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.

The International Conference "Primordial Nucleosynthesis and Evolution of Early Universe" was held in the presence of Prof. William Fowler on 4 - 8 September 1990 at the Sanjo Conference Hall, the University of Tokyo. This conference was co-sponsored by IUPAP, the International Union of Pure and Applied Physics, and by the University of Tokyo. The number of participants was 156, 58 from 15 foreign countries and 98 from Japan. About 120 contributions were submitted orally or as posters. Originally this conference was planned as a small gathering on Primordial Nucleosynthesis as indicated in the title, since primordial nucleosynthesis is the most important probe of the early stage of the universe. As is well known, light element abundances strongly depend on the time evolution of temperature and density. In this sense we can say that primordial nucleosynthesis is both the thermometer and speedometer of the early universe. Moreover, recently it has been claimed that primordial nucleosynthesis is an indicator of inhomogeneity of the early universe too. Now research of the primordial nucleosynthesis is in a boom. We, however, decided to include observational cosmology, of observations. taking into account the recent remarkable results Nowadays, to reveal the large scale structure of the universe and discover its origin is a main subject in cosmology. We invited distinguished scientists from all over the world, and very fortunately almost all these people accepted to attend this conference.

Clusters and superclusters of galaxies are the largest objects in the Universe. They have been the subject of intense observational studies at a variety of wavelengths, from radio to X-ray which has provoked much theoretical debate and advanced our understanding of the recent evolution of the large-scale structure of the Universe. The current status of the subject is reviewed in this volume by active researchers who lectured at a NATO Advanced Study Institute held in Cambridge, England in July 1991. Much of the material is presented in a pedagogical manner and will appeal to scientists, astronomers and graduate students interested in extragalactic astronomy.

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.

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.

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.

This book deals with diffraction radiation, which implies the boundary problems of electromagnetic radiation theory. Diffraction radiation is generated when a charged particle moves near a target edge at a distance ( - Lorentz factor, - wave length). Diffraction radiation of non-relativistic particles is widely used to design intense emitters in the cm wavelength range. Diffraction radiation from relativistic charged particles is important for noninvasive beam diagnostics and design of free electron lasers based on Smith-Purcell radiation which is diffraction radiation from periodic structures. Different analytical models of diffraction radiation and results of recent experimental studies are presented in this book. The book may also serve as guide to classical electrodynamics applications in beam physics and electrodynamics. It can be of great use for young researchers to develop skills and for experienced scientists to obtain new results.

Dr. KURT GODEL'S sixtieth birthday (April 28, 1966) and the thirty fifth anniversary of the publication of his theorems on undecidability were celebrated during the 75th Anniversary Meeting of the Ohio Ac ademy of Science at The Ohio State University, Columbus, on April 22, 1966. The celebration took the form of a Festschrift Symposium on a theme supported by the late Director of The Institute for Advanced Study at Princeton, New Jersey, Dr. J. ROBERT OPPENHEIMER: "Logic, and Its Relations to Mathematics, Natural Science, and Philosophy." The symposium also celebrated the founding of Section L (Mathematical Sciences) of the Ohio Academy of Science. Salutations to Dr. GODEL were followed by the reading of papers by S. F. BARKER, H. B. CURRY, H. RUBIN, G. E. SACKS, and G. TAKEUTI, and by the announcement of in-absentia papers contributed in honor of Dr. GODEL by A. LEVY, B. MELTZER, R. M. SOLOVAY, and E. WETTE. A short discussion of "The II Beyond Godel's I" concluded the session."

This NATO Advanced Study Institute course provided an updated understanding, from a fundamental and deep point of view, of the progress and current problems in the early universe, cosmic microwave background radiation, large-scale struc ture, dark matter problem, and the interplay between them. Emphasis was placed on the mutual impact of fundamental physics and cosmology, both at the theo retical and experimental or observational levels, within a deep and well defined programme, and a global unifying view, which, in addition, provides of careful inter-disciplinarity. In addition, each course of this series introduced and promoted topics or sub jects which, although not of a purely astrophysical or cosmological nature, were of relevant physical interest for astrophysics and cosmology. Deep understanding, clarification, synthesis, and careful interdisciplinarity within a fundamental physics framework, were the main goals of the course. Lectures ranged from a motivation and pedagogical introduction for students and participants not directly working in the field to the latest developments and most recent results. All lectures were plenary, had the same duration, and were followed by a discus sion. The course brought together experimentalists and theoreticans physicists, astro physicists and astronomers from a wide variety of backgrounds, including young scientists at the post-doctoral level, senior scientists and advanced graduate stu dents as well.

NASA's Advanced Composition Explorer (ACE) was launched on August 25, 1997, carrying six high-resolution spectrometers that measure the abundances of the elements, isotopes, and ionic charge states of energetic nuclei in space. Data from these instruments is being used to measure and compare the composition of the solar corona, the nearby interstellar medium, and cosmic-ray sources in the Galaxy, and to study particle acceleration processes in a variety of environments. ACE also includes three instruments that monitor solar wind and energetic particle activity near the inner Lagrangian point, "1.5 million kilometers sunward of Earth, and provide continuous, real-time data to NOAA for use in forecasting space weather. Eleven of the articles in this volume review scientific progress and outline questions that ACE will address in solar, space-plasma, and cosmic-ray physics. Other articles describe the ACE spacecraft, the real-time solar-wind system, and the instruments used to measure energetic particle composition.

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.

The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out.

Background material on techniques in PDE theory, differential geometry, and causal theory is provided.

This volume is dedicated to the one hundredth anniversary of the publication of Hermann Minkowski's paper "Raum und Zeit" in 1909 [1]. The paper presents the textofthetalkMinkowskigaveatthe80thMeetingoftheGermanNaturalScientists and Physicians in Cologne on September 21, 1908. Minkowski's work on the spacetime representation of special relativity had a huge impact on the twentieth century physics, which can be best expressed by merely stating what is undeniable - that modern physics would be impossible wi- out the notion of spacetime. It is suf cient to mention as an example only the fact that general relativity would be impossible without this notion; Einstein succeeded to identifygravitywith the curvatureofspacetime onlywhen he overcamehis initial hostile reactionto Minkowski'sfour-dimensionalrepresentationof special relativity and adopted spacetime as the correct relativistic picture of the world. While there exists an unanimous consensus on the mathematical signi cance of spacetime for theoretical physics, for a hundred years there has been no consensus on the nature of spacetime itself. The rst sign of this continuing controversy was Sommerfeld's remark in his notes on Minkowski's article [2]: "What will be the epistemologicalattitudetowardsMinkowski'sconceptionofthetime-spaceproblem is another question, but, as it seems to me, a question which does not essentially touch his physics".

It has often been noted that a kind of double dynamics char- terizes the development of science. On the one hand the progress in every discipline appears as the consequence of an increasing specialization, implying the restriction of the inquiry to very partial fields or aspects of a given domain. On the other hand, an opposite (but one might better say a complementary) trend points towards the construction of theoretical frameworks of great ge- rality, the aim of which seems to correspond not so much to the need of providing "explanations" for the details accumulated through partial investigation, as to the desire of attaining an - rizon of global comprehension of the whole field. This intell- tual dialectics is perceivable in every discipline, from mathe- tics, to physics, to biology, to history, to economics, to sociology, and it is not difficult to recognize there the presence of the two main attitudes according to which human beings try to make "intelligible" the world surrounding them (including themselves), attitudes which are sometimes called analysis and synthesis. They correspond respectively to the spontaneous inclination which pushes us to try to understand things by seeing "how they are made", in the sense of "looking into them" and breaking them into their constitutive parts, or rather to encompass things in a global picture, where they are accounted for as occupying a place, or playing a role, which are understandable from the point of view of the whole.

Outstanding progress in near-infrared detection technology and in real-time image processing has led astronomers to start undertaking all-sky surveys in the 1--2 mum range (project DENIS in Europe and 2MASS in the U.S.A.), surveys which will have a considerable impact in various areas of astronomy. This book gathers the contributions of more than 80 specialists involved in fields of interest as different as low mass stars, late stages of stellar evolution, star formation, stellar populations of the Galaxy and the Magellanic Clouds, the local structure of the Universe, and observational cosmology. It describes the impact on these fields of the exhaustive data bases and catalogs of stars and galaxies that these surveys will provide. The considerable interest of these documents for the future of infrared space and ground-based projects and the complementarity with other currently ongoing or planned surveys in other spectral ranges are emphasized.

The twenty-second Coral Gables conference "UNIFIED SYMMETRY: In the Small and In the Large" continued with the efforts to unify the small and the large. The information gathered with the Huble telescope has in part, in the absence of the SCC , provided a basis for the physicists to unify cosmology and elementary particle physics. The congressional cancellation of the biggest experimental project on the frontiers of physics should not be regarded as an insurmountable obstacle to progress in theoretical physics. The physicists' rise to prominence was mostly reached through their creation of the nuclear era. The post cold war era has somewhat reduced the political, military, and, in part, the social role of the physicist. Some in the administration and the Congress would like physicists to focus on the directly utilitarian aspects of science. Thus, some people do not realize that this regimentation of science would inhibit the creativity. The contributions of solid state physics research to the advancement of technology is the result of physics freely pursued independently of its applications. Modern Physics beginning with Newton's theory of gravity has enabled us to create the space age, to contribute to various technologies, and to impact on our technological modus vivendi.

In Controversy, Trevor Palmer fully documents how traditional gradualistic views of biological and geographic evolution are giving way to a catastrophism that credits cataclysmic events, such as meteorite impacts, for the rapid bursts and abrupt transitions observed in the fossil record. According to the catastrophists, new species do not evolve gradually; they proliferate following sudden mass extinctions. Placing this major change of perspective within the context of a range of ancient debates, Palmer discusses such topics as the history of the solar system, present-day extraterrestrial threats to earth, hominid evolution, and the fossil record.

A history of the attempts to test the predictions of Newtonian Gravity, describing in detail recent experimental efforts to verify both the inverse-square law and the Equivalence Principle. Interest in these questions has increased in recent years, as it has become recognised that deviations from Newtonian gravity could be a signal for a new fundamental force in nature. This is the first book devoted entirely to this subject, and will thus be useful to both graduate students and researchers interested in this field. It describes the ideas that underlie searches for such deviations, focusing on macroscopic tests. A comprehensive bibliography of some 450 entries supplements the text.

Stellar astrophysics still provides the basic framework for deciphering the imprints left over by the evolving universe on all scales. Advances or shortcomings in the former field have direct consequences in our ability to understand the global properties of the latter.

This volume contains the most recent updates on a variety of topics that, though independent by themselves, are inevitably connected on a cosmological scale. These include comprehensive articles by leaders in fields extending from stellar atmospheres through properties of the stellar component in the Milky Way up to the stellar environment in high redshift galaxies.

The wide coverage of astrophysical themes makes this volume very valuable for researchers and Ph.D. students in astrophysics.

This symposium was organized at the B.M. Birla Science Centre, Hyderabad, India, and provided a platform for frontier physicists to exchange ideas and review the latest work and developments on a variety of interrelated topics. A feature of the symposium, as well as the proceedings, is the B.M. Birla Memorial Lecture by Nobel Laureate Professor Gerard 't Hooft. There were participants from the USA, several European countries, Russia and CIS countries, South Africa, Japan, India and elsewhere, of whom some forty scientists presented papers. Spanning a wide range of contemporary issues in fundamental physics from string theory to cosmology, the proceedings present many of these talks and contributions.

In May 1976, when one of us was temporarily associated with Stras bourg Observatory for lecturing on distance determination methods (Heck 1978), Pierre Lacroute - then in his last year as Director there - mod estly requested comments on a project he had been cherishing for quite a few years, and which he had been presenting to visitors and colleagues: an astrometric satellite. His persuasiveness and persistence won support from the scientific com munity, from the French space agency CNES and from the European Space Agency (ESA): the Hipparcos satellite was born. It was fitting that Lacroute lived long enough after his retirement to attend the launch of his brainchild in 1989 and to see it successfully operational. He knew however he would not enjoy the completion of this long and ambitious mission (he passed away on 14 January 1993, a few days before reaching the age of 87). In May 1997, in the prestigious setting of San Giorgio :Maggiore in Venice, ESA organized a symposium celebrating the presentation of the Hipparcos and Tycho catalogues. That conference signalled also the re lease of the first scientific results based at least partially on Hipparcos data. An impressive proceedings volume (Battrick 1997) of more than nine hundred pages, gathering together almost two hundred contributions, gave evidence of numerous studies in progress, in addition to papers starting to appear in the classical journals. The well-maintained ESA Hipparcos web site (http://astro. estec. esa.

Presenting the history of space-time physics, from Newton to Einstein, as a philosophical development DiSalle reflects our increasing understanding of the connections between ideas of space and time and our physical knowledge. He suggests that philosophy's greatest impact on physics has come about, less by the influence of philosophical hypotheses, than by the philosophical analysis of concepts of space, time and motion, and the roles they play in our assumptions about physical objects and physical measurements. This way of thinking leads to interpretations of the work of Newton and Einstein and the connections between them. It also offers ways of looking at old questions about a priori knowledge, the physical interpretation of mathematics, and the nature of conceptual change. Understanding Space-Time will interest readers in philosophy, history and philosophy of science, and physics, as well as readers interested in the relations between physics and philosophy.

Over the past five de-:: ades researchers have sought to develop a new framework that would resolve the anomalies attributable to a patchwork formulation of relativistic quantum mechanics. This book chronicles the development of a new paradigm for describing relativistic quantum phenomena. What makes the new paradigm unique is its inclusion of a physically measurable, invariant evolution parameter. The resulting theory has been sufficiently well developed in the refereed literature that it is now possible to present a synthesis of its ideas and techniques. My synthesis is intended to encourage and enhance future research, and is presented in six parts. The environment within which the conventional paradigm exists is described in the Introduction. Part I eases the mainstream reader into the ideas of the new paradigm by providing the reader with a discussion that should look very familiar, but contains subtle nuances. Indeed, I try to provide the mainstream reader with familiar "landmarks" throughout the text. This is possible because the new paradigm contains the conventional paradigm as a subset. The foundation of the new paradigm is presented in Part II, fol owed by numerous applications in the remaining three parts. The reader should notice that the new paradigm handles not only the broad class of problems typically dealt with in conventional relativistic quantum theory, but also contains fertile research areas for both experimentalists and theorists. To avoid developing a theoretical framework without physical validity, numerous comparisons between theory and experiment are provided, and several predictions are made.

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1990 under the title "Predictability, Stability, and Chaos in N-Body Dynamical Systems". The Institute was the latest in a series held at three-yearly inter vals from 1972 to 1987 in dynamical astronomy, theoretical mechanics and celestial mechanics. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received Proceedings. The 1990 Institute attracted 74 participants from 16 countries, six outside the NATO group. Fifteen series of lectures were given by invited speakers; additionally some 40 valuable presentations were made by the younger participants, most of which are included in these Proceedings. The last twenty years in particular has been a time of increasingly rapid progress in tackling long-standing and also newly-arising problems in dynamics of N-body systems, point-mass and non-point-mass, a rate of progress achieved because of correspondingly rapid developments of new computer hardware and software together with the advent of new analytical techniques. It was a time of exciting progress culminating in the ability to carry out research programmes into the evolution of the outer Solar 8 System over periods of more than 10 years and to study star cluster and galactic models in unprecedented detail.