Quantum Dynamics is a major survey of quantum theory based on Walter Greiner's long-running and highly successful course at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in particle physics. Volume 1, Quantum Mechanics I - An Introduction, lays the foundation for the rest of the course. Starting from black-body radiation, the photo-electric effect and wave-particle duality, Greiner goes on to discuss the uncertainty relations, spin and many-body systems, then discusses applications to the hydrogen atom and the Stern-Gerlach and Einstein-de Haas experiments. The mathematics of representation theory, S-matrices, perturbation theory, eigenvalues and hypergeometric differential equations are presented in detail, with 84 fully and carefully worked examples and exercises to consolidate the material. Volume 2 presents a particularly appealing and successful theme in advanced quantum mechanics - symmetries. After a brief introduction to symmetries in classical mechanics, the text turns to their relevance in quantum mechanics, the consequences of rotation symmetry and the general theory of Lie groups. The Isospin group, hypercharge, SU (3) and their applications are all dealt with in depth before a chapter on charm and SU (3) leads to the frontiers of research in particle physics. Almost a hundred detailed, worked examples and problems make this a truly unique text on a fascinating side of modern physics.
From the reviews: "This book excels by its variety of modern examples in solid state physics, magnetism, elementary particle physics [...] I can recommend it strongly as a valuable source, especially to those who are teaching basic statistical physics at our universities." Physicalia
Quantum Dynamics" is a major survey of quantum theory based on Walter Greiner's long-running and highly successful courses at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in particle physics. Volume 2 presents a particularly appealing and successful theme in advanced quantum mechanics - symmetries. After a brief introduction to symmetries in classical mechanics, the text turns to their relevance in quantum mechanics, the consequences of rotation symmetry and the general theory of Lie groups. The Isospin group, hypercharge, SU (3) and their applications are all dealt with in depth before a chapter on charm and SU (3) leads to the frontiers of research in particle physics. Almost a hundred detailed, worked examples and problems make this a truly unique text on a fascinating side of modern physics.
Since the need for a third edition of this book has arisen, we have endeavoured to improve and extend it in several ways. At many places small changes were made, misprints have been corrected, and references have been added. In Chap. 5 new theoretical and experimental results on the Lamb shift in heavy atoms and on the anomalous magnetic moment of the muon are reported. We have also added a number of new topics in Chaps. 3, 5, and 7 in the form of examples and exercises. Example 3. 19 contains a detailed treatment of electron-positron pair production in the collision of a high-energy photon with a laser beam. This is supplemented by Exercise 3. 20 where a closed solution of the Dirac equation in the field of a plane wave is derived. Furthermore, Example 5. 4 on the running coupling constant in QED and Example 7. 6 on the supercritial point charge prob lem have been added. Finally, Example 7. 8 treats the birefringence of the QED vacuum in a strong magnetic field. We thank all colleagues and readers who have informed us about misprints in the book and are grateful to the team at Springer-Verlag for expertly handling the preparation of this new edition. Frankfurt am Main, Walter Greiner August 2002 Joachim Reinhardt Preface to the Second Edition The need for a second edition of our text on Quantum Electrodynamics has given us the opportunity to implement some corrections and amendments.
The series of texts on Classical Theoretical Physics is based on the highly successful courses given by Walter Greiner. The volumes provide a complete survey of classical theoretical physics and an enormous number of worked out examples and problems.
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 reference and workbook provides not only a complete survey of classical electrodynamics, but also an enormous number of worked examples and problems to show the reader how to apply abstract principles to realistic problems. The book will prove useful to graduate students in electrodynamics needing a practical and comprehensive treatment of the subject.
The third edition of this outstanding volume has been extensively revised and enlarged to cover all new aspects in Quantum chromodynamics. It first reviews relativistic quantum field theory and details scattering theory in the framework of scalar quantum electrodynamics. The book then introduces the gauge theory of quarks and gluons. In addition, more advanced chapters present a through discussion of perturbative and nonperturbative techniques in state-of-the-art QCD. Throughout, worked-out examples provide hands-on experience for students in theoretical physics. Research scientists will also find the book an ideal reference.
Theoretical physics has become a many-faceted science. For the young stu dent it is difficult enough to cope with the overwhelming amount of new scientific material that has to be learned, let alone obtain an overview of the entire field, which ranges from mechanics through electrodynamics, quantum mechanics, field theory, nuclear and heavy-ion science, statistical mechanics, thermodynamics, and solid-state theory to elementary-particle physics. And this knowledge should be acquired in just 8-10 semesters, during which, in addition, a Diploma or Master's thesis has to be worked on or examinations prepared for. All this can be achieved only if the university teachers help to introduce the student to the new disciplines as early on as possible, in order to create interest and excitement that in turn set free essential new energy. At the Johann Wolfgang Goethe University in Frankfurt we therefore con front the student with theoretical physics immediately, in the first semester. Theoretical Mechanics I and II, Electrodynamics, and Quantum Mechanics I - An Introduction are the basic courses during the first two years. These lectures are supplemented with many mathematical explanations and much support material. After the fourth semester of studies, graduate work begins, and Quantum Mechanics II - Symmetries, Statistical Mechanics and Ther modynamics, Relativistic Quantum Mechanics, Quantum Electrodynamics, the Gauge Theory of Weak Interactions, and Quantum Chromo dynamics are obligatory.
Intended for advanced undergraduates and beginning graduate students, this text is based on the highly successful course given by Walter Greiner at the University of Frankfurt, Germany. The two volumes on classical mechanics provide not only a complete survey of the topic but also an enormous number of worked examples and problems to show students clearly how to apply the abstract principles to realistic problems.
Theoretical physics has become a many-faceted science. For the young student it is difficult enough to cope with the overwhelming amount of new scientific material that has to be learned, let alone to obtain an overview of the entire field, which ranges from mechanics through electrodynamics, quantum mechanics, field theory, nuclear and heavy-ion science, statistical mechanics, thermodynamics, and solid state theory to elementary-particle physics. And this knowledge should be acquired in just 8-10 semesters during which, in addition, a Diploma or Master's thesis has to be worked on or examinations prepared for. All this can be achieved only if the university teachers help to introduce the student to the new disciplines as early on as possible, in order to create interest and excitement that in turn set free essential new energy. Naturally, all inessential material must simply be eliminated. At the Johann Wolfgang Goethe University in Frankfurt we therefore confront the student with theoretical physics immediately in the first semester. Theoretical Mechanics I and II, Electrodynamics, and Quantum Mechanics I - an Introduction are the basic courses during the first two years. These lectures are supplemented with many mathematical explanations and much support material. After the fourth semester of studies, graduate work begins and Quantum Mechanics II - Symme tries, Statistical Mechanics and Thermodynamics, Relativistic Quantum Mechanics, Quantum Electrodynamics, the Gauge Theory of Weak Interactions, and Quantum Chromodynamics are obligatory.
Gauge Theory of Weak Interactions treats the unification of electromagnetic and weak interactions and considers related phenomena. First, the Fermi theory of beta decay is presented, followed by a discussion of parity violation, clarifying the importance of symmetries. Then the concept of a spontaneously broken gauge theory is introduced, and all necessary mathematical tools are carefully developed. The "standard model" of unified electroweak interactions is thoroughly discussed including current developments. The final chapter contains an introduction to unified theories of strong and electroweak interactions. Numerous solved examples and problems make this volume uniquely suited as a text for an advanced course. This second edition has been corrected and is presented in a new cover and format.
More than a generation of Gennan-speaking students around the world have worked their way to an understanding and appreciation of the power and beauty of modern theoretical 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 field of science in a series of closely related textbooks is not a new one. Many older physicists 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 use of consistent notation, logical ordering of topics and coherence 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. The present five volume set, Theoretical Physics, is in fact only that part of the complete set of textbooks developed by Greiner and his students that presents the quantum theory. I have long urged him to make the remaining volumes on classical mechanics and dynamics, on electromagnetism, on nuclear and particle physics, and on special topics available to an English-speaking audience as well, and we can hope for these companion volumes covering all of theoretical physics some time in the future.
Quantum Chromodynamics is a thorough introduction for students in theoretical physics and scientists needing a reference and exercise book in this field. The book presents the necessary mathematical tools together with many examples and worked problems. In introductory chapters the reader becomes familiar with the hadron spectrum, while the SU(N) symmetry groups and the relativistic field theory are briefly recapitulated; then a discussion of scalar quantum electrodynamics and scattering reactions follow before gauge quark-quark interactions, perturbational QCD, renormalization groups, and tests of pertubational QCD are all treated in detail. Chapters on non-perturbational QCD and quasi-phenomenological applications conclude the text.
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.
Supplementing "Quantum Mechanics. An Introduction" and "Quantum Mechanics. Symmetries", this book covers an important additional course on quantum mechanics, including an introduction to quantum statistics, the structure of atoms and molecules, and the Schrödinger wave equation. 72 fully worked examples and problems consolidate the material.
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 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.
Nuclear molecules are analogous to ordinary electronic molecules. Valence nucleons are circling nuclear cores and thus bind them. They appear in collisions of nuclei on nuclei, and in fission and fusion processes. Here a lively field of research has developed over the past 20 years. Nuclear Molecules are the strongest deformed nuclear complexes and play an important role in nuclear structure (cluster) physics. They are also of considerable interest for the synthesis of elements in astrophysics (cosmology). Most of the various nuclear molecular phenomena are discussed.This book is the first monograph exclusively written to cover the theoretical aspects of nuclear molecular phenomena in heavy ion collisions. The experimental evidence is presented and confronted with theory.
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-Nordström 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.
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