Current Problems In Elementary Particle And Mathematical Physics

This book grew-how could it be otherwise?-out of a series oflectures which the author held at the University of Heidelberg. The purpose ofthese lectures was to give an introduction to the phenomenology of elementary particles for students both of theoretical and experimental orientation. With the present book the author has set himself the same aim. The reader is assumed to be familiar with ordinary nonrelativistic quantum mechanics as presented, e.g., in the following books: Quantum Mechanics, by L.1. Schiff (McGraw-Hill, New York, 1955); Quantum Mechanics, Vol. I, by K. Gottfried (W.A. Benjamin, Reading, Ma., 1966). The setup of the present book is as follows. In the first part we present some basic general principles and concepts which are used in elementary particle physics. The reader is supposed to learn here the "language" of particle physics. An introductory chapter deals with special relativity, of such funda mental importance for particle physics, which most ofthe time is high energy, i.e., highly relativistic physics. Further chapters of this first part deal with the Dirac equation, with the theory of quantized fields, and with the general definitions of the scattering and transition matrices and the cross-sections.

Professor Gerard G. Emch has been one of the pioneers of the C-algebraic approach to quantum and classical statistical mechanics. In a prolific scientific career, spanning nearly five decades, Professor Emch has been one of the creative influences in the general area of mathematical physics. The present volume is a collection of tributes, from former students, colleagues and friends of Professor Emch, on the occasion of his 70th birthday. The articles featured here are a small yet representative sample of the breadth and reach of some of the ideas from mathematical physics.It is also a testimony to the impact that Professor Emch's work has had on several generations of mathematical physicists as well as to the diversity of mathematical methods used to understand them.

In this final volume I have tried to present the subject of statistical mechanics in accordance with the basic principles of the series. The effort again entailed following Gustav Mahler's maxim, "Tradition = Schlamperei" (i.e., filth) and clearing away a large portion of this tradition-laden area. The result is a book with little in common with most other books on the subject. The ordinary perturbation-theoretic calculations are not very useful in this field. Those methods have never led to propositions of much substance. Even when perturbation series, which for the most part never converge, can be given some asymptotic meaning, it cannot be determined how close the nth order approximation comes to the exact result. Since analytic solutions of nontrivial problems are beyond human capabilities, for better or worse we must settle for sharp bounds on the quantities of interest, and can at most strive to make the degree of accuracy satisfactory.

This book has come into being as a result of scientific debates. And these debates have determined its structure. The first chapter is in the form of Socratic dialogues between a mathematician (MATH.), two physicists (pHYS. and EXP.) and a philosopher (PHIL.). However, although one of the authors is a theoretical physicist and the other a mathematician, the reader must not think that their opinions have been divided among the participants of the dialogues. We have tried to convey the inner tension of the topic under discussion and its openness. The attitudes of the participants reflect more the possible evaluations of the situation rather than the actual views of the authors. What is more, the subject "elementary particles" as dealt with in the 3 6 dialogue stretches over (2-3) 10 years of historical time and a space of 10 ±1 pages of scientific literature. For this reason, a complete survey of it is un achievable. But, of course, every researcher constructs his own history of his science and sees a certain list of its main pOints. We have attempted to float several possible pictures of this kind. Therefore the fact that Math and Phys talk about the history of element ary particles is not an attempt to present the scientific history of this realm of physics.

The Third Anniversary Symposium, held in January 1965, was devoted mainly to various topics in elementary particle physics, with a few lectures on many-body problems and a short supple mentary program in mathematics. * In the Introductory Address Professor V. Weisskopf, Director General of CERN, Geneva, presented a broad survey of the then current scene in elementary particle physics, the most dominant trend in which is the concept of symmetry. He traced the use of the concept of rotational invariance and symmetry under permutation of identical objects in the realm of atomic spectra and how, with the inclusion of isotopic spin, such use was extended to the study of properties of nuclei. Professor Weisskopf also described how, in ad dition, elementary particles are characterized by a new quantum number, the hypercharge, which, with isotopic spin, is part of a wider symmetry SU(3). He mentioned three classes of experiments at CERN, one in search of quarks, one to investigate the existence of vector bosons suggested by theories as possible mediators of weak interaction, and one to test the existence of cosmic forces to explain C P or T violation. The quotations from Newton's Opticks at the beginning and the end of the lecture were strikingly relevant. Two lectures dealt with the application of SU(3) symmetry to weak and strong interactions, respectively. Ph. Meyer of the Uni versity of Paris, Orsay summarized his work on the conserved vector current hypothesis in relation to broken symmetries.

In recent years, gauge fields have attracted much attention in elementary par ticle physics. The reason is that great progress has been achieved in solving a number of important problems of field theory and elementary particle physics by means of the quantum theory of gauge fields. This refers, in particular, to constructing unified gauge models and theory of strong interactions between the elementary particles. This book expounds the fundamentals of the quantum theory of gauge fields and its application for constructing unified gauge models and the theory of strong interactions. In writing the book, the authors' aim was three-fold: firstly, to outline the basic ideas underlying the unified gauge models and the theory of strong inter actions; secondly, to discuss the major unified gauge models, the theory of strong interactions and their experimental implications; and, thirdly, to acquaint the reader with a rather special mathematical approach (path-in tegral method) which has proved to be well suited for constructing the quantum theory of gauge fields. Gauge fields are a vigorously developing area. In this book, we have select ed for presentation the more or less traditional and commonly accepted mate rial. There also exist a number of different approaches which are presently being developed. The most important of them are touched upon in the Conclusion.