*Charge, Flux, and Metric*

Author: Friedrich W Hehl,Yuri N. Obukhov

Publisher: Springer Science & Business Media

ISBN: 1461200512

Category: Science

Page: 113

View: 7972

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Search Results for: foundations-of-electrodynamics

## Foundations of Classical Electrodynamics

In this book we display the fundamental structure underlying classical electro dynamics, i. e. , the phenomenological theory of electric and magnetic effects. The book can be used as a textbook for an advanced course in theoretical electrodynamics for physics and mathematics students and, perhaps, for some highly motivated electrical engineering students. We expect from our readers that they know elementary electrodynamics in the conventional (1 + 3)-dimensional form including Maxwell's equations. More over, they should be familiar with linear algebra and elementary analysis, in cluding vector analysis. Some knowledge of differential geometry would help. Our approach rests on the metric-free integral formulation of the conservation laws of electrodynamics in the tradition of F. Kottler (1922), E. Cartan (1923), and D. van Dantzig (1934), and we stress, in particular, the axiomatic point of view. In this manner we are led to an understanding of why the Maxwell equa tions have their specific form. We hope that our book can be seen in the classical tradition of the book by E. J. Post (1962) on the Formal Structure of Electro magnetics and of the chapter "Charge and Magnetic Flux" of the encyclopedia article on classical field theories by C. Truesdell and R. A. Toupin (1960), in cluding R. A. Toupin's Bressanone lectures (1965); for the exact references see the end of the introduction on page 11. .
## Foundations of Applied Electrodynamics

Foundations of Applied Electrodynamics takes a fresh look at the essential concepts and methods of electrodynamics as a whole, uniting the most relevant contemporary topics under a common mathematical framework. It contains clear explanations of high-level concepts as well as the mutual relationships between the essential ideas of electromagnetic theory. Starting with the fundamentals of electrodynamics, it methodically covers a wide spectrum of research and applications that stem from electromagnetic phenomena, before concluding with more advanced topics such as quantum mechanics. Includes new advances and methodologies in applied electrodynamics, and provides the whole picture of the theory of electrodynamics in most active areas of engineering applications Systematically deals with eigenvalue problems, integral equation formulations and transient phenomena in various areas of applied electrodynamics Introduces the complete theory of spherical vector wave functions, and presents the upper bounds of the product of gain and bandwidth for an arbitrary antenna Presents the field approach to multiple antenna system, which provides a theoretical tool for the prediction of channel models of MIMO, and is also the basis of wireless power transmission system One of the first books on electromagnetics that contains the general theory of relativity, which is needed in the design of mobile systems such as global positioning system (GPS) By summarising both engineering and theoretical electromagnetism in one volume, this book is an essential reference for practicing engineers, as well as a guide for those who wish to advance their analytical techniques for studying applied electrodynamics.
## Foundations of electrodynamics

## Foundations of Electrodynamics

Electrodynamics involves the study of electric charges and their interaction with magnetic and electric fields. This advanced undergraduate text presupposes some knowledge of electricity and magnetism, making substantial use of vector analysis. The authors define their goal as "a serious attempt to develop electrodynamics on a postulational basis and to define each concept in the most general way." 1960 edition.
## Foundations of Classical and Quantum Electrodynamics

This advanced textbook covers many fundamental, traditional and new branches of electrodynamics, as well as the related fields of special relativity, quantum mechanics and quantum electrodynamics. The book introduces the material at different levels, oriented towards 3rd-4th year bachelor, master, and PhD students. This is so as to describe the whole complexity of physical phenomena, instead of a mosaic of disconnected data. The required mathematical background is collated in Chapter 1, while the necessary physical background is included in the main text of the corresponding chapters and also given in appendices. The content is based on teaching material tested on students over many years, and their training to apply general theory for solving scientific and engineering problems. To this aim, the book contains approximately 800 examples and problems, many of which are described in detail. Some of these problems are designed for students to work on their own with only the answers and descriptions of results, and may be solved selectively. The examples are key ingredients to the theoretical course; the user should study all of them while reading the corresponding chapters. Equally suitable as a reference for researchers specialized in science and engineering.
## Collective Electrodynamics

Carver Mead offers a radically new approach to the standard problems of electromagnetic theory.
## Foundations of Radiation Theory and Quantum Electrodynamics

## Elektrodynamik

## Electrodynamics of Continua I

The electrodynamics of continua is a branch ofthe physical sciences concerned with the interaction of electromagnetic fields with deformable bodies. De formable bodies are considered to be continua endowed with continuous distributions of mass and charge. The theory of electromagnetic continua is concerned with the determination of deformations, motions, stress, and elec tromagnetic fields developed in bodies upon the applications of external loads. External loads may be of mechanical origin (e.g., forces, couples, constraints placed on the surface of the body, and initial and boundary conditions arising from thermal and other changes) and/or electromagnetic origin (e.g., electric, magnetic, and current fields). Because bodies of different constitutions respond to external stimuli in a different way, it is imperative to characterize properly the response functions relevant to a given class of continua. This is done by means of the constitutive theory. For example, an elastic dielectric responds to electromagnetic fields in a totally different way than a magnetic fluid. The present book is intended to present a unified approach to the subject matter, based on the principles of contemporary continuum physics.
## Conceptual Foundations of Quantum Field Theory

Multi-author volume on the history and philosophy of physics.
## Fundamentals of Electrodynamics

Fundamentals of Electrodynamics is primarily a textbook for graduate students in physics. It is also a valuable at the senior level and as a profession reference book. It will be especially welcome to graduate students planning to do their doctoral research in quantum field theory or elementary particle physics. Fundamentals of Electrodynamics is a textbook for a one or two semester graduate or senior level course in electrodynamics or electromagnetic theory. It seeks to unify classical electrodynamics by using hamilton's principles and the symmetry properties of space and time as basic assumtions. For this reason special relativity is introduced much earlier than in most other texts. With this approach one is able to reduce the number of assumptions to a relatively fe that support the entire subject; in particular, from such basic assumptions, both the relativistic equations of motion for particles and Maxwell's equations for the electrodynamic field are derived. The text is broad in scope and covers, in addition to basic theory, applications to radiation theory, self-force of an electron, natural breadth of spectral lines, geometric optics, electrodynamics of material media, and propagation in moving media. The book contains worked-out examples with sample problems at the end of each chapter. Mathematical appendixes are included and the book is largely self-contained. This textbook conveys the unified nature of electrodynamics and points out, not only the beauty but also the limitations of the theory. The limitations are shown to rise from basic defects in the fundamental assumptions of the theory. The authors present analyses of the logical foundations of classical electrodynamics so that the student can better understand the problems that arise in modern theories, such as quantum electrodynamics. Also, by examining the nature of basic assumption and limits of applicability of a well-developed theory, the authors prepare the student for more difficult theories in elementary particle physics or quantum field theories.
## Electrodynamics from Ampère to Einstein

Three quarters of a century elapsed between Ampere's definition of electrodynamics and Einstein's reform of the concepts of space and time. The two events occurred in utterly different worlds: the French Academy of Sciences of the 1820s seems very remote from the Bern Patent Office of the early 1900s, and the forces between two electric currents quite foreign to the optical synchronization of clocks. Yet Ampere's electrodynamics and Einstein's relativity are firmly connected through a historical chain involving German extensions of Ampere's work, competition with British field conceptions, Dutch synthesis, and fin de siecle criticism of the aether-matter connection. Olivier Darrigol retraces this intriguing evolution, with a physicist's attention to conceptual and instrumental developments, and with a historian's awareness of their cultural and material embeddings. This book exploits a wide range of sources, and incorporates the many important insights of other scholars. Thorough accounts are given of crucial episodes such as Faraday's redefinition of charge and current, the genesis of Maxwell's field equations, and Hertz's experiments on fast electric oscillations. Thus there emerges a vivid picture of the intellectual and instrumental variety of nineteenth-century physics. The most influential investigators worked at the crossroads between different disciplines and traditions: they did not separate theory from experiment, they frequently drew on competing traditions, and their scientific interests extended beyond physics into chemistry, mathematics, physiology, and other areas. By bringing out these important features, this book offers a tightly connected and yet sharply contrasted view of early electrodynamics. Olivier Darrigol is a Research Director at the Centre National de la Recherche Scientifique, Paris. His research focuses on the history of quantum theory and of electrodynamics.
## Foundations of High-Energy Astrophysics

Written by one of today’s most highly respected astrophysicists, Foundations of High-Energy Astrophysics is an introduction to the mathematical and physical techniques used in the study of high-energy astrophysics. Here, Mario Vietri approaches the basics of high-energy astrophysics with an emphasis on underlying physical processes as opposed to a more mathematical approach. Alongside more traditional topics, Vietri presents new subjects increasingly considered crucial to understanding high-energy astrophysical sources, including the electrodynamics of cosmic sources, new developments in the theory of standard accretion disks, and the physics of coronae, thick disks, and accretion onto magnetized objects. The most thorough and engaging survey of high-energy astrophysics available today, Foundations of High-Energy Astrophysics introduces the main physical processes relevant to the field in a rigorous yet accessible way, while paying careful attention to observational issues. Vietri’s book will quickly become a classic text for students and active researchers in astronomy and astrophysics. Those in adjoining fields will also find it a valuable addition to their personal libraries.
## Klassische Elektrodynamik

The German translation of this classic of theoretical physics is now available in a further revised edition. This renders theoretical electrodynamics even more comprehensible than before. Unique to this textbook of electrodynamics are the incomparably large number of calculated examples and special cases and the many exercises at the end of each chapter.
## Field, Force, Energy and Momentum in Classical Electrodynamics (Revised Edition)

The classical theory of electrodynamics is based on Maxwell's equations and the Lorentz law of force. This book begins with a detailed analysis of these equations, and proceeds to examine their far-reaching consequences. The traditional approach to electrodynamics treats the ‘microscopic’ equations of Maxwell as fundamental, with electric charge and electric current as the sole sources of the electric and magnetic fields. Subsequently, polarization and magnetization are introduced into Maxwell's equations to account for the observed behavior of material media. The augmented equations, known as Maxwell's ‘macroscopic’ equations, are considered useful for practical applications, but are also ultimately reducible to the more fundamental ‘microscopic’ equations. In contrast, this textbook treats Maxwell's ‘macroscopic’ equations as the foundation of classical electrodynamics, and treats electrical charge, electrical current, polarization, and magnetization as the basic constituents of material media. The laws that govern the distribution of electromagnetic energy and momentum in space-time are also introduced in an early chapter, then discussed in great detail in subsequent chapters. The text presents several examples that demonstrate the solution of Maxwell's equations in diverse situations, aiming to enhance the reader’s understanding of the flow of energy and momentum as well as the distribution of force and torque throughout the matter-field systems under consideration. This revised edition of Field, Force, Energy and Momentum in Classical Electrodynamics features revised chapters, some of which include expanded discussions of fundamental concepts or alternative derivations of important formulas. The new edition also features three additional chapters covering Maxwell’s equations in spherical coordinates (Chapter 10), the author’s recent discussion (and streamlined proof) of the Optical Theorem (Chapter 13), and the fascinating connections between electromagnetism and Einstein’s special theory of relativity (Chapter 15). A new appendix covers the SI system of units that has been used throughout the book. The book is a useful textbook for physics majors studying classical electrodynamics. It also serves as a reference for industry professionals and academic faculty in the fields of optics and advanced electronics.
## Relativity: The Theory and Its Philosophy

Relativity: The Theory and its Philosophy provides a completely self-contained treatment of the philosophical foundations of the theory of relativity. It also surveys the most essential mathematical techniques and concepts that are indispensable to an understanding of the foundations of both the special and general theories of relativity. In short, the book includes a crash course in applied mathematics, ranging from elementary trigonometry to the classical tensor calculus. Comprised of 11 chapters, this book begins with an introduction to fundamental mathematical concepts such as sets, relations, and functions; N-tuples, vectors, and matrices; and vector algebra and calculus. The discussion then turns to the concept of relativity and elementary foundations of Newtonian mechanics, as well as the principle of special relativity and its interpretation by means of empiricism and rationalism. Subsequent chapters focus on the status of the doctrine of conventionalism in the theory of special relativity; the commensurability of classical and relativistic mechanics; mathematical foundations of special relativistic physics; and the classical or Newtonian theory of gravitation. The principle of general covariance and its relation to the principle of general relativity are also examined. The final chapter addresses the fundamental question as to the actual information concerning the structure of spacetime that is conveyed to us through the theory of general relativity. This monograph will be of interest to students, teachers, practitioners, and researchers in physics, mathematics, and philosophy.
## The Foundations of Science

This work by the French mathematician Henri Poincaré, translated into English in 1913, elegantly expounds his philosophy of science.
## Electromagnetic Phenomena in Matter

Modern electrodynamics in different media is a wide branch of electrodynamics which combines the exact theory of electromagnetic fields in the presence of electric charges and currents with statistical description of these fields in gases, plasmas, liquids and solids; dielectrics, conductors and superconductors. It is widely used in physics and in other natural sciences (such as astrophysics and geophysics, biophysics, ecology and evolution of terrestrial climate), and in various technological applications (radio electronics, technology of artificial materials, laser-based technological processes, propagation of bunches of charges particles, linear and nonlinear electromagnetic waves, etc.). Electrodynamics of matter is based on the exact fundamental (microscopic) electrodynamics but is supplemented with specific descriptions of electromagnetic fields in various media using the methods of statistical physics, quantum mechanics, physics of condensed matter (including theory of superconductivity), physical kinetics and plasma physics. This book presents in one unique volume a systematic description of the main electrodynamic phenomena in matter: - A large variety of theoretical approaches used in describing various media - Numerous important manifestations of electrodynamics in matter (magnetic materials, superconductivity, magnetic hydrodynamics, holography, radiation in crystals, solitons, etc.) - A description of the applications used in different branches of physics and many other fields of natural sciences - Describes the whole complexity of electrodynamics in matter including material at different levels. - Oriented towards 3-4 year bachelors, masters, and PhD students, as well as lectures, and engineers and scientists working in the field. - The reader will need a basic knowledge of general physics, higher mathematics, classical mechanics and microscopic (fundamental) electrodynamics at the standard university level - All examples and problems are described in detail in the text to help the reader learn how to solve problems - Advanced problems are marked with one asterisk, and the most advanced ones with two asterisks. Some problems are recommended to be solved first, and are are marked by filled dots; they are more general and important or contain results used in other problems.
## Electromagnetic Foundations of Solar Radiation Collection

This text seeks to illuminate, mainly for the electrical power engineers of the future, the topic of large scale solar flux gathering schemes, which arguably represent the major source of renewable power available. The aim of the content is to impart, from an electromagnetic perspective, a deep and sound understanding of the topic of solar flux collection, ranging from the characteristics of light to the properties of antennas. To do this five chapters are employed to provide a thorough grounding in relevant aspects of electromagnetism and electromagnetic waves including optics, electromagnetic radiation and reception, aperture antennas and array antennas and the quantum electrodynamics aspects of optical absorption, as it relates to photovoltaic techniques. The principles developed in these chapters are then used to underpin and elucidate the main chapters on photovoltaic collectors, concentrated solar power collectors, satellite based collection systems and optical nantennas. To establish the novel and transformative renewable technologies, which civilisation will soon require, in order to achieve sustainability quickly and effectively, the availability of professional engineers and scientists with a thorough and commanding grasp of the fundamental science is an absolutely essential prerequisite. This book provides this for solar power generating systems.
## High-Field Electrodynamics

Tremendous technological developments and rapid progress in theory have opened a new area of modern physics called high-field electrodynamics: the systematic study of the interaction of relativistic electrons or positrons with ultrahigh-intensity, coherent electromagnetic radiation. This advanced undergraduate/graduate-level text provides a detailed introduction to high-field electrodynamics, from its fundamentals to some of its important modern applications. The author describes a broad collection of theoretical techniques, and where possible, approaches derivations by at least two different routes to yield deeper physical insight and a wider range of mathematical and physical techniques. He also discusses some of the outstanding ramifications of electrodynamics in areas ranging from quantum optics, squeezed states, and the Einstein-Podolsky-Rosen paradox to rotating black holes, non-Abelian gauge field theories, and the Bohm-Aharanov effect. High-Field Electrodynamics gives a comprehensive description of the theoretical tools needed to approach this novel discipline. It highlights important modern applications and serves as a starting point for more advanced and specialized research at the frontiers of modern physics.

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