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.

Kallen's Quantenelektrodynamik provides a concise treatment of the subject. Its strong points are the careful attention to ex­ planatory detail, the methodical coverage of all the maj or results and the straightforward, lucid style. Certainly it will be a val­ uable reference for one learning the subject or for one who re­ quires the details of the practical results. Of course modern quantum field theory has now grown far beyond its dramatic be­ ginnings in electrodynamics and we have therefore included some references to introduce the reader to the more recent and more specialized literature. We have corrected some minor errors: we would appreciate it if readers would inform us of any others which they find. We thank Professors Paul Urban and C. MtSller for permission to use the biographical material on Kallen. We also wish to thank Springer-Verlag for undertaking publication of this edition by an unorthodox method, but one which will reduce the cost to the reader. In particular, we are grateful to Dr. H. Mayer-Kaupp and Mr. Herb Stillman for their kind cooperation. Finally, we thank Mr. Michael Teague for reading and commenting on the first dozen sections and we thank Mrs. Joanne Downs for ed iting and typing the final manuscript. May 1972 C. K. Iddings M. Mizushima Department of PhysiCS and Astrophysics University of Colorado Boulder, Colorado 80302 .. ., IN MEMORIAM PROFESSOR GUNNAR KALLEN On October 13, 1968, Professor Gunnar Kallen of the University of Lund, Sweden, died in an airplane accident near Hanover.

The laws of nature encompass the small, the large, the few, and the many. In this book, we are concerned with classical (i.e., not quantum) many-body systems, which refers to any microscopic or macroscopic system that contains a large number of interacting entities. The nearest-neighbor Ising model, originally developed in 1920 by Wilhelm Lenz, forms a cornerstone in our theoretical understanding of collective effects in classical many-body systems and is to date a paradigm in statistical physics.

This book is an English translation from a Hungarian book designed for graduate and postgraduate students about the use of variational principles in theoretical physics. Unlike many academic textbooks, it dashes across several lecture disciplines taught in physics courses. It emphasizes and demonstrates the use of the variational technique and philosophy behind the basic laws in mechanics, relativity theory, electromagnetism, and quantum mechanics. The book is meant for advanced students and young researchers in theoretical physics but, also, more experienced researchers can benefit from its reading.

This thesis makes significant advances towards an understanding of superconductivity in the cuprate family of unconventional, high-temperature superconductors. Even though the high-temperature superconductors were discovered over 35 years ago, there is not yet a general consensus on an acceptable theory of superconductivity in these materials. One of the early proposals suggested that collective magnetic excitations of the conduction electrons could lead them to form pairs, which in turn condense to form the superconducting state at a critical temperature Tc. Quantitative calculations of Tc using experimental data were, however, not available to verify the applicability of this magnetic mechanism.

We are pleased by the positive resonance of our book which now necessitates a fourth edition. We have used this opportunity to implement corrections of misprints and amendments at several places, and to extend and improve the discussion of many of the exercises and examples. We hope that our presentation of the method of equivalent photons (Example 3. 17), the form factor of the electron (Example 5. 7), the infrared catastrophe (Example 5. 8) and the energy shift of atomic levels (Example 5. 9)arenow even better to understand.

We are pleased by the positive resonance of our book which now necessitates a fourth edition. We have used this opportunity to implement corrections of misprints and amendments at several places, and to extend and improve the discussion of many of the exercises and examples. We hope that our presentation of the method of equivalent photons (Example 3. 17), the form factor of the electron (Example 5. 7), the infrared catastrophe (Example 5. 8) and the energy shift of atomic levels (Example 5. 9)arenow even better to understand.