The NATO Advanced Study Institute on Quantum Electrodynamics of Strong Fields was held at Lahnstein on the Rhine from 15-26 June, 1981. The school was devoted to the advances, theoretical and exper imental, in the physics of strong fields made during the past decade. The topic of the first week was almost exclusively quantum electrodynamics, with discussions of symmetry breaking in the ground state, of the physics of heavy ion collisions and of precision tests of perturbative quantum electrodynamics. 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 call on a body of lecturers who not only have made considerable personal contributions to these advances but who are also noted for their lecturing skills. Their dedication for their subject was readily transmitted to the stu dents resulting in a very successful school. This enthusiasm is also reflected in their contributions to these Proceedings which, as I believe, will in time become a standard source of reference for future work on the physics of strong fields and will help to spread the benefits of the school to a larger audience than those who were able to attend. I regret that the Soviet colleagues Ya. B. Zeldovich and V. S. Popov were unable to participate.

The need for a second edition of our text on Quantum Electrodynamics has given us the opportunity to implement some corrections and amendments. We have corrected a number of misprints and minor errors and have supplied additional explanatory remarks at various places. Furthermore some new material has been included on the magnetic moment of the muon (in Example 5. 6) and on the Lamb shift (in Example 5. 8). Finally, we have added the new Example 3. 17 which explains the equivalent photon method. We thank several colleagues for helpful comments and also are grateful to Dr. R. Mattiello who has supervised the preparation of the second edition of the book. Furthermore we acknowledge the agreeable collaboration with Dr. H. J. K6lsch and his team at Springer-Verlag, Heidelberg. Frankfurt am Main, Walter Greiner July 1994 Joachim Reinhardt Preface to the First Edition 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 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.

Quantum field theory, which started with Paul Dirac’s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity. Quantum Field Theory: A Modern Perspective presents Professor Nair’s view of certain topics in field theory loosely knit together as it grew out of courses on field theory and particle physics taught at Columbia University and the City College of CUNY. The first few chapters, up to Chapter 12, contain material that generally goes into any course on quantum field theory, although there are a few nuances of presentation which readers may find to be different from other books. This first part of the book can be used for a general course on field theory, omitting, perhaps, the last three sections in Chapter 3, the last two in Chapter 8 and sections 6 and 7 in Chapter 10. The remaining chapters cover some of the more modern developments over the last three decades, involving topological and geometrical features. The introduction given to the mathematical basis of this part of the discussion is necessarily brief and should be accompanied by books on the relevant mathematical topics as indicated in the bibliography. Professor Nair also concentrates on developments pertinent to a better understanding of the standard model. There is no discussion of supersymmetry, supergravity, developments in field theory inspired by string theory, etc. There is also no detailed discussion of the renormalization group. Each of these topics would require a book in its own right to do justice to the topic. Quantum Field Theory: A Modern Perspective serves as a portal to so many more topics of detailed and ongoing research, referring readers to more detailed treatments for many specific topics. The book also contains extensive references, providing readers a more comprehensive perspective on the literature and the historical development of the subject. V. Parameswaran Nair is Professor of Physics at City College of The City University of New York (CUNY). Professor Nair has held Visiting Professorships at The Abdus Salam International Center for Theoretical Physics, Rockefeller University, Institute for Advanced Study at Princeton, and Massachusetts Institute of Technology.

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.

What happens to light when it is trapped in a box? Cavity Quantum Electrodynamics addresses a fascinating question inphysics: what happens to light, and in particular to itsinteraction with matter, when it is trapped inside a box? With theaid of a model-building approach, readers discover the answer tothis question and come to appreciate its important applications incomputing, cryptography, quantum teleportation, andopto-electronics. Instead of taking a traditional approach thatrequires readers to first master a series of seemingly unconnectedmathematical techniques, this book engages the readers' interestand imagination by going straight to the point, introducing themathematics along the way as needed. Appendices are provided forthe additional mathematical theory. Researchers, scientists, and students of modern physics can referto Cavity Quantum Electrodynamics and examine the field thoroughly.Several key topics covered that readers cannot find in any otherquantum optics book include: * Introduction to the problem of the "vacuum catastrophe" and thecosmological constant * Detailed up-to-date account of cavity QED lasers andthresholdless lasing * Examination of cavities with movable walls * First-principles discussion about cavity QED in opencavities * Pedagogical account of microscopic quantization indielectrics Complementing the coverage of the most advanced theory andtechniques, the author provides context by discussing thehistorical evolution of the field and its discoveries. In thatspirit, "recommended reading," provided in each chapter, leadsreaders to both contemporary literature as well as key historicalpapers. Despite being one of many specialties within physics, cavityquantum electrodynamics serves as a window to many of thefundamental issues of physics. Cavity Quantum Electrodynamics willserve as an excellent resource for advanced undergraduate quantummechanics courses as well as for graduate students, researchers,and scientists who need a comprehensive introduction to the field.

An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.

Taking a heuristic approach to relativistic quantum mechanics, Practical Quantum Electrodynamics provides a complete introduction to the theory, methodologies, and calculations used for explaining the physical interaction of charged particles. This book combines the principles of relativity and quantum theory necessary for performing the ca