Download or read book Symplectic Matrices First Order Systems And Special Relativity written by Mark Kauderer and published by World Scientific Publishing Company. This book was released on 1994-06-09 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent developments in canonical transforms, matrix theory, block Kronecker multiplications, and other areas are applied to extend and simplify results in the theory of first order systems and special relativity. Especially noteworthy are the author's results on Fourier transforms in dimensions lower than the surrounding space and his approach to the Doppler effect, which has never been published previously and supersedes previous works on this topic, which failed to solve the Doppler effect exactly. Some of the goals of this work are: to develop the theory of complex symmetric matrices as the rigorous foundations of first order systems, to exhibit in full generality the author's method of duality, and to discuss the neglected area of three dimensional effects in special relativity. The section on special relativity has been especially simplified so that it may be used as a beginning graduate text in this area. It includes the first full discussion of the Lorentz group in a book since Silberstein's pioneering 1913 treatment.
Download or read book Matrix Mathematics written by Dennis S. Bernstein and published by Princeton University Press. This book was released on 2009-07-06 with total page 1182 pages. Available in PDF, EPUB and Kindle. Book excerpt: When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations,Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms. Covers hundreds of important and useful results on matrix theory, many never before available in any book Provides a list of symbols and a summary of conventions for easy use Includes an extensive collection of scalar identities and inequalities Features a detailed bibliography and author index with page references Includes an exhaustive subject index with cross-referencing
Download or read book Symplectic Geometry and Quantum Mechanics written by Maurice A. de Gosson and published by Springer Science & Business Media. This book was released on 2006-08-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.
Download or read book Geometric Optics on Phase Space written by Kurt Bernardo Wolf and published by Springer Science & Business Media. This book was released on 2004-07-21 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional Fourier transform currently used for image processing. The reader will appreciate the beautiful similarities between Hamilton's mechanics and this approach to optics. The appendices link the geometry thus introduced to wave optics through Lie methods. The book addresses researchers and graduate students.
Download or read book Linear Canonical Transforms written by John J. Healy and published by Springer. This book was released on 2015-11-26 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.
Download or read book Principles Of Newtonian And Quantum Mechanics The The Need For Planck s Constant H Second Edition written by Maurice A De Gosson and published by World Scientific. This book was released on 2016-11-10 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this book deals, as the first, with the foundations of classical physics from the 'symplectic' point of view, and of quantum mechanics from the 'metaplectic' point of view. We have revised and augmented the topics studied in the first edition in the light of new results, and added several new sections. The Bohmian interpretation of quantum mechanics is discussed in detail. Phase space quantization is achieved using the 'principle of the symplectic camel', which is a deep topological property of Hamiltonian flows. We introduce the notion of 'quantum blob', which can be viewed as the fundamental phase space unit. The mathematical tools developed in this book are the theory of the symplectic and metaplectic group, the Maslov index in a rigorous form, and the Leray index of a pair of Lagrangian planes. The concept of the 'metatron' is introduced, in connection with the Bohmian theory of motion. The short-time behavior of the propagator is studied and applied to the quantum Zeno effect.
Download or read book Emergence Of The Quantum From The Classical Mathematical Aspects Of Quantum Processes written by Maurice A De Gosson and published by World Scientific. This book was released on 2017-11-10 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical.Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field.
Download or read book Optical Systems and Processes written by Joseph Shamir and published by SPIE Press. This book was released on 1999 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise, comprehensive reference text covering electro-optical systems, optical system design, optical physics, holography, Fourier optics, and optical metrology. It emphasizes physical insight aimed at engineering applications. This book is suitable as an advanced undergraduate or graduate level text; problems and solutions are included.
Download or read book Free and Guided Optical Beams written by S. Martellucci and published by World Scientific. This book was released on 2004 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, learn how to count by tens.
Download or read book Free And Guided Optical Beams Proceedings Of The International School Of Quantum Electronics written by Sergio Martellucci and published by World Scientific. This book was released on 2004-08-30 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optical beams are electromagnetic waves that remain essentially concentrated around a mean axis upon free propagation or that are guided by suitable structures. The study of these beams has existed long ago and since then this field has been a focus of active investigation. However, in recent years, the interest on optical beams has further increased, due to the availability of many types of laser sources, characterized by very different properties, as far as their polarization, coherence, spectral content, and spatial distribution are concerned.This book contains lectures presented in the 35th International School of Quantum Electronics at the Ettore Majorana Centre in Erice, Sicily. It gives the latest coverage on the development and advance in “Free and Guided Optical Beams”. The purpose of these lectures was to give an updated overview, as complete as possible, on topics concerning the propagation of light beams in free space, in materials, and in guiding structures, and to provide the tools needed to its study, both from the theoretical and the application point of view.The lectures presented here are written in extended review-like format. Both introductory fundamental topics and recent research results are reviewed, making this an indispensible book for novice as well as experts in this field.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Download or read book An Introduction to Beam Physics written by Martin Berz and published by Taylor & Francis. This book was released on 2014-12-03 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of beam physics touches many areas of physics, engineering, and the sciences. In general terms, beams describe ensembles of particles with initial conditions similar enough to be treated together as a group so that the motion is a weakly nonlinear perturbation of a chosen reference particle. Particle beams are used in a variety of areas,
Download or read book Scalar Vector and Matrix Mathematics written by Dennis S. Bernstein and published by Princeton University Press. This book was released on 2018-02-27 with total page 1593 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. Fully updated and expanded with new material on scalar and vector mathematics Covers the latest results in matrix theory Provides a list of symbols and a summary of conventions for easy and precise use Includes an extensive bibliography with back-referencing plus an author index
Download or read book Symplectic Matrices written by Mark Kauderer and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symplectic Difference Systems Oscillation and Spectral Theory written by Ondřej Došlý and published by Springer Nature. This book was released on 2019-09-06 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which are based on the recently developed central object - the comparative index. The book contains numerous results and citations, which were till now scattered only in journal papers. The book also provides new applications of the theory of matrices in this field, in particular of the Moore-Penrose pseudoinverse matrices, orthogonal projectors, and symplectic matrix factorizations. Thus it brings this topic to the attention of researchers and students in pure as well as applied mathematics.
Download or read book Nonoscillation and Oscillation Theory for Functional Differential Equations written by Ravi P. Agarwal and published by CRC Press. This book was released on 2004-08-30 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes the qualitative theory of differential equations with or without delays, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology. The authors address oscillatory and nonoscillatory properties of first-order delay and neutral delay differential eq
Download or read book Journal of the Optical Society of America written by and published by . This book was released on 1993 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Communications in Difference Equations written by Saber N. Elaydi and published by CRC Press. This book was released on 2000-07-06 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of carefully refereed and edited papers were originally presented at the Fourth International Conference on Difference Equations held in Poznan, Poland. Contributions were from a diverse group of researchers from several countries and featured discussions on the theory of difference equations, open problems and conjectures, as well
