The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity (perihelion precession of Mercury, and light deflection by the sun). ------ Textbook features: detailed figures, worked examples, problems and solutions, boxed inserts, highlighted special topics, highlighted important math etc., helpful summaries, appendix, index.

This book is a pedagogical introduction to supergravity, a gravitational field theory that includes supersymmetry (symmetry between bosons and fermions) and is a generalization of Einstein's general relativity. Supergravity provides a low-energy effective theory of superstring theory, which has attracted much attention as a candidate for the unified theory of fundamental particles, and it is a useful tool for studying non-perturbative properties of superstring theory such as D-branes and string duality. This work considers classical supergravities in four and higher spacetime dimensions with their applications to superstring theory in mind. More concretely, it discusses classical Lagrangians (or field equations) and symmetry properties of supergravities. Besides local symmetries, supergravities often have global non-compact symmetries, which play a crucial role in their applications to superstring theory. One of the main features of this book is its detailed discussion of these non-compact symmetries. The aim of the book is twofold. One is to explain the basic ideas of supergravity to those who are not familiar with it. Toward that end, the discussions are made both pedagogical and concrete by stating equations explicitly. The other is to collect relevant formulae in one place so as to be useful for applications to string theory. The subjects discussed in this book include the vielbein formulation of gravity, supergravities in four dimensions, possible types of spinors in various dimensions, superalgebras and supermultiplets, non-linear sigma models for non-compact Lie groups, electric-magnetic duality symmetries, supergravities in higher dimensions, dimensional reductions, and gauged and massive supergravities.

This book, explores the conceptual foundations of Einstein's theory of relativity: the fascinating, yet tangled, web of philosophical, mathematical, and physical ideas that is the source of the theory's enduring philosophical interest.

Originally published in 1986.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The 2011 Nobel Prize in Physics was awarded for the discovery of cosmic acceleration due to dark energy, a discovery that is all the more perplexing as nobody knows what dark energy actually is. We put the modern concept of cosmological vacuum energy into historical context and show how it grew out of disparate roots in quantum mechanics (zero-point energy) and relativity theory (the cosmological constant, Einstein's "greatest blunder"). These two influences have remained strangely aloof and still co-exist in an uneasy alliance that is at the heart of the greatest crisis in theoretical physics, the cosmological-constant problem.

In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.

Through examining the work of W. B. Yeats, James Joyce, and Samuel Beckett, Katherine Ebury shows cosmology had a considerable impact on modernist creative strategies, developing alternative reading models of difficult texts such as Finnegans Wake and 'The Trilogy'.

This book offers an essential bridge between college-level introductions and advanced graduate-level books on special relativity. It begins at an elementary level, presenting and discussing the basic concepts normally covered in college-level works, including the Lorentz transformation. Subsequent chapters introduce the four-dimensional worldview implied by the Lorentz transformations, mixing time and space coordinates, before continuing on to the formalism of tensors, a topic usually avoided in lower-level courses. The book's second half addresses a number of essential points, including the concept of causality; the equivalence between mass and energy, including applications; relativistic optics; and measurements and matter in Minkowski spacetime. The closing chapters focus on the energy-momentum tensor of a continuous distribution of mass-energy and its covariant conservation; angular momentum; a discussion of the scalar field of perfect fluids and the Maxwell field; and general coordinates.
Every chapter is supplemented by a section with numerous exercises, allowing readers to practice the theory. These exercises constitute an essential part of the textbook, and the solutions to approximately half of them are provided in the appendix.

Beyond Einstein's Gravity is a graduate level introduction to extended theories of gravity and cosmology, including variational principles, the weak-field limit, gravitational waves, mathematical tools, exact solutions, as well as cosmological and astrophysical applications. The book provides a critical overview of the research in this area and unifies the existing literature using a consistent notation. Although the results apply in principle to all alternative gravities, a special emphasis is on scalar-tensor and f(R) theories. They were studied by theoretical physicists from early on, and in the 1980s they appeared in attempts to renormalize General Relativity and in models of the early universe. Recently, these theories have seen a new lease of life, in both their metric and metric-affine versions, as models of the present acceleration of the universe without introducing the mysterious and exotic dark energy. The dark matter problem can also be addressed in extended gravity. These applications are contributing to a deeper understanding of the gravitational interaction from both the theoretical and the experimental point of view. An extensive bibliography guides the reader into more detailed literature on particular topics.

Quantum gravity has developed into a fast-growing subject in physics and it is expected that probing the high-energy and high-curvature regimes of gravitating systems will shed some light on how to eventually achieve an ultraviolet complete quantum theory of gravity. Such a theory would provide the much needed information about fundamental problems of classical gravity, such as the initial big-bang singularity, the cosmological constant problem, Planck scale physics and the early-time inflationary evolution of our Universe. While in the first part of this book concepts of quantum gravity are introduced and approached from different angles, the second part discusses these theories in connection with cosmological models and observations, thereby exploring which types of signatures of modern and mathematically rigorous frameworks can be detected by experiments. The third and final part briefly reviews the observational status of dark matter and dark energy, and introduces alternative cosmological models. Edited and authored by leading researchers in the field and cast into the form of a multi-author textbook at postgraduate level, this volume will be of benefit to all postgraduate students and newcomers from neighboring disciplines wishing to find a comprehensive guide for their future research.

In 1908 Hermann Minkowski gave the four-dimensional(spacetime) formulationof special relativity[1]. In fact,HenriPoincare[ ' 2] rst noticedin1906that the Lorentz transformations had a geometric interpretation as rotations in a four-dimensional space with time as the fourth dimension. However it was Minkowski, who succe- fully decoded the profound message about the dimensionality of the world hidden in the relativity postulate, which re ects the experimental fact that natural laws are the same in all inertial reference frames. Unlike Poincare, ' Minkowski did not regardspacetime - the uni cation of space and time - as a convenientmathematical space, but insisted that this absolute four-dimensional world, as Minkowski called it, represents physical phenomena and the world more adequately than the relativity postulate: "the word relativity-postulate...seems to me very feeble. Since the pos- late comes to mean that only the four-dimensional world in space and time is given by the phenomena...I prefer to call it the postulate of the absolute world"[3]. The impact of Minkowski's ideas on the twentieth century physics has been so immense that one cannot imagine modern physics without the notion of spacetime. It would hardly be an exaggeration to say that spacetime has been the greatest discoveryinphysicsofall times. Theonlyotherdiscoverythatcomesclosetospa- time is Einstein's general relativity, which revealed that gravity is a manifestation of the curvature of spacetime. But it was the discovery of spacetime, which paved the way for this deep understanding of what gravity really is. Einstein saw the link betweenthegeometryofspacetimeandgravitationonlyafterheovercamehis initial hostile attitude toward the notion of spacetime.

The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more "utilitarian" treatments of the subject. The book is divided into four parts, entitled respectively "Origins", "Dynamics", "Symmetries", and "Scales". The emphasis is conceptual - the aim is to build the theory up systematically from some clearly stated foundational concepts - and therefore to a large extent anti-historical, but two historical Chapters ("Origins") are included to situate quantum field theory in the larger context of modern physical theories. The three remaining sections of the book follow a step by step reconstruction of this framework beginning with just a few basic assumptions: relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The ``Dynamics" section of the book lays out the basic structure of quantum field theory arising from the sequential insertion of quantum-mechanical, relativistic and locality constraints. The central role of symmetries in relativistic quantum field theories is explored in the third section of the book, while in the final section, entitled "Scales", we explore in detail the feature of quantum field theories most critical for their enormous phenomenological success - the scale separation property embodied by the renormalization group properties of a theory defined by an effective local Lagrangian.The book includes a wide range of problems at chapter ends. Solutions can be requested via the publisher's web site.

This is the first comprehensive treatment of active galactic nuclei--the cosmic powerhouses at the core of many distant galaxies. The term "active galactic nuclei" refers to quasars, radio galaxies, Seyfert galaxies, blazars, and related objects, all of which are believed to share a similar central engine--a supermassive black hole many times the mass of the Sun. Astrophysicists have studied these phenomena for the past several decades and have begun to develop a consensus about many of their properties and internal mechanisms. Julian Krolik, one of the world's leading authorities on the subject, sums up leading ideas from across the entire range of research, making this book an invaluable resource for astronomers, physicists interested in applications of the theory of gravitation, and graduate students.

Krolik begins by addressing basic questions about active galactic nuclei: What are they? How can they be found? How do they evolve? He assesses the evidence for massive black holes and considers how they generate power by accretion. He discusses X-ray and g-ray emission, radio emission and jets, emission and absorption lines, anisotropic appearance, and the relationship between an active nucleus and its host galaxy. He explores the mysteries of what ignites, fuels, and extinguishes active galactic nuclei, and concludes with a general review of where the field now stands. The book is unique in paying careful attention to relevant physics as well as astronomy, reflecting in part the importance of general relativity to understanding active galactic nuclei. Clear, authoritative, and detailed, this is crucial reading for anyone interested in one of the most dynamic areas of astrophysics today.

Over the past years the author has developed a quantum language going beyond the concepts used by Bohr and Heisenberg. The simple formal algebraic language is designed to be consistent with quantum theory. It differs from natural languages in its epistemology, modal structure, logical connections, and copulatives. Starting from ideas of John von Neumann and in part also as a response to his fundamental work, the author bases his approach on what one really observes when studying quantum processes. This way the new language can be seen as a clue to a deeper understanding of the concepts of quantum physics, at the same time avoiding those paradoxes which arise when using natural languages. The work is organized didactically: The reader learns in fairly concrete form about the language and its structure as well as about its use for physics.

One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-' We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities." add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one, should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.

The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.

Carl Friedrich von Weizsacker s "Aufbau der Physik," first published in 1985, was intended as an overview of his lifelong concern: an understanding of the unity of physics. That is, the idea of a quantum theory of binary alternatives (the so-called ur-theory), a unified quantum theoretical framework in which spinorial symmetry groups are considered to give rise to the structure of space and time.

The book saw numerous reprints, but it was published in German only.

The present edition, in English, provides a newly arranged and revised version, in which some original chapters and sections have been deleted, and a new chapter about further insights and results of ur-theoretic research of the late 1980 s and 1990 s, mainly by the work of Thomas Gornitz, has been included, as well as a general introduction to Weizsacker s Philosophy of Physics.

Carl Friedrich von Weizsacker also enjoys high esteem by a much broader audience for his socio-cultural, political and religious thoughts and writings. In him the intercultural and interdisciplinary dialogue has found one of its most important proponents: a great thinker who combines the perspectives of science, philosophy, religion and politics with a view towards the challenges as well as the responsibilities of our time."

Ever since its infancy, humankind has been seeking answers to some very basic and profound questions. Did the Universe begin? If it did, how old is it, and where did it come from? What is its shape? What is it made of? Fascinating myths and brilliant in- itions attempting to solve such enigmas can be found all through the history of human thought. Every culture has its own legends, itsownworldcreationtales, itsphilosophicalspeculations, itsre- gious beliefs. Modern science, however, cannot content itself with fanciful explanations, no matter how suggestive they are. No- days, our theories about the Universe, built upon rational ded- tion, have to survive the hard test of experiment and observation. Cosmology, the science which studies the origin and evo- tion of the Universe, had to overcome enormous dif?culties before it could achieve the same level of dignity as other physical dis- plines. At ?rst, it had no serious physical model and mathematical tools that could be used to address the complexity of the problems it had to face. Then, it suffered from a chronic lack of experim- tal data, which made it almost impossible to test the theoretical speculations. Given this situation, answering rigorously the many questions on the nature of the Universe seemed nothing more than a delusion. Today, however, things have changed. We live in the golden age of cosmology: an exciting moment, when, for the ?rst time, we are able to scienti?cally understand our Univers

This book describes a paradigm change in modern physics from the philosophy and mathematical expression of the quantum theory to those of general relativity. The approach applies to all domains - from elementary particles to cosmology. The change is from the positivistic views in which atomism, nondeterminism and measurement are fundamental, to a holistic view in realism, wherein matter - electrons, galaxies, - are correlated modes of a single continuum, the universe. A field that unifies electromagnetism, gravity and inertia is demonstrated explicitly, with new predictions, in terms of quaternion and spinor field equations in a curved spacetime. Quantum mechanics emerges as a linear, flatspace approximation for the equations of inertia in general relativity.

This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.

This volume is intended as a systematic introduction to gauge field theory for advanced undergraduate and graduate students in high energy physics. The discussion is restricted to the classical (non-quantum) theory in Minkowski spacetime. Particular attention has been given to conceptual aspects of field theory, accurate definitions of basic physical notions, and thorough analysis of exact solutions to the equations of motion for interacting systems.

This book is aimed at theoretical as well as primarily physicists graduate students in field working quantum theory, quantum gravity, theories, gauge to sdme and and, it is not extent, general relativity cosmology. Although aimed at a I that it also be of level, hope in mathematically rigorous may terest to mathematical and mathematicians in physicists working spectral of differential mani geometry, spectral asymptotics on operators, analysis differential and mathematical methods in folds, geometry quantum theory. Thisbook will be considered too abstract some but certainly by physicists, not detailed and most mathematicians. This in completeenoughby means, thatthe material is at the level of particular, presented "physical" So, rigor. there theorems and areno and technicalcalculationsare lemmas, proofs long omitted. I tried detailed to a ofthe basic Instead, give presentation ideas, methodsandresults. Itried makethe to as andcom Also, exposition explicit as the lessabstractandhaveillustratedthe plete possible, methods language and results withsome As is well "onecannot examples. known, cover every in an text. The in this thing," especially introductory approach presented book the lines is a further of the so called along goes (and development) fieldmethod ofDe Witt. As a Ihavenot dealt at background consequence, allwithmanifoldswith boundary, non Laplacetype (ornonminimal) opera Riemann Cartan manifolds well with as as recent tors, developments many and advanced such Ashtekar's more as topics, approach, supergravity, strings, matrix etc. The membranes, interested reader is referred models, M theory tothe literature.

This volume presents a selection of 434 letters from and to the Dutch physicist and Nobel Prize winner Hendrik Antoon Lorentz (1853-1928), covering the period from 1883 until a few months before his death in February 1928. The sheer size of the available correspondence (approximately 6000 letters from and to Lorentz) preclude a full publication. The letters included in this volume have been selected according to various criteria, the most important of which is scientific importance. A second criterion has been the availability of letters both from and to Lorentz, so that the reader can follow the exchange between Lorentz and his correspondent. Within such correspondences a few unimportant items, dealing with routine administrative or organizational matters, have been omitted. An exception to the scientific criterion is the exchange of letters between Lorentz and Albert Einstein, Max Planck, Woldemar Voigt, and Wilhelm Wien during World War I: these letters have been included because they shed important light on the disruption of the scientific relations during the war and on the political views of these correspondents as well as of Lorentz. similar reasons the letters exchanged with Einstein and Planck on post-war political issues have been included. Biographical sketch Hendrik Antoon Lorentz was born on July 18, 1853 in the Dutch town of Arnhem. He was the son of a relatively well-to-do owner of a nursery.

Is time, even locally, like the real line? Multiple structures of time, implicit in physics, create a consistency problem. A tilt in the arrow of time is suggested as the most conservative hypothesis which provides approximate consistency within physics and with topology of mundane time. Mathematically, the assumed constancy of the velocity of light (needed to measure time) implies functional differential equations of motion, that have both retarded and advanced deviating arguments with the hypothesis of a tilt. The novel features of such equations lead to a nontrivial structure of time and quantum-mechanical behaviour. The entire argument is embedded in a pedagogical exposition which amplifies, corrects, and questions the conventionally accepted approach. The exposition includes historical details and explains, for instance, why the entropy law is inadequate for time asymmetry, and why notions such as time asymmetry (hence causality) may be conceptually inadequate. The first three parts of the book are especially suited as supplementary reading material for undergraduate and graduate students and teachers of physics. The new ideas are addressed to researchers in physics and philosophy of science concerned with relativity and the interpretation of quantum mechanics.

This mathematically-oriented introduction takes the point of view that students should become familiar, at an early stage, with the physics of relativistic continua and thermodynamics within the framework of special relativity. Therefore, in addition to standard textbook topics such as relativistic kinematics and vacuum electrodynamics, the reader will be thoroughly introduced to relativistic continuum and fluid mechanics. There is emphasis on the 3+1 splitting technique.

Special and General Relativity are concisely developed together with essential aspects of nuclear and particle physics. Problem sets are provided for many chapters, making the book ideal for a course on the physics of white dwarf and neutron star interiors. Norman K. Glendenning is Senior Scientist Emeritus at the Nuclear Science Division, Institute for Nuclear and Particle Astrophysics, Lawrence Berkeley National Laboratory at the University of California, Berkeley. He is the author of numerous books.