State-of-the-art survey by leading experts in the field. Major foci are superheavy nuclei and neutron-rich exotic nuclei. In addition new developments in nuclear fission and nuclear cluster decay are shown. Finally developments in relativistic heavy ion collisions and the physics of supercritical fields are detailed.

This book explores the role of singularities in general relativity (GR): The theory predicts that when a sufficient large mass collapses, no known force is able to stop it until all mass is concentrated at a point. The question arises, whether an acceptable physical theory should have a singularity, not even a coordinate singularity. The appearance of a singularity shows the limitations of the theory. In GR this limitation is the strong gravitational force acting near and at a super-massive concentration of a central mass. First, a historical overview is given, on former attempts to extend GR (which includes Einstein himself), all with distinct motivations. It will be shown that the only possible algebraic extension is to introduce pseudo-complex (pc) coordinates, otherwise for weak gravitational fields non-physical ghost solutions appear. Thus, the need to use pc-variables. We will see, that the theory contains a minimal length, with important consequences. After that, the pc-GR is formulated and compared to the former attempts. A new variational principle is introduced, which requires in the Einstein equations an additional contribution. Alternatively, the standard variational principle can be applied, but one has to introduce a constraint with the same former results. The additional contribution will be associated to vacuum fluctuation, whose dependence on the radial distance can be approximately obtained, using semi-classical Quantum Mechanics. The main point is that pc-GR predicts that mass not only curves the space but also changes the vacuum structure of the space itself. In the following chapters, the minimal length will be set to zero, due to its smallness. Nevertheless, the pc-GR will keep a remnant of the pc-description, namely that the appearance of a term, which we may call "dark energy", is inevitable. The first application will be discussed in chapter 3, namely solutions of central mass distributions. For a non-rotating massive object it is the pc-Schwarzschild solution, for a rotating massive object the pc-Kerr solution and for a charged massive object it will be the Reissner-Nordstroem solution. This chapter serves to become familiar on how to resolve problems in pc-GR and on how to interpret the results. One of the main consequences is, that we can eliminate the event horizon and thus there will be no black holes. The huge massive objects in the center of nearly any galaxy and the so-called galactic black holes are within pc-GR still there, but with the absence of an event horizon! Chapter 4 gives another application of the theory, namely the Robertson-Walker solution, which we use to model different outcomes of the evolution of the universe. Finally the capability of this theory to predict new phenomena is illustrated.

This book presents the extended Lagrange and Hamilton formalisms of point mechanics and field theory in the usual tensor language of standard textbooks on classical dynamics. The notion 'extended' signifies that the physical time of point dynamics as well as the space-time in field theories are treated as dynamical variables. It thus elaborates on some important questions including: How do we convert the canonical formalisms of Lagrange and Hamilton that are built upon Newton's concept of an absolute time into the appropriate form of the post-Einstein era? How do we devise a Hamiltonian field theory with space-time as a dynamical variable in order to also cover General Relativity?In this book, the authors demonstrate how the canonical transformation formalism enables us to systematically devise gauge theories. With the extended canonical transformation formalism that allows to map the space-time geometry, it is possible to formulate a generalized theory of gauge transformations. For a system that is form-invariant under both a local gauge transformation of the fields and under local variations of the space-time geometry, we will find a formulation of General Relativity to emerge naturally from basic principles rather than being postulated.

The subject of this workshop (held May-June 1989) plays the central role in high energy heavy ion collisions; contains the possibilities of various phase transitions (gas vapor, meson condensation, quark gluon plasma); and plays an important role in the static and dynamical behavior of stars, especi"

The development of coherent radiation sources for sub-angstrom wavelengths - i.e. in the hard X-ray and gamma-ray range - is a challenging goal of modern physics. The availability of such sources will have many applications in basic science, technology and medicine and in particular, they may have a revolutionary impact on nuclear and solid state physics, as well as on the life sciences. The present state-of-the-art lasers are capable of emitting electromagnetic radiation from the infrared to the ultraviolet, while free electron lasers (X-FELs) are now entering the soft X-ray region. Moving further, i.e. into the hard X and/or gamma ray band, however, is not possible without new approaches and technologies.

In this book we introduce and discuss one such novel approach -the radiation formed in a Crystalline Undulator -whereby electromagnetic radiation is generated by a bunch of ultra-relativistic particles channeling through a periodically bent crystalline structure. Under certain conditions, such a device can emit intensive spontaneous monochromatic radiation and even reach the coherence of laser light sources.

Readers will be presented with the underlying fundamental physics and be familiarized with the theoretical, experimental and technological advances made during the last one and a half decades in exploring the various features of investigations into crystalline undulators. This research draws upon knowledge from many research fields - such as materials science, beam physics, the physics of radiation, solid state physics and acoustics, to name but a few. Accordingly, much care has been taken by the authors to make the book as self-contained as possible in this respect, so as to also provide a usefulintroduction to this emerging field to a broad readership of researchers and scientist with various backgrounds.

This new edition has been revised and extended to take recent developments in the field into account."

This volume collects the invited lectures and contributed talks of the NATO Advanced Studies Institute (ASI) held in Kemer/Turkey, from 22nd September to 2 October 2003. The meeting brought together experts from several fields in nuclear physics in which rapid progress has been made in recent years.
Ultrarelativistic heavy ion collisions have been investigated at CERN and at the Relativistic Heavy Ion Collider (RHIC). Several talks review the present status of experiments and develop the theory of nuclear reactions at ultrarelativistic collisions energies. The properties of hot and dense hadronic matter are studied and the predictions of Quantum Chromodynamics (QCD) for quark deconfinement and the phase transition to the Quark Gluon Plasma are described. The dynamical description of phase transitions in small systems and the methods of nonequilibrium many body theory are covered by several speakers. Furthermore the available information on the nuclear equation of state, the properties of cold dense quark matter, and colour superconductivity are presented in this volume. The close connection of these questions with astrophysics is drawn in several contributions related to the structure of stars, the dark matter problem, and the early universe. A second focal point of the ASI, besides highly energetic heavy ion collisions, is the physics of exotic nuclei far off stability and superheavy elements. Several leading experts in this field discuss the structure, the decay modes and lifetimes of superheavy nuclei both from the theoretical and the experimental points of view. Additional topics are the description of fusion and fission processes, the properties of halo nuclei and nucleibeyond the line of particle stability.

Nuclear physics is an exciting, broadly faceted field. It spans a wide range of topics, reaching from nuclear structure physics to high-energy physics, astrophysics and medical physics (heavy ion tumor therapy). New developments are presented in this volume and the
status of research is reviewed. A major focus is put on nuclear structure physics, dealing with superheavy elements and with various forms of exotic nuclei: strange nuclei, very neutron rich nuclei, nuclei of antimatter. Also quantum electrodynamics of strong fields is addressed, which is linked to the occurrence of giant nuclear systems in, e.g., U+U collisions. At high energies nuclear physics joins with elementary particle physics. Various chapters address the theory of
elementary matter at high densities and temperature, in particular the quark gluon plasma which is predicted by quantum chromodynamics (QCD) to occur in high-energy heavy ion collisions. In the field of nuclear
astrophysics, the properties of neutron stars and quark stars are discussed. A topic which transcends nuclear physics is discussed in two chapters: The proposed pseudo-complex extension of Einstein's General Relativity leads to the prediction that there are no black
holes and that big bang cosmology has to be revised. Finally, the interdisciplinary nature of this volume is further accentuated by chapters on protein folding and on magnetoreception in birds and many other animals."

This book explores the role of singularities in general relativity (GR): The theory predicts that when a sufficient large mass collapses, no known force is able to stop it until all mass is concentrated at a point. The question arises, whether an acceptable physical theory should have a singularity, not even a coordinate singularity. The appearance of a singularity shows the limitations of the theory. In GR this limitation is the strong gravitational force acting near and at a super-massive concentration of a central mass. First, a historical overview is given, on former attempts to extend GR (which includes Einstein himself), all with distinct motivations. It will be shown that the only possible algebraic extension is to introduce pseudo-complex (pc) coordinates, otherwise for weak gravitational fields non-physical ghost solutions appear. Thus, the need to use pc-variables. We will see, that the theory contains a minimal length, with important consequences. After that, the pc-GR is formulated and compared to the former attempts. A new variational principle is introduced, which requires in the Einstein equations an additional contribution. Alternatively, the standard variational principle can be applied, but one has to introduce a constraint with the same former results. The additional contribution will be associated to vacuum fluctuation, whose dependence on the radial distance can be approximately obtained, using semi-classical Quantum Mechanics. The main point is that pc-GR predicts that mass not only curves the space but also changes the vacuum structure of the space itself. In the following chapters, the minimal length will be set to zero, due to its smallness. Nevertheless, the pc-GR will keep a remnant of the pc-description, namely that the appearance of a term, which we may call "dark energy", is inevitable. The first application will be discussed in chapter 3, namely solutions of central mass distributions. For a non-rotating massive object it is the pc-Schwarzschild solution, for a rotating massive object the pc-Kerr solution and for a charged massive object it will be the Reissner-Nordstroem solution. This chapter serves to become familiar on how to resolve problems in pc-GR and on how to interpret the results. One of the main consequences is, that we can eliminate the event horizon and thus there will be no black holes. The huge massive objects in the center of nearly any galaxy and the so-called galactic black holes are within pc-GR still there, but with the absence of an event horizon! Chapter 4 gives another application of the theory, namely the Robertson-Walker solution, which we use to model different outcomes of the evolution of the universe. Finally the capability of this theory to predict new phenomena is illustrated.

State-of-the-art survey by leading experts in the field. Major foci are superheavy nuclei and neutron-rich exotic nuclei. In addition new developments in nuclear fission and nuclear cluster decay are shown. Finally developments in relativistic heavy ion collisions and the physics of supercritical fields are detailed.

Nuclear physics is an exciting, broadly faceted field. It spans a wide range of topics, reaching from nuclear structure physics to high-energy physics, astrophysics and medical physics (heavy ion tumor therapy). New developments are presented in this volume and the status of research is reviewed. A major focus is put on nuclear structure physics, dealing with superheavy elements and with various forms of exotic nuclei: strange nuclei, very neutron rich nuclei, nuclei of antimatter. Also quantum electrodynamics of strong fields is addressed, which is linked to the occurrence of giant nuclear systems in, e.g., U+U collisions. At high energies nuclear physics joins with elementary particle physics. Various chapters address the theory of elementary matter at high densities and temperature, in particular the quark gluon plasma which is predicted by quantum chromodynamics (QCD) to occur in high-energy heavy ion collisions. In the field of nuclear astrophysics, the properties of neutron stars and quark stars are discussed. A topic which transcends nuclear physics is discussed in two chapters: The proposed pseudo-complex extension of Einstein's General Relativity leads to the prediction that there are no black holes and that big bang cosmology has to be revised. Finally, the interdisciplinary nature of this volume is further accentuated by chapters on protein folding and on magnetoreception in birds and many other animals.

The NATO Advanced Study Institute on Physios of St~ong Fields was held at Maratea/Italy from 1-14 June, 1986. The school was devoted to the advances, theoretical and experimental, in physics of strong fields made during the past five years. The topic of the first week was almost exclusively quantum electrodynamics, with dis cussions of symmetry breaking in the ground state, of the physics of strong fields in heavy ion collisions and of precision tests of perturba tive quantum electrodynamics. The famous positron lines found at GSI (Darmstadt) and the related question "new particle versus vacuum decay" - (yes or no or both) - constituted the center of experimental advances. This was followed in the second week by the presentation of a broad range of other areas where strong fields occur, reaching from nuclear physics over quantum chromodynamics to gravitation theory and astrophysics. We were fortunate to be able to calIon a body of lecturers who not only made considerable personal contributions to this research but who are also noted for their lecturing skills. Their enthusiasm and dedication for their work was readily transmitted to the students resulting in a very suc cessful school.

The NATO Advanced Study Institute on The Nuclear Equatioo of State was held at Peiiiscola Spain from May 22- June 3, 1989. The school was devoted to the advances, theoretical and experimental, made during the past fifteen years in the physics of nuclear matter under extreme conditions, such as high compression and high temperature. Moie than 300 people had applied for participatio- this demonstrates the tremendous interest in the various subjects presented at the school. Indeed, the topic of this school, namely the Nuclear Equatioo of State, * plays the central role in high energy heavy ion collisions; * contains the intriguing possibilities of various phase transitions (gas - vapor, meson condensation, quark - gluon plasma); * plays an important role in the static and dynamical behavior of stars, especially in supernova explosions and in neutron star stability. The investigation on the nuclear equation of state can only be accomplished in the laboratory by compressing and heating up nuclear matter and the only mechanism known to date to achieve this goal is through shock compression and -heating in violent high energy heavy ion collisions. This key mechanism has been proposed and highly disputed in of high energy heavy ion physics, the early 70's. It plays a central role in the whole field and particularly in our discussions during the two weeks at Peiiiscola.

The fundamental goal of physics is an understanding of the forces of nature in their simplest and most general terms. Yet there is much more involved than just a basic set of equations which eventually has to be solved when applied to specific problems. We have learned in recent years that the structure of the ground state of field theories (with which we are generally concerned) plays an equally funda mental role as the equations of motion themselves. Heisenberg was probably the first to recognize that the ground state, the vacuum, could acquire certain prop erties (quantum numbers) when he devised a theory of ferromagnetism. Since then, many more such examples are known in solid state physics, e. g. supercon ductivity, superfluidity, in fact all problems concerned with phase transitions of many-body systems, which are often summarized under the name synergetics. Inspired by the experimental observation that also fundamental symmetries, such as parity or chiral symmetry, may be violated in nature, it has become wide ly accepted that the same field theory may be based on different vacua. Practical ly all these different field phases have the status of more or less hypothetical models, not (yet) directly accessible to experiments. There is one magnificent ex ception and this is the change of the ground state (vacuum) of the electron-posi tron field in superstrong electric fields."

Ladies and gentlemen, dear colleagues, welcome to Kemer to the NATO Advanced Study Institute Structure and Dynamics of Elementary Matter. We have chosen Kemer as the place of our NASI because it is located in a be- tiful and hospitable surrounding. This part of the Mediterranean at the Turkish Riviera is a historic region where many cultures meet (e.g., the Oriental and the Greek and Roman European cultures) and where you ?nd numerous places which played a role in ancient science and in early Christianity. Moreover, with the hotel Ceylan Inter-Continental we have found a most excellent me- ing place, directly located at the beach, equipped with wonderful swimming pools and restaurants - an absolutely ?rst-class location. Our NASIwill deal withthemost recent developmentsin high-energyheavy ionphysicsandinthesearchforsuperheavynuclei-tworatherdistinctareasof research. Indeed, we want to bring two very active communities of nuclear and high-energy physics into close contact. The meeting is both a school and has also the character of a conference: A school because there are many advanced students, many of which are themselves already top researchers and who are contributing with their own research in seminars and posters. It is also a c- ference because new results in the exciting and wonderful ?elds of low- and high-energy heavy ion physics will be presented. We are mainly focussing on the topics of superheavy elements and of hot and dense nuclear matter.

The series of texts on Classical Theoretical Physics is based on the highly successful series of courses given by Walter Greiner at the Johann Wolfgang Goethe University in Frankfurt am Main, Germany. Intended for advanced undergraduates and beginning graduate students, the volumes in the series provide not only a complete survey of classical theoretical physics but also an enormous number of worked examples and problems to show students clearly how to apply the abstract principles to realistic problems.

The series of texts Classical Theoretical Physics is based on the highly successful series of courses given by Walter Greiner and his colleagues at the Johann Wolfgang Goethe University in Frankfurt am Main, Germany. Intended for advanced undergraduates and beginning graduate students, the volumes in this series will provide not only a complete survey of classical theoretical physics but also an enormous number of worked examples and problems to show students clearly how to apply the underlying principles to realistic problems. Thermodynamics and Statistical Physics covers: Thermodynamics - basic definitions of thermodynamics, equilibrium, state variables - the first and second laws - phase transitions and chemical reactions - thermodynamic potentials Statistical Mechanics - statistics of microscopic states and connection to the entropy - the microcanonical, canonical and grand canonical ensembles - applications of Boltzmann statistics Quantum Statistics - the density operator - many-particle wave functions - ideal quantum systems - the ideal Bose gas and applications to blackbody radiation, Kirchhoff's law, and lattice vibrations - the ideal Fermi gas and applications to condensed-matter physics, astrophysics, and nuclear physics - relativistic Bose and Fermi gases and applications to particle physics Real Gases and Phase Transitions - real gases and the virial expansion - classification of phase transitions and critical indices - the Ising and Heisenberg models

Quantum Mechanics -- Special Chapters is an important additional course for third-year students. Starting with the quantization of a free electromagnetic field and its interaction with matter, it discusses second quantization and interacting quantum fields. After re-normalization problems and a general treatment of nonrelativistic quantum field theory, these methods are applied to problems from solid-state physics and plasma physics: quantum gas, superfluidity, plasmons, and photons. The book concludes with an introduction to quantum statistics, the structure of atoms and molecules, and the Schrödinger wave equation formulated by Feynman path integrals. 72 fully and carefully worked examples and problems consolidate the material.

Relativistic Quantum Mechanics. Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles. Chapter 1 deals with the Klein-Gordon equation and its properties and applications. The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions. Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles. Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner). The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course.This third edition has been slightly revised to bring the text up-to-date.

The series of texts on Classical Theoretical Physics is based on the highly successful series of courses given by Walter Greiner at the Johann Wolfgang Goethe University in Frankfurt am Main, Germany. Intended for advanced undergraduates and beginning graduate students, the volumes in the series provide not only a complete survey of classical theoretical physics but also an enormous number of worked examples and problem to show students clearly how to apply the abstract principles to realistic problems.

The development of coherent radiation sources for sub-angstrom wavelengths - i.e. in the hard X-ray and gamma-ray range - is a challenging goal of modern physics. The availability of such sources will have many applications in basic science, technology and medicine and in particular, they may have a revolutionary impact on nuclear and solid state physics, as well as on the life sciences. The present state-of-the-art lasers are capable of emitting electromagnetic radiation from the infrared to the ultraviolet, while free electron lasers (X-FELs) are now entering the soft X-ray region. Moving further, i.e. into the hard X and/or gamma ray band, however, is not possible without new approaches and technologies. In this book we introduce and discuss one such novel approach -the radiation formed in a Crystalline Undulator - whereby electromagnetic radiation is generated by a bunch of ultra-relativistic particles channeling through a periodically bent crystalline structure. Under certain conditions, such a device can emit intensive spontaneous monochromatic radiation and even reach the coherence of laser light sources. Readers will be presented with the underlying fundamental physics and be familiarized with the theoretical, experimental and technological advances made during the last one and a half decades in exploring the various features of investigations into crystalline undulators. This research draws upon knowledge from many research fields - such as materials science, beam physics, the physics of radiation, solid state physics and acoustics, to name but a few. Accordingly, much care has been taken by the authors to make the book as self-contained as possible in this respect, so as to also provide a useful introduction to this emerging field to a broad readership of researchers and scientist with various backgrounds. This new edition has been revised and extended to take recent developments in the field into account. 

More than a generation of German-speaking students around the world have worked theirwaytoanunderstandingandappreciationofthepowerandbeautyofmodernt- oretical physics-with mathematics, the most fundamental of sciences-using Walter Greiner's textbooks as their guide. The idea of developing a coherent, complete presentation of an entire eld of s- ence in a series of closely related textbooks is not a new one. Many older physicians remember with real pleasure their sense of adventure and discovery as they worked their ways through the classic series by Sommerfeld, by Planck, and by Landau and Lifshitz. From the students' viewpoint, there are a great many obvious advantages to be gained through the use of consistent notation, logical ordering of topics, and - herence of presentation; beyond this, the complete coverage of the science provides a unique opportunity for the author to convey his personal enthusiasm and love for his subject. These volumes on classical physics, nally available in English, complement Greiner's texts on quantum physics, most of which have been available to Engli- speaking audiences for some time. The complete set of books will thus provide a coherent view of physics that includes, in classical physics, thermodynamics and s- tistical mechanics, classical dynamics, electromagnetism, and general relativity; and in quantumphysics, quantummechanics,symmetries, relativistic quantummechanics, quantum electro- and chromodynamics, and the gauge theory of weak interactions.

The need for this handbook is a direct consequence of a very large accumulation of new theoretical and experimental data on nucleur properties. The first five chapters are devoted to the presentation of experimental and theoretical aspects of the following topics: atomic masses of stable and radioactive nuclides; an intuitive way to understand the empirical trends of masses, based on a microscopic theory; Penning traps used as a modern mass spectrometer of high resolving power, accuracy and sensitivity; basic theoretical concepts and experimental techniques used to measure the nucleur shape parameters; new decay modes by hadron and cluster emission; the proton (p), and the beta-delayed particle emissions: neutron (n), 2n, 3n, 4n, p, 2p, 3p, d, t, etc. This book is intended for students and professionals in nuclear physics, radioactivity, astrophysics, high- energy physics and elementary particles. Also industrial applications of nuclear radiation, nuclear medicine, and environmental science.

Quantum Mechanics - An Introduction lays the foundations for the rest of the course on quantum mechanics, advanced quantum mechanics and field theory. Starting from black-body radiation, the photoelectric effect, and wave-particle duality, Greiner goes on to discuss the uncertainty relations, spin, and many-body systems; he includes applications to the hydrogen atom and the Stern-Gerlach and Einstein-de Haas experiments. The mathematics of representation theory, S matrices, perturbation theory, eigenvalue problems, and hypergeometric differential equations are presented in detail, with 88 fully and carefully worked examples and exercises to consolidate the material. The book supplies the historical and phenomenological background and steadily builds a wave-mechanical treatment of matter. This fourth edition includes improved explanatory remarks, plus several new examples and exercises

L'ouvrage Mecanique Quantique - Introduction - jette les bases du cours de mecanique quantique et de la theorie des champs. En partant de la radiation du corps noir, de l'effet photoelectrique et de la dualite onde - particule, l'auteur expose les relations de l'incertitude, le spin, et les systemes a plusieurs corps. Il inclut les applications a l'atome d'hydrogene et les experiences de Stern-Gerlach, et de Einstein-de Haas. Sont aussi presentes en details l'aspect mathematique de la theorie de representation, les matrices S, la theorie de la pertubation, les problemes des valeurs propres, les equations differentielles hypergeometriques. Le lecteur trouvera aussi plus de 80 exemples et exercices, ainsi que leur corrige, et ceci afin de consolider le propos du livre. Chaque exercice a ete soigneusement choisi et traite pour que l'ouvrage soit l'outil de base et de reference de son lecteur."