Twenty-five years of Schladming Winter School 1. The Start Twenty-five years ago P. Urban had the idea of organizing a winter school in the Austrian mountains. The very concept of a school was not new: to bring physicists together in an environment which differs totally from the daily world of institutes and laboratories, to contrast hard classroom work in lectures by distinguished speakers with a relaxed atmosphere, to provide opportunities for entering newly developing fields and exchanging ideas, all this had already resulted in a few summer schools in southern Europe and the US. The idea of combining physics with skiing rather than swimming was, however, new. After some sampling by a few younger members of Ur ban's group, Schladming was selected as an appropriate place. At that time skiing was not very much developed here; there were few lifts, but a road to Hochwurzen and a regular bus service opened at least one longer track. The first meeting took place in a classroom of the local school, w here some 40 participants were squeezed into benches designed for children. In the next year we moved into the dining hall of a small inn, which does not exist any more (an attempt to serve beer during the lectures was stopped by the orga nizing committee). Only in later years did we find a permanent home here in the Stadtsaal.

This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad overview on actual and future research directions in this fascinating and rapidly expanding area.

Eight carefully written articles on the interactions between the ideas and concepts of particle physics and those of astrophysics make up this book. Two long introductory lectures give a survey of modern concepts in particle physics and in astrophysics and cosmology, stressing features of common interest. The other six contributions deal with the physics of supernova explosions, with black holes, with neutrino oscillations, with the importance of phase transitions for the large-scale structure of the Universe, and with the use of the ideas of quantum gravity for computer simulations. These rather detailed review articles will be of value for many years to come. The book is intended for graduate students and researchers both in particle physics and in astrophysics.

th This volume contains the written versions of invited lectures presented at the 28 "Internationale Universitatswochen fUr Kernphysik" in Schladming, Austria in March 1989. The generous support of our sponsors, the Austrian Ministry of Science and Research, the Government of Styria, and others, made it again possible to invite expert lecturers. The courses were centered on elementary particle physics to be performed with large accelerators accessible in the immediate future, including some reports on the current situation. Thanks to the efforts of the speakers it was possible to obtain excellent surveys. After the School the lecture notes were revised and partially rewritten in TPC by the authors, whom we thank for their labour. Unfortunately the report on the situation at SLAC by M. Swartz could not be included. Thanks are also due to the publishers for their patience. Graz, Austria H. Latal December 1989 H. Mitter v Contents Phenomenology of and Beyond the Standard Electroweak Model By A. Bartl, H. Pietschmann, and H. Stremnitzer (With 6 Figures) 1 1. The Standard Model (H. Pietschmann) . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 Defining the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 3 Testing the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 4 Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 5 Open Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 6 Hypotheses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2. Beyond the Standard Model: Supersymmetry (A. Bartl) . . . . . . . . . . . . 9 2. 1 Supersymmetric Extension of the Standard Model . . . . . . . . . . . . 10 2. 2 Production and Decay of Supersymmetric Particles . . . . . . . . . . . 17 3. Beyond the Standard Model: Composite Models (H.

For scientific, technological and organizational reasons, the end of World War II (in 1945) saw a rapid acceleration in the tempo of discovery and understanding in nuclear physics, cosmic rays and quantum field theory, which together triggered the birth of modern particle physics. The first fifteen years (1945-60) following the war's end ? the ?Startup Period? in modern particle physics -witnessed a series of major experimental and theoretical developments that began to define the conceptual contours (non-Abelian internal symmetries, Yang-Mills fields, renormalization group, chirality invariance, baryon-lepton symmetry in weak interactions, spontaneous symmetry breaking) of the quantum field theory of three of the basic interactions in nature (electromagnetic, strong and weak). But it took another fifteen years (1960-75) ? the ?Heroic Period? in modern particle physics ? to unravel the physical content and complete the mathematical formulation of the standard gauge theory of the strong and electroweak interactions among the three generations of quarks and leptons. The impressive accomplishments during the ?Heroic Period? were followed by what is called the ?period of consolidation and speculation (1975-1990)?, which includes the experimental consolidation of the standard model (SM) through precision tests, theoretical consolidation of SM through the search for more rigorous mathematical solutions to the Yang-Mills-Higgs equations, and speculative theoretical excursions ?beyond SM?.Within this historical-conceptual framework, the author ? himself a practicing particle theorist for the past fifty years ? attempts to trace the highlights in the conceptual evolution of modern particle physics from its early beginnings until the present time. Apart from the first chapter ? which sketches a broad overview of the entire field ? the remaining nine chapters of the book offer detailed discussions of the major concepts and principles that prevailed and were given wide currency during each of the fifteen-year periods that comprise the history of modern particle physics. Those concepts and principles that contributed only peripherally to the standard model are given less coverage but an attempt is made to inform the reader about such contributions (which may turn out to be significant at a future time) and to suggest references that supply more information. Chapters 2 and 3 of the book cover a range of topics that received dedicated attention during the ?Startup Period? although some of the results were not incorporated into the structure of the standard model. Chapters 4-6 constitute the core of the book and try to recapture much of the conceptual excitement of the ?Heroic Period?, when quantum flavordynamics (QFD) and quantum chromodynamics (QCD) received their definitive formulation. [It should be emphasized that, throughout the book, logical coherence takes precedence over historical chronology (e.g. some of the precision tests of QFD are discussed in Chapter 6)]. Chapter 7 provides a fairly complete discussion of the chiral gauge anomalies in four dimensions with special application to the standard model (although the larger unification models are also considered). The remaining three chapters of the book (Chapters 7-10) cover concepts and principles that originated primarily during the ?Period of Consolidation and Speculation? but, again, this is not a literal statement. Chapters 8 and 9 report on two of the main directions that were pursued to overcome acknowledged deficiencies of the standard model: unification models in Chapter 8 and attempts to account for the existence of precisely three generations of quarks and leptons, primarily by means of preon models, in Chapter 9. The most innovative of the final three chapters of the book is Chapter 10 on topological conservation laws. This last chapter tries to explain the significance of topologically non-trivial solutions in four-dimensional (space-time) particle physics (e.g. 't Hooft-Polyakov monopoles, instantons, sphalerons, global SU(2) anomaly, Wess-Zumino term, etc.) and to reflect on some of the problems that have ensued (e.g. the ?strong CP problem? in QCD) from this effort. It turns out that the more felicitous topological applications of field theory are found ? as of now ? in condensed matter physics; these successful physical applications (to polyacetylene, quantized magnetic flux in type-II low temperature superconductivity, etc.) are discussed in Chapter 10, as a good illustration of the conceptual unity of modern physics.

This volume contains the written versions of invited lectures presented at the 29th "Internationale Universitatswochen fiir Kernphysik" in Schladming, Aus tria, in March 1990. The generous support of our sponsors, the Austrian Ministry of Science and Research, the Government of Styria, and others, made it possible to invite expert lecturers. In choosing the topics of the course we have tried to select some of the currently most fiercely debated aspects of quantum field theory. It is a pleasure for us to thank all the speakers for their excellent presentations and their efforts in preparing the lecture notes. After the school the lecture notes were revised by the authors and partly rewritten ~n '!EX. We are also indebted to Mrs. Neuhold for the careful typing of those notes which we did not receive in '!EX. Graz, Austria H. Mitter July 1990 W. Schweiger Contents An Introduction to Integrable Models and Conformal Field Theory By H. Grosse (With 6 Figures) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1 1. Introduction ............................................. . 1 1.1 Continuous Integrable Models .......................... . 1 1.2 "Solvable" Models of Statistical Physics ................. . 2 1.3 The Yang-Baxter Relation ............................. . 3 1.4 Braids and I(nots .................................... . 3 1.5 Confonnal Field Theory d = 2 ......................... . 3 2. Integrable Continuum Models - The Inverse Scattering Method - Solitons .................... . 4 2.1 A General Scheme for Solving (Linear) Problems ......... . 4 2.2 The Direct Step ...................................... . 6 2.3 The Inverse Step ..................................... .

The objectives of the conference are to develop greater understanding of physics research and its applications to promote new industries; to innovate knowledge about recent breakthroughs in physics, both the fundamental and technological aspects; to implement of international cooperation in new trends in physics research and to improve the performance of the physics research facilities in Egypt. This proceedings highlights the latest results in the fields of astrophysics, atomic, molecular, condensed matter, laser, nuclear and particle physics. The peer refereed papers collected in this volume were written by international experts in these laser fields.

The International Conference on the History of Original Ideas and Basic Discoveries, held at the "Ettore Majorana" Centre for Scientific Culture in Erice, Sicily, July 27-August 4, 1994, brought together sixty of the leading scientists including many Nobel Laureates in high energy physics, principal contributors in other fields of physics such as high Tc superconductivity, particle accelerators and detector instrumentation, and thirty-six talented younger physicists selected from candidates throughout the world. The scientific program, including 49 lectures and a discussion session on the "Status and Future Directions in High Energy Physics" was inspired by the conference theme: The key experimental discoveries and theoretical breakthroughs of the last 50 years, in particle physics and related fields, have led us to a powerful description of matter in terms of three quark and three lepton families and four fundamental interactions. The most recent generation of experiments at e+e- and proton-proton colliders, and corresponding advances in theoretical calculations, have given us remarkably precise determinations of the basic parameters of the electroweak and strong interactions. These developments, while showing the striking internal consistency of the Standard Model, have also sharpened our view of the many unanswered questions which remain for the next generation: the origin and pattern of particle masses and families, the unification of the interactions including gravity, and the relation between the laws of physics and the initial conditions of the universe.

The final volume of this new innovative and informative three-volume set explains and explores the essential basic and advanced concepts from various areas within the nanosciences. This volume primarily focuses on increasing awareness of sustainable nanochemistry, meaning the social and economic impact of nanochemistry, in order to mitigate ecological resource depletion and to promote the exploration of nature as a resource for future benefits. This volume adopts a pharmacological lens, examining the multitude of ways in which nano-research can contribute to the development of pharmaceutical drugs and paying particular attention to toxicology and renewable energy within nanochemistry. Under the vast expertise of the editor, the volume contains 34 entries contributed by renowned international scientists and scholars. The content in this volume covers topics such as anti-HIV agents, ecotoxicology, solar cells and photovoltaic phenomena, spectral-SAR, and more—alphabetically organized and accompanied by equations, figures, and brief letters in order to emphasize the potential applications of the concepts discussed.