods in Quantum Chemistry presents several modern quantum chemical tools that are being applied to electronic states of atoms and molecules. Organized into six chapters, the book emphasizes the quantum chemical methods whose developments and implementations have been presented in the language of second quantization. The opening chapter of the book examines the representation of the electronic Hamiltonian, other quantum-mechanical operators, and state vectors in the second-quantization language. This chapter also describes the unitary transformations among orthonormal orbitals in an especially convenient manner. In subsequent chapters, various tools of second quantization are used to describe many approximation techniques, such as Hartree-Fock, perturbation theory, configuration interaction, multiconfigurational Hartree-Fock, cluster methods, and Green’s function. This book is an invaluable source for researchers in quantum chemistry and for graduate-level students who have already taken introductory courses that cover the fundamentals of quantum mechanics through the Hartree-Fock method as applied to atoms and molecules.

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.

Download or read book Foundations of Quantization for Probability Distributions written by Siegfried Graf and published by Springer. This book was released on 2007-05-06 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.

Download or read book Elementary Methods of Molecular Quantum Mechanics written by Valerio Magnasco and published by Elsevier. This book was released on 2006-12-20 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Methods of Molecular Quantum Mechanics shows the methods of molecular quantum mechanics for graduate University students of Chemistry and Physics. This readable book teaches in detail the mathematical methods needed to do working applications in molecular quantum mechanics, as a preliminary step before using commercial programmes doing quantum chemistry calculations.This book aims to bridge the gap between the classic Coulson’s Valence, where application of wave mechanical principles to valence theory is presented in a fully non-mathematical way, and McWeeny’s Methods of Molecular Quantum Mechanics, where recent advances in the application of quantum mechanical methods to molecular problems are presented at a research level in a full mathematical way. Many examples and mathematical points are given as problems at the end of each chapter, with a hint for their solution. Solutions are then worked out in detail in the last section of each Chapter. * Uses clear and simplified examples to demonstrate the methods of molecular quantum mechanics * Simplifies all mathematical formulae for the reader* Provides educational training in basic methodology

Download or read book Methods of Quantization written by Gerald Vincent Dunne and published by . This book was released on 1988 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Quantization Methods in the Theory of Differential Equations written by Vladimir E. Nazaikinskii and published by CRC Press. This book was released on 2002-05-16 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a systematic and mathematically rigorous exposition of methods for studying linear partial differential equations. It focuses on quantization of the corresponding objects (states, observables and canonical transformations) in the phase space. The quantization of all three types of classical objects is carried out in a unified way with the use of a special integral transform. This book covers recent as well as established results, treated within the framework of a universal approach. It also includes applications and provides a useful reference text for graduate and research-level readers.

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.

Download or read book New Non Perturbative Methods and Quantization on the Light Cone written by P. Grange and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the several distinct ways of formulating and quantizing a Hamiltonian system, the light cone approach enjoys special status because it has the largest stability group. The aim of this volume is to present recent achievements and open problems in this rather unusual quantization framework to a large audience. The formulation is set up in a comprehensive introduction where the issues are also clearly indicated with specific examples: vacuum structure, signature of non-perturbative effects, chiral symmetry breaking, light cone gauge theories, etc. The following chapters address these topics through a selection of the most relevant contributions presented at Les Houches. This volume should prove valuable to newcomers in the field, and graduates and academics.

Download or read book Vector Quantization and Signal Compression written by Allen Gersho and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: Herb Caen, a popular columnist for the San Francisco Chronicle, recently quoted a Voice of America press release as saying that it was reorganizing in order to "eliminate duplication and redundancy. " This quote both states a goal of data compression and illustrates its common need: the removal of duplication (or redundancy) can provide a more efficient representation of data and the quoted phrase is itself a candidate for such surgery. Not only can the number of words in the quote be reduced without losing informa tion, but the statement would actually be enhanced by such compression since it will no longer exemplify the wrong that the policy is supposed to correct. Here compression can streamline the phrase and minimize the em barassment while improving the English style. Compression in general is intended to provide efficient representations of data while preserving the essential information contained in the data. This book is devoted to the theory and practice of signal compression, i. e. , data compression applied to signals such as speech, audio, images, and video signals (excluding other data types such as financial data or general purpose computer data). The emphasis is on the conversion of analog waveforms into efficient digital representations and on the compression of digital information into the fewest possible bits. Both operations should yield the highest possible reconstruction fidelity subject to constraints on the bit rate and implementation complexity.

Download or read book Lectures on the Geometry of Quantization written by Sean Bates and published by American Mathematical Soc.. This book was released on 1997 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.

Download or read book Mathematical Aspects Of Weyl Quantization And Phase written by Daniel Abrom Dubin and published by World Scientific. This book was released on 2000-06-12 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book analyzes in considerable generality the quantization-dequantization integral transform scheme of Weyl and Wigner, and considers several phase operator theories. It features: a thorough treatment of quantization in polar coordinates; dequantization by a new method of “motes”; a discussion of Moyal algebras; modifications of the transform method to accommodate operator orderings; a rigorous discussion of the Dicke laser model for one mode, fully quantum, in the thermodynamic limit; analysis of quantum phase theories based on the Toeplitz operator, the coherent state operator, the quantized phase space angle, and a sequence of finite rank operators.

Download or read book Path Integral Quantization and Stochastic Quantization written by Michio Masujima and published by Springer. This book was released on 2003-07-01 with total page 287 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. For the description of the classical theory, we have two methods, one based on the Lagrangian formalism and the other based on the Hamiltonian formal ism. The Harniltonian formalisni is derived from the Lagrangian formalism. In the standard formalism of quantum mechanics, we usually make use of the Hamiltonian formalism. This fact originates from the following circumstance which dates back to the birth of quantum mechanics. The first formalism of quantum 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". Bsed on the optical analogy, we obtain the Schrodinger equation as a result of the inverse of the Eikonal approximation to the Hamilton Jacobi equation, and thus we arrive at "wave mechanics" . The second formalism of quantum mechanics is Heisenberg's "matrix me chanics". In this approach, we arrive at the Heisenberg equation of motion frorn consideration of the consistency of the Ritz combination principle, the Bohr quantization condition and the Fourier analysis of a physical quantity. These two forrnalisrns make up the Hamiltonian formalism of quantum me chanics.

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.