This book reflects our own struggle to understand the semiclassical behaviour of quantized fields in the presence of boundaries. Along many years, motivated by the problems of quantum cosmology and quantum field theory, we have studied in detail the one-loop properties of massless spin-l/2 fields, Euclidean Maxwell the ory, gravitino potentials and Euclidean quantum gravity. Hence our book begins with a review of the physical and mathematical motivations for studying physical theories in the presence of boundaries, with emphasis on electrostatics, vacuum v Maxwell theory and quantum cosmology. We then study the Feynman propagator in Minkowski space-time and in curved space-time. In the latter case, the corre sponding Schwinger-DeWitt asymptotic expansion is given. The following chapters are devoted to the standard theory of the effective action and the geometric im provement due to Vilkovisky, the manifestly covariant quantization of gauge fields, zeta-function regularization in mathematics and in quantum field theory, and the problem of boundary conditions in one-loop quantum theory. For this purpose, we study in detail Dirichlet, Neumann and Robin boundary conditions for scalar fields, local and non-local boundary conditions for massless spin-l/2 fields, mixed boundary conditions for gauge fields and gravitation. This is the content of Part I. Part II presents our investigations of Euclidean Maxwell theory, simple super gravity and Euclidean quantum gravity.

Space missions subject human beings or any other target of a spacecraft to a radiation environment of an intensity and composition not available on earth. Whereas for missions in low earth orbit (LEO), such as those using the Space Shuttle or Space Station scenario, radiation exposure guidelines have been developed and have been adopted by spacefaring agencies, for exploratory class missions that will take the space travellers outside the protective confines of the geomagnetic field sufficient guidelines for radiation protection are still outstanding. For a piloted Mars mission, the whole concept of radiation protection needs to be reconsidered. Since there is an increasing interest ci many nations and space agencies in establishing a lunar base and lor exploring Mars by manned missions, it is both, timely and important to develop appropriate risk estimates and radiation protection guidelines which will have an influence on the design and structure of space vehicles and habitation areas of the extraterrestrial settlements. This book is the result of a multidisciplinary effort to assess the state of art in our knowledge on the radiation situation during deep space missions and on the impact of this complex radiation environment on the space traveller. ]t comprises the lectures by the faculty members as well as short contributions by the students given at the NATO Advanced Study Institute "Biological Effects and Physics of Solar and Galactic Cosmic Radiation" held in Armacao de Pera, Portugal, 12-23 October, 1991.

First published in 1973, this influential work discusses Einstein's General Theory of Relativity to show how two of its predictions arise: first, that the ultimate fate of many massive stars is to undergo gravitational collapse to form 'black holes'; and second, that there was a singularity in the past at the beginning of the universe. Starting with a precise formulation of the theory, including the necessary differential geometry, the authors discuss the significance of space-time curvature and examine the properties of a number of exact solutions of Einstein's field equations. They develop the theory of the causal structure of a general space-time, and use it to prove a number of theorems establishing the inevitability of singularities under certain conditions. A Foreword contributed by Abhay Ashtekar and a new Preface from George Ellis help put the volume into context of the developments in the field over the past fifty years.

The basic subjects and main topics covered by this book are: (1) Physics of Black Holes (classical and quantum); (2) Thermodynamics, entropy and internal dynamics; (3) Creation of particles and evaporation; (4) Mini black holes; (5) Quantum mechanics of black holes in curved spacetime; (6) The role of spin and torsion in the black hole physics; (7) Equilibrium geometry and membrane paradigm; (8) Black hole in string and superstring theory; (9) Strings, quantum gravity and black holes; (10) The problem of singularity; (11) Astrophysics of black holes; (12) Observational evidence of black holes. The book reveals the deep connection between gravitational, quantum and statistical physics and also the importance of black hole behaviour in the very early universe. An important new point discussed concerns the introduction of spin in the physics of black holes, showing its central role when correctly put into the Einstein equations through the geometric concept of torsion, with the new concept of a time-temperature uncertainty relation, minimal time, minimal entropy, quantization of entropy and the connection of black hole with wormholes. Besides theoretical aspects, the reader will also find observational evidence for black holes in active galactic nuclei, in binary X-ray sources and in supernova remnants. The book will thus interest physicists, astronomers, and astrophysicists at different levels of their career who specialize in classical properties, quantum processes, statistical thermodynamics, numerical collapse, observational evidence, general relativity and other related problems.

This volume consists of invited talks and contributed papers presented at the NATO Advanced Study Institute "The Post Recombination Universe" which was held in Cambridge in the summer of 1987. There have, in recent years, been numerous meetings devoted to problems in observational cosmology. The attention given reflects the exciting rate of de velopment of the subject, and a survey of the proceedings from these symposia reveals that a great deal of emphasis has been given to consideration of the very early universe on the one hand, and to large scale structure in the universe at the present epoch on the other. The theme of this meeting was chosen to comple ment these efforts by focussing on the state of the universe at quite early times, but at those epochs which are still accessible to direct observations. The meet ing provided a broad coverage of the post recombination universe by drawing on experts from a wide variety of fields covering theory, background radiation fields and discrete sources at high redshift. Events in the moderately early universe will have left their mark in a great range of wavebands, from X-rays to the microwave region, and the evolution of the universe can be revealed by studies of the inter galactic medium, gravitational lensing and the abundance and clustering of high redshift sources. All of these subjects received much attention at the meeting, and the papers demonstrate the rich interplay between these areas in the rapidly expanding world of observational cosmology."

When my colleague Dr. Paul Kent asked me which branch of Physics was most lively and which would lend itself best to a small high quality Symposium, I had no hesitation in answering 'Cosmology'. It seemed very timely that a meeting should take place which would bring together scientists interested in all branches of Astronomy, including Cosmic Rays, and Elementary Particles too and endeavour to put at least some of the pieces of the jigsaw together. The vast majority of the papers presented were later produced ~n appropriate camera-ready form and are published in this volume. I am very grateful to the authors for their ready cooperation. Grateful thanks are also extended to the Board of Management of the Foster-Wills and Theodor Heuss Scholarships, Oxford University and the Deutscher Akademischer Austauschdienst (German Academic Exchange Service) who funded the Symposium. The Director of the German Academic Exchange Service, Frau M.E. Schmitz and her colleague Mrs. Susan Putt, organized the whole meeting in a most exemplary fashion. Finally, on behalf of all participants and guests, s~ncere thanks are offered to Paul Kent as Convenor for initiating the Symposium, arranging the social events and organizing accommodation in such magnificent surroundings. Christ Church was the horne of Lewis Carrol and we were ever mindful - and appropriately so - of Alice. A. W. Wolfendale Durham, February 10th, 1982 vii A. W. Wolfendale (ed.), Progress in Cosmology, vii.

In 1905, Albert Einstein offered a revolutionary theory--special relativity--to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborate to gain objective knowledge of the world. To encompass both the general and special theory, he uses the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.

This book is based upon the lectures delivered from 18 to 22 June 2007 at the INFN-LaboratoriNazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci, with the participation of prestigious lecturers, including S. Ferrara, M. Gnaydin, P. Levay, T. Mohaupt, and A. Zichichi. All lectures were given at a pedagogical, introductory level, a feature which is re?ected in the s- ci?c "?avor" of this volume, which has also bene?ted much from the extensive discussions and related reworking of the various contributions. This is the fourth volume in a series of books on the general topics of sup- symmetry, supergravity, black holes, and the attractor mechanism. Indeed, based on previous meetings, three volumes have already been published: BELLUCCI S. (2006). Supersymmetric Mechanics - Vol. 1: Supersymmetry, NoncommutativityandMatrixModels.(vol.698, pp.1-229).ISBN:3-540-33313-4. Berlin, Heidelberg: Springer Verlag (Germany). Springer Lecture Notes in Physics Vol. 698. BELLUCCIS., S.FERRARA, A.MARRANI.(2006).SupersymmetricMech- ics - Vol. 2: The Attractor Mechanism and Space Time Singularities. (vol. 701, pp. 1-242). ISBN-13: 9783540341567. Berlin, Heidelberg: Springer Verlag (G- many). Springer Lecture Notes in Physics Vol. 701. BELLUCCIS.(2008).SupersymmetricMechanics-Vol.3: AttractorsandBlack HolesinSupersymmetricGravity.(vol.755, pp.1-373).ISBN-13:9783540795223. Berlin, Heidelberg: Springer Verlag (Germany). Springer Lecture Notes in Physics 755. In this volume, we have included two contributions originating from short p- sentations of recent original results given by participants, i.e., Wei Li and Filipe Moura.

P. de Bernardis, S. Masi , G. Moreno Dipartimento di Fisica, Universita' "La Sapienza" 00184 Roma Italy ABSTRACT. Anisotropy measurement techniques and results are reviewed, with special attention given to experimental problems. The cosmological relevance of the dipole anisotropy, the only anisotropy truly detected in the Cosmic Background Radiation, is discussed. 1. INTRODUCTION Anisotropy of the Cosmic Background Radiation at 2.7 K (CBR hereafter) is a cosmological topic with a wide range of applications. In order to define anisotropy let us consider fig. 1 a, where the celestial sphere is shown with two beams A and B, with beamwidth 0 and angular separation e. We define the anisotropy of CBR at angular scale e in terms of the difference i'2,1 between the CBR flux I(ex,u) measured in the two beams. At small angular scales (e ) a "stochastic" approach is preferred, and the anisotropy is defined as .cJ I = GBP (1) I e where the brackets indicate averages over the whole celestial sphere. At large angular scales e>l a deterministic approach is preferred, and the CBR flux I(ex, S) is expressed as a sum of spherical harmonics (2) I (ex, S) = I ~ aIm Y (ex, S) lm I,m The alm coefficients give the dipole, quadrupole and higher order components of the anisotropy. 257 P. Galeotti and D. N. Schramm (eds.), Gauge Theory and the Early Universe, 257-282.

The theory of General Relativity, after its invention by Albert Einstein, remained for many years a monument of mathemati cal speculation, striking in its ambition and its formal beauty, but quite separated from the main stream of modern Physics, which had centered, after the early twenties, on quantum mechanics and its applications. In the last ten or fifteen years, however, the situation has changed radically. First, a great deal of significant exper en tal data became available. Then important contributions were made to the incorporation of general relativity into the framework of quantum theory. Finally, in the last three years, exciting devel opments took place which have placed general relativity, and all the concepts behind it, at the center of our understanding of par ticle physics and quantum field theory. Firstly, this is due to the fact that general relativity is really the "original non-abe lian gauge theory," and that our description of quantum field in teractions makes extensive use of the concept of gauge invariance. Secondly, the ideas of supersymmetry have enabled theoreticians to combine gravity with other elementary particle interactions, and to construct what is perhaps the first approach to a more finite quantum theory of gravitation, which is known as super gravity."

Many large-scale projects for detecting gravitational radiation are currently being developed, all with the aim of opening a new window onto the observable Universe. As a result, numerical relativity has recently become a major field of research, and Elements of Numerical Relativity and Relativistic Hydrodynamics is a valuable primer for both graduate students and non-specialist researchers wishing to enter the field.

A revised and significantly enlarged edition of LNP 673 Elements of Numerical Relativity, this book starts with the most basic insights and aspects of numerical relativity before it develops coherent guidelines for the reliable and convenient selection of each of the following key aspects: evolution formalism; gauge, initial, and boundary conditions; and various numerical algorithms. And in addition to many revisions, it includes new, convenient damping terms for numerical implementations, a presentation of the recently-developed harmonic formalism, and an extensive, new chapter on matter space-times, containing a thorough introduction to relativistic hydrodynamics.

While proper reference is given to advanced applications requiring large computational resources, most tests and applications in this book can be performed on a standard PC.

This workshop was intended as an update and an extension of the workshop 011 the "Spectral Evolution of Galaxies" that was held in Erice two years ago. It concentrates 011 Ilew developments concerning galaxies seen at large look back times. This seemed also a good opportunity to look ahead to the next generation of ground- and space based instrumentation, and to consider various future strategies for collecting information concerning the edge of the observable universe. The main idea was to bring together people with specialities in modelling galaxy components (such as stars, clusters, gas, and dust) as well as whole stellar systems (stellar populations, star formation rates, chemical enrichment), and people specialized in making direct measurements of galaxies and clusters at large look back times. The confrontation of expectations and observations was planned to be the central theme of the conference, which explains the title "Towards Understanding Galaxies at Large Redshift." The first part of the workshop focussed on the physical processes that operate in galaxies, and that would likely have some observable manifestation at large redshifts. In the second part the most recent observational work was reported, and we were pleased to have the participation of most of the groups active in this field. The last part was directed towards new approaches to be made possible by the next generation of instrumentation, although in general all the contributions were indeed in this spirit of setting more ambitious goals."

Any student working with the celebrated Feynman Lectures will ?nd a chapter in it with the intriguing title Electromagnetic Mass [2, Chap. 28]. In a way, it looks rather out of date, and it would be easy to skate over it, or even just skip it. And yet all bound state particles we know of today have electromagnetic mass. It is just that we approach the question differently. Today we have multiplets of mesons or baryons, and we have colour symmetry, and broken ?avour symmetry, and we think about mass and energy through Hamiltonians. This book is an invitation to look at all these modern ideas with the help of an old light. Everything here is quite standard theory, in fact, classical electromagnetism for the main part. The reader would be expected to have encountered the theory of elec tromagnetism before, but there is a review of all the necessary results, and nothing sophisticated about the calculations. The reader could be any student of physics, or any physicist, but someone who would like to know more about inertia, and the clas sical precursor of mass renormalisation in quantum ?eld theory. In short, someone who feels it worthwhile to ask why F= ma.

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.

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 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."

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.

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.

In light of the barrage of popular books on physics and cosmology, one may question the need for another. Here, two books especially come to mind: Steven Weinberg's The First Three Minutes, written 12 years ago, and the recent best-seller ABriefHistory of Time by Stephen Hawking. The two books are complementary. Weinberg-Nobel prize winner/physicist-wrote from the standpoint of an elementary particle physicist with emphasis on the contents of the universe, whereas Hawking wrote more as a general relativist with emphasis on gravity and the geometry of the universe. Neither one, however, presented the complete story. Weinberg did not 13 venture back beyond the time when temperature was higher than 10 K and 32 perhaps as high as 10 K. He gave no explanation for the origin of particles and the singularity or source of the overwhelming radiation energy in our uni verse of one billion photons for each proton. Hawking presents a uni verse that has no boundaries, was not created, and will not be destroyed. The object of this book is to describe my new theory on the creation of our uni verse in a multi-universe cosmos. The new cosmological model eliminates the troublesome singularity-big bang theory and explains for the first time the origin of matter and the overwhelming electromagnetic radiation contained in the universe. My new theory also predicted the existence ofhigh-energy gamma rays, which were recendy detected in powerful bursts.

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.