This book evolved out of some one hundred lectures given by twenty experts at a special instructional conference sponsored by the University Grants Commis sion, India. It is pedagogical in style and self-contained in several interrelated areas of physics which have become extremely important in present-day theoretical research. The articles begin with an introduction to general relativity and cosmology as well as particle physics and quantum field theory. This is followed by reviews of the standard gauge models of high-energy physics, renormalization group and grand unified theories. The concluding parts of the book comprise discussions in current research topics such as problems of the early universe, quantum cosmology and the new directions towards a unification of gravitation with other forces. In addition, special concise treatments of mathematical topics of direct relevance are also included. The content of the book was carefully worked out for the mutual education of students and research workers in general relativity and particle physics. This ambitious programe consequently necessitated the involvement of a number of different authors. However, care has been taken to ensure that the material meshes into a unified, cogent and readable book. We hope that the book will serve to initiate and guide a student in these different areas of investigation starting from first principles and leading to the exciting current research problems of an interdisciplinary nature in the context of the origin and structure of the universe."

Scientists in the late twentieth century are not the first to view galaxy formation as a phenomenon worthy of explanation in terms of the known laws of physics. Already in 1754 Kant regarded the problem as essentially solved. In his Univerlal Natural Hutory and Theory 0/ the H eaven$ he wrote; "If in the immesurable space in which all the suns of the Milky Way have formed themselves, we assume a point around which, through some cause or other, the first formation of nature out of chaoo began, there the largest mass and a body of extraordinary attraction will have arisen which has thereby become capable of compelling all the systems in the process of being formed within an enormous sphere around it, to fall towards itself as their centre, and to build up a system around it on the great scale . . . . Observation puts this conjecture almost beyond doubt. " More than 200 years later, a similar note of confidence was voiced by Zel'dovicb at an IAU symposium held in Tallin in 1911; "Extrapolating . . . to the next symposium somewhere in the early eighties one can be pretty sure that the question of the formation of galaxies and clusters will be solved in the next few years. " Perhaps few astronomers today would share Kant's near certainty or feel that Zel'dovich's prophecy has been fulfilled, Many, however, will sympathize with the optimistic olltlook of these two statements.

The second Erice course in the school of Particle-Astrophysics was held in May, 1988. The topic choosen was Dark Matter. This is one of the most exciting top ics at the interface of particle physics and astrophysics. It is developing rapidly now due to a coming together not only of the theoretical concepts from the early universe with the theoretical concepts of galaxy formation, but also the coming to gether of the theorists, experimentalists and observers. It is with Dark Matter, the combined interrelated topics of galaxy formation and the generation of large scale structure that we see a confrontation of the exotic ideas from the early universe, such as phase transitions and unification, coming face to face with the realities of traditional observational cosmology. These realities have recently been heightened by the tremendous number of new observations, demonstrating that large scale structure of the universe is far more complex than anybody had suspected. In particular, we now see large scale foam, apparent large scale velocity fields, indicating devations from the Hubble flow, large scales of the order 100 Mpc, and galaxy formation occurring at high red shifts much greater than unity. We also see an apparent correlation of clusters of galaxies that may even exceed the c- relation of galaxies despite their being on much larger scales with lower average densities."

This book is the result of a Meeting held in L'Aquila (Italy) from the 19th to the 23rd of June 1989. The aim of the Meeting was to gather together the people actively working on the Cosmic Microwave Background radiation, both from an experimental and from a theoretical point of view. In view of the intensive current activity in this field, including ongoing (COBE) and forthcoming (RELIC II, ISO, AELITA, etc. ) space missions, a meeting fully dedicated to this important topic was timely. The meeting also celebrated the 25th anniversary of the Microwave Background discovery made in 1964 by the Nobel Prize winners A. Penzias and R. Wilson. We greatly regret that we were not able to have them at the Meeting. There is of course another person whose absence we regret, namely R. H. Dicke, who motivated a generation of experimentalists and theoreticians to open and study this new field of research. As organizers of the Meeting, we would like to express our gratitude to the people who contributed to its success. We want to thank the members of the Scientific Organizing Committee for their assistance, suggestions and encouragement, the invited speakers for their excellent presentations, and the chairmen for their help in handling the various Sessions. We would like to thank P. Palazzi for her help in secretarial work, dr. L.

The 1980's have been times of great excitement in Astrophysics and Cosmology. Professors Dennis Sciama and Fabio Mardirossian and all the other Members of the Organizing Committees are to be congratulated for having given us a taste of this excitement in Trieste, by inviting the leaders of the subject to the meeting they have organized. The excitement has corne from the new observations of the three-dimensional structure of the universe through a large number of new measurements of redshifts. These have revealed that clusters of galaxies are distributed on the surface of big empty bubbles of diameters of the order of 20-50 Mpc. Additionally, there is some evidence for invisible dark matter (whose composition is not known) as well as evidence for the gravitational lens effect. To cap this has corne the supernova of 1987, an event which last occurred 383 years ago. For the first time in history, the neutrino flux from the supernova was measured, giving limits to neutrino masses and numbers of neutrino types. (The dark matter problem is related to Particle Physics - beyond this standard model). It is good to be alive when all this happens and to try to comprehend this. Once again, our appreciation to the organisers and to those who presented their beautiful results.

The essays in this topical volume inquire into one of the most fundamental issues of philosophy and of the cognitive and natural sciences: the riddle of time. The central feature is the tension between the experience and the conceptualization of time, reflecting an apparently unavoidable antinomy of subjective first-person accounts and objective traditional science. Is time based in the physics of inanimate matter, or does it originate in the operation of our minds? Is it essential for the constitution of reality, or is it just an illusion? Issues of time, temporality, and nowness are paradigms for interdisciplinary work in many contemporary fields of research. The authors of this volume discuss profoundly the mutual relationships and inspiring perspectives. They address a general audience.

In the development of Fundamental Physics on one side, and of Astronomy/Cosmology on the other side, periods of parallell, relatively independent progress seem to alternate with others of intense interaction and mutual influence. To this latter case belong the very beginnings of Modern Physics, with Galileo and Newton. There is now a widespread feeling that another of such flourishing periods may have started some ten years ago, with the advent of Unified Theories and the introduction of Inflationary Cosmologies. The interaction between the two disciplines has become tighter ever since, spurring studies of e. g. astronomical and particle Dark Matter candidates, Superstrings and Cosmic Strings, phase transitions in the Early Universe, etc. etc. Then the recent birth of Neutrino Astronomy has added further flavor to this splendid conjunction. It was indeed with the clear perception of this trend that six years ago CERN and ESO decided to jointly organize a series of symposia focusing on the interactions between Astronomy, Cosmology, and Fundamental Physics, to be held about every two years. The aim of these meetings is to bring together astronomers, cosmologists, and particle physicists to exchange information, to discuss scientific issues of common interest, and to take note of the latest devolopments in each discipline that are relevant to the other. The First ESO-CERN Symposium was held at CERN (Geneva) on November 21-25, 1983. Then for its Second edition the ESO-CERN Symposium moved to Garching bei Miinchen, where ESO headquarters are located, and took place on March 17-21, 1986.

The sixteenth European Conference on Few Body Problems in Physics has taken place from June 1 to June 6, 1998, in Autrans, a little village in the mountains, close to Grenoble. The Conference follows those organized in Peniscola (1995), Amsterdam (1993), Elba (1991), Uzhgorod (1990) ... The present one has been organized by a group of physicists working in different fields at the University Joseph Fourier of Grenoble who find in this occasion a good opportunity to join their efforts. The core of the organizing committee was nevertheless located at the Institut des Sciences Nucleaires, whose physicists, especially in the group of theoretical physics, have a long tradition in the domain. The Few Body Conference has a natural tendency to be a theoretical one - the exchange about the methods used in different fields is the common point to most participants. It also has a tendency to be a hadronic physics one - the corresponding physics community, perhaps due to the existence of experimen tal facilities devoted to the study of few body systems, is better organized. In preparing the scientific program, we largely relied on the advices of the Inter national Advisory Committee, while avoiding to follow these trends too closely."

The contemporary trends in the quantum unification of all interactions including gravity motivate this Course. The main goal and impact of modern string theory is to provide a consistent quantum theory of gravity. This, Course is intended to provide an updated understanding of the last developments and current problems of string theory in connection with gravity and the physics at the Planck energy scale. It is also the aim of this Course to discuss fundamental problems of quantum gravity in the present-day context irrespective of strings or any other models. Emphasis is given to the mutual impact of string theory, gravity and cosmology, within a deep a well defined programme, which provides, in addition, a careful interdisciplinarity. Since the most relevant new physics provided by strings concerns the quantization of gravity, we must, at least, understand string quantization in curved space-times to start. Curved space-times, besides their evident relevance m classical gravitation, are also important at energies of the order of the Planck scale. At the Planck energy, gravitational interactions are at least as important as the rest and can not be neglected anymore. Special care is taken here to provide the grounds of the different lines of research in competition (not just only one approach); this provides an excellent opportunity to learn about the real state of the discipline, and to learn it in a critical way.

This volwne is the proceedings of the third school in particle astrophysics that Schramm and Galeotti have organized at Erice. The focus of thirs third school was the Generation of Cosmological Large-Scale Structure. It was held in November of 1996. The fIrst school in the series was on "Gauge Theory and the Early Universe" in May 1986, the second was on "Dark Matter in the Universe" in May 1988. All three schools have been successful under the auspices of the NATO Advanced Study Institute. This volume is thus the third in the series of the proceedings of these schools. The choice of the topic for this third school was natural, since the problem of generating a large-scale structure has become the most pressing problem in cosmology today. In particular, it is this generation of structure that is the interface between astronomical observations and particle models for the early universe. To date, all models for generating structures inevitably require new fundamental physics beyond the standard, SU x SU X U , model of high energy physics. The 3 2 I seeds for generating structures usually invoke unifIcation physics, and the matter needed to clump and form them seems to require particle properties that have not been seen in laboratories to date.

The theory, observations, and applications ofgravitational lensingconstitute one ofthe most rapidly growing branches ofextragalactic astrophysics. The deflection of light from very distant sources by intervening masses provides a unique possibility for the investigation of both background sources and lens mass distributions. Gravitational lensing manifestsitselfmost distinctly through multiply imaged QSOs and the formation of highly elongated im ages of distant galaxies ('arcs') and spectacular ring-like images of extra galactic radio sources. But the effects of gravitational light deflection are not limited to these prominent image configurations; more subtle, since not directly observable, consequences of lensing are the, possibly strong, mag nification of sources, which may permit observation of intrinsically fainter, or more distant, sources than would be visible without these natural tele scopes. Such light deflection can also affect the source counts of QSOs and of other compact extragalactic sources, and can lead to flux variability of sources owing to propagation effects. Trying to summarizethe theory and observationalstatus ofgravitational lensing in a monograph turned out to be a bigger problem than any of the authors anticipated when we started this project at the end of 1987, encour aged by Martin Harwit, who originally approached us. The development in the field has been very rapid during the last four years, both through the ory and through observation, and many sections have been rewritten several times, as the previous versions became out of date.

The International Conference on the History of Original Ideas and Basic Discoveries, held at the "Ettore Majorana" Centre for Scientific Culture in Erice, Sicily, July 27-August 4, 1994, brought together sixty of the leading scientists including many Nobel Laureates in high energy physics, principal contributors in other fields of physics such as high Tc superconductivity, particle accelerators and detector instrumentation, and thirty-six talented younger physicists selected from candidates throughout the world. The scientific program, including 49 lectures and a discussion session on the "Status and Future Directions in High Energy Physics" was inspired by the conference theme: The key experimental discoveries and theoretical breakthroughs of the last 50 years, in particle physics and related fields, have led us to a powerful description of matter in terms of three quark and three lepton families and four fundamental interactions. The most recent generation of experiments at e+e- and proton-proton colliders, and corresponding advances in theoretical calculations, have given us remarkably precise determinations of the basic parameters of the electroweak and strong interactions. These developments, while showing the striking internal consistency of the Standard Model, have also sharpened our view of the many unanswered questions which remain for the next generation: the origin and pattern of particle masses and families, the unification of the interactions including gravity, and the relation between the laws of physics and the initial conditions of the universe.

Der vorliegende Klassiker bietet Studierenden und Forschenden in den Gebieten der Theoretischen und Mathematischen Physik eine ideale Einfuhrung in die Differentialgeometrie und Topologie. Beides sind wichtige Werkzeuge in den Gebieten der Astrophysik, der Teilchen- und Festkoerperphysik. Das Buch fuhrt durch: - Pfadintegralmethode und Eichtheorie - Mathematische Grundlagen von Abbildungen, Vektorraumen und Topologie - Fortgeschrittene Konzepte der Geometrie und Topologie und deren Anwendungen im Bereich der Flussigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie - Eine Zusammenfuhrung von Geometrie und Topologie: Faserbundel, charakteristische Klassen und Indextheoreme - Anwendungen von Geometrie und Topologie in der modernen Physik: Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer geometrischen Perspektive

In one ofthe fundamental notions is that any physical theory of of energy the hand: in mechanics at one considers the objects energy of, say, moving in fieldtheories is one interested inthe offield masses; energy configurations. A unified treatment of this which both to mechanics question, applies and to field Hamiltonian a formalism. We will theory, proceeds through shortly reviewbelowhowsuch iscarried aprocedure out inthe ofscalarfields theory Minkowski let at this on mention that an space time; us, stage, important often inthe isthat ofthe issue, ignored conditions sat textbooks, boundary isfied the set of fields under consideration. While by this issuecanbe safely for when the ignored usual field many purposes considering theories, such scalar fields or the = as on electromagnetism, ft constj hypersurfaces, where t is a it sometimes critical Minkowski time, a rolewhen other plays of classes are considered. Inthe of the hypersurfaces case situation is gravity for t= worse: even Minkowskian slicesthe f constj asymptotically boundary terms crucial. is ofthe are one main differencesbetweentheArnowitt (This Deser Misner for Sect. 5. 4 mass which is (ADM) gravity (cf. below), given a andthe usual for by boundary integral, field theories in energyexpression Minkowski wheretheHamiltonian is volume space time, a usually integral. ) in field the itsmost role in Now, theory plays important theradiation energy where it can be radiated the field.

Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this 2004 book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

Like a river, the progress of science has a tendency to run tast or slow. Once the water meets a dam, it may stop for a while, but eventually it will flow over the top and run fast again. In scientific research, a breakthrough to overcome a simile>r barrier is often made by a small number of scientists, or perhaps by a single person of special creativity, extraordinary talent and unusual perseverance. Through such individuals science can proceed in great strides. No one can deny that Professor Kazuo Takayanagi is one of these special individuals who have played a leading role in the field of atomic and molecular physics, as well as space physics. This book is dedicated to Professor Takayanagi on the occasion of his retirement from the Institute of Space and Astronautical Science. Professor Takayanagi was born in 1926 and grew up in Tomakomai in Hokkaido, the northern island of Japan. In his boyhood, he was interested in natural sciences, particularly astronomy. On 5th February, 1943, when he was attending secondary school, a solar eclipse was seen in his town. He organized a group of students from his school to observe the eclipse. He still remembers the scene: it grew so dark during the eclipse that two stars, Vega and Arcturus, could be seen. After graduation from the University of Tokyo in 1948, he entered the graduate school there.

This 2004 textbook fills a gap in the literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most elegant, successful, and relevant applications of general relativity. Among the topics discussed are congruencies of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity. Although the book is self-contained, it is not meant to serve as an introduction to general relativity. Instead, it is meant to help the reader acquire advanced skills and become a competent researcher in relativity and gravitational physics. The primary readership consists of graduate students in gravitational physics. It will also be a useful reference for more seasoned researchers working in this field.

The tremendous progress in astronomical observations over the past sixty years has revealed a vast structured universe whose fundamental parti cles are galaxies, and clusters thereof. The interpretation of the new astronomical evidence owes much to Einstein's insights and deductions. All our knowledge of the world derives from the light, more generally the energy, which reaches us from near and far. Einstein recognised the vital role of energy as the solE basis of our information about the workings of nature; his Special Theory of Relativity showed how our understanding of space and time Is linked with measurements involving reflecting light signals. He further demonstrated that matter exists in two interchangeable forms - a mass form and an energy form - which interact closely at all levels. His General Theory of Relativity dealt with the nature of this interaction in the context of gravitational fields, and led to a view of the universe which was soon observationally confirmed. Einstein's methods and results form the theoretical basis of modern cosmology which has spawned many 'models' of the universe; how ever, they all deal with an Einstein-type universe and they all employ his geometric approach to describe it."

The visible universe is a small perturbation on the material universe. Zwicky and Sinclair Smith in the 1930s gave evidence of invisible mass in the Coma and Virgo Clusters of Galaxies. Better optical data has only served to confound their critics and the X-ray data confirms that the gravitational potentials are many times larger than those predicted on the basis of the observed stars. Dynamical analyses of individual galaxies have found that significant extra mass is needed to explain their rotational velocities. On much larger scales, tens of megaparsecs, there is suggestive evidence that there is even more mass per unit luminosity. What is this non-luminous stuff of which the universe is made'? How much of it is there? Need there be only one kind of stuff? There are three basic possi bili ties:- all of it is ordinary (baryonic) matter, all of it is some other kind of (non-baryonic) matter, or some of it is baryonic and some is non-baryonic.

A small country builds a world-class telescope in its backyard and lives happily ever after (or at least for a quarter century). That in a nutshell is the story told in this collection of essays. The country of course is the Netherlands, and the telescope is the Westerbork Synthesis Radio Tele scope (WSRT), brainchild of Jan Oort. Living happily in this context is a continuing record of discovery and as such also a continuing basis for se curing observing time on facilities in other countries and operating at other frequencies. As our community celebrates the Silver Anniversary of the radio tele scope at Westerbork, it is fitting that we pause to take account of the scientific discoveries and insights it made possible. Initially the instrument represented the very significant step away from university-run, specialist facilities to a well-supported, common-user radio imager also having spec tral and polarization capabilities. It pioneered the mode of operation now common for satellite observatories, in which data is taken and calibrated by technicians and provided to researchers ready for analysis. It has been a major source of discovery in, among other areas, research on neutral hy drogen and studies of dark matter in galaxies.

edited by c. H. Lineweaver, J. G. Bartlett, A. Blanchard Observatoire Astronomique de Strasbourg, Strasbourg, France M. Signore Ecole normale superieure, Paris, France and J. Silk Departments of Astronomy and Physics, University of California at Berkeley, Berkeley, CA, U. S. A. Kluwer Academic Publishers Dordrecht / Boston / London Published in cooperation with NATO Scientific Affairs Division ISBN-13:978-94-010-6512-2 e-ISBN-13:978-94-009-0051-6 DOI:10. 107/ 978-94-009-0051-6 Softcover reprint of the hardcover 1st edition 1997 Dedication We dedicate these proceedings to the people who paid for it: taxpayers of the NATO alliance. Table of Contents PREFACE IX LIST OF PARTICIPANTS XI LISTOF CONTRIBUTORS Xlll I. Introduction, Mathematical Tools and Background An Introduction to CBR Studies: Spectrum, Degree-Scale Fluctuations, Foregrounds and Interferometry R. B. Partridge ElementsofGeneral Relativity, Cosmology and the Cosmic Microwave Background Jose L. Sanz 33 Statisticsand Random Functions in Astrophysics BernhardIT. Jones 67 Structure Formation Joseph Silk III II. eMB Anistropies CalculationofCosmic Background Radiation Anisotropies and Implications Emory F. Bunn 135 The CMB Anistropy Experiments: Cosmic Microwave Background George F. Smoot 185 viii III. CMB Spectrum The CMBR-Spectrum: ATheoretical Introduction Albert Stebbins 241 The CMB Spectrum George F. Smoot 271 IV. Astroparticle Physics Inflation and the Cosmic Background Radiation: What Every Cosmologist Needs to Know Michael S. Turner 309 Primordial Chemistry and Cosmic Background Radiation M. Signori, P. Encrenaz, R. MaoJi, B. Melchiorri, F. Melchiorri and D. Puy 345 The Cosmic Background Radiation and Elementary Particles Pierre Salati 365 V.

The main goal of this work is to revisit the proof of the global stability of Minkowski space by D. Christodoulou and S. Klainerman, [Ch-KI]. We provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets. This can also be interpreted as a proof of the global stability of the external region of Schwarzschild spacetime. The proof, which is a significant modification of the arguments in [Ch-Kl], is based on a double null foliation of spacetime instead of the mixed null-maximal foliation used in [Ch-Kl]. This approach is more naturally adapted to the radiation features of the Einstein equations and leads to important technical simplifications. In the first chapter we review some basic notions of differential geometry that are sys tematically used in all the remaining chapters. We then introduce the Einstein equations and the initial data sets and discuss some of the basic features of the initial value problem in general relativity. We shall review, without proofs, well-established results concerning local and global existence and uniqueness and formulate our main result. The second chapter provides the technical motivation for the proof of our main theorem.

In a distilled and pedagogical fashion, the contributions to this volume of the famous summer school in Les Houches cover the recent developments in supersymmetric string theory, the gauge theory/string theory correspondence and string duality. Further chapters deal with quantum gravity and D-brane geometry. Black hole mechanics and cosmology are treated too, as well as the AdS-CFT correspondence. The book is a comprehensive introduction to the recent developments in string/M-theory and quantum gravity. It addresses graduate students in physics and astrophysics.

This book is a new edition of "Tensors and Manifolds: With Applications to Mechanics and Relativity" which was published in 1992. It is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanse of modern mathematics and its application in modern physics. It aims to fill the gap between the basic courses and the highly technical and specialised courses which both mathematics and physics students require in their advanced training, while simultaneously trying to promote, at an early stage, a better appreciation and understanding of each other's discipline. The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics. The existing material from the first edition has been reworked and extended in some sections to provide extra clarity, as well as additional problems. Four new chapters on Lie groups and fibre bundles have been included, leading to an exposition of gauge theory and the standard model of elementary particle physics. Mathematical rigour combined with an informal style makes this a very accessible book and will provide the reader with an enjoyable panorama of interesting mathematics and physics.

The scalar-tensor theory of gravitation is one of the most popular alternatives to Einstein's theory of gravitation. This book provides a clear and concise introduction to the theoretical ideas and developments, exploring scalar fields and placing them in context with a discussion of Brans-Dicke theory. Topics covered include the cosmological constant problem, time variability of coupling constants, higher dimensional space-time, branes and conformal transformations. The authors emphasize the physical applications of the scalar-tensor theory and thus provide a pedagogical overview of the subject, keeping more mathematically detailed sections for the appendices. This book is suitable for graduate courses in cosmology, gravitation and relativity. It will also provide a valuable reference for researchers.