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It has been sixteen years since the unification of electro Magnetism with the weak interactions was developed by Glashow, Salam, and Weinberg. Well before that proposal was fully confirmed by experiment, work began on unifying strong interactions with the electroweak. Now there is a growing effort to incorporate some theory of quantum gravity into the scheme. This enormous complex of theoreti cal and experimental efforts was the subject of the Fourth Workshop on Grand Unification held in Philadelphia and attended by over two hundred physicists. During the workshop, experimental and theoretical talks alternated as shown by the program summary on page 409. However, to display the logical scope of the workshop the proceedings are organized into five subject areas. Howard Georgi opened the workshop with a keynote address in which he reminds us of some of the simple properties of the particle spectrum that have not yet been understood. The first subject area, and also the largest, is proton decay and underground physics. This is introduced by ~Jill iam r1arciano' s review of the SU(5) predictions with particular attention paid to the theoretical uncertainties. Spokesmen for the major underground experiments present current results on proton decay, nn oscillations, and magnetic monopole flux: B. V. Sreekantan for the Kolar gold field experiment after 1. 9 years of operation, Earl Peterson for the Soudan detector after 0. 55 years, and Bruce Cortez for the rr'lB detector after 0. 22 years.
The book reviews a large number of 1- and 2-dimensional equations that describe nonlinear phenomena in various areas of modern theoretical and mathematical physics. It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields. We hope that the book will be useful also for experts in hydrodynamics, solid-state physics, nonlinear optics electrophysics, biophysics and physics of the Earth. The first two chapters of the book present some results from the repre sentation theory of Lie groups and Lie algebras and their counterpart on supermanifolds in a form convenient in what follows. They are addressed to those who are interested in integrable systems but have a scanty vocabulary in the language of representation theory. The experts may refer to the first two chapters only occasionally. As we wanted to give the reader an opportunity not only to come to grips with the problem on the ideological level but also to integrate her or his own concrete nonlinear equations without reference to the literature, we had to expose in a self-contained way the appropriate parts of the representation theory from a particular point of view.
The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.
Ten years have passed since It Hooft and Polyakov demonstrat ed that superheavy magnetic monopoles were a natural consequence of any Grand Unified Theory (GUT) in which the unifying group contains a U(l) factor as a subgroup. An analysis of these GUTs in an expanding, cooling universe yields a phase transition at an energy ~l015 GeV and at a cosmic time ~lO-35 seconds after the big bang. The general consequences of GUTs and this phase transition are the prediction of proton decay, the production of superheavy magnetic monopoles, and an understanding of the observed excess of matter over anti-matter in the universe. Attempts to provide experimental verification of GUTs has led to valiant experimental efforts in recent years to observe nucleon decay in massive underground detectors. Experiments to search for superheavy monopoles may eventually require similar efforts. Since the unification scale is unreachable in the laboratory, monopole detectors must search for relics of the big bang. Much theoretical groundwork has been accomplished in recent years with the development of GUTs. In Part I of this book, Erick Weinberg gives a theoretical overview of the role of magnetic monopoles in the various unification schemes. Monopoles in the context of the newly revived Kaluza-Klein theories are presented by several authors and are summarized by Qaisar Shafi. Mike Turner begins Part II with a discussion of monopoles in standard big bang cosmology. Paul Steinhardt follows with his perspectives on the inflationary universe; C.
Accompanying CD-ROM contains Microsoft Windows program Kepler which calculates the effects of any perturbation of the Kepler problem and plots the resulting trajectories.