This book contains the proceedings of two international conferences: a satellite meeting of the IUPAP Statphys-19 Conference and the Seventh Nankai Workshop, held in Tianjin, China in August 1995. The central theme of the two conferences, which drew participants from 18 countries, was the Yang-Baxter equation and its development and applications. With topics ranging from quantum groups, vertex and spin models, to applications in condensed matter physics, this book reflects the current research interest of integrable systems in statistical mechanics.
The Oskar Klein Memorial Lecture series has become a very successful tradition in Swedish physics since it started in 1988. Theoretical high-energy physics dominates the subjects of the lectures, mirroring one of Klein's own main interests.This single volume is a compilation of the unique lectures previously produced in three separate volumes. The lectures are by world renowned experts in physics who have all contributed to the excitement of the field over the years. They continue to be of value to students and teachers alike.
With Translated Reprints by O KleinThe Oskar Klein Memorial Lectures, instituted in 1988 and supported by the Royal Swedish Academy of Sciences through its Nobel Committee for Physics, are given at Stockholm University in Sweden, where Oskar Klein was professor in Theoretical Physics 1930-1962.Volume 1 contains the 1988 lectures on “Symmetry and Physics” and “From the Bethe-Hulthén Hypothesis to the Yang-Baxter Equation,” given by C N Yang, Nobel Prize winner (1957) and professor at the State University of New York at Stony Brook. The 1989 lectures on “Beyond the Standard Models,” referring to models for cosmology and elementary particles, and on “Precision Tests of Quantum Mechanics” were given by Steven Weinberg, Nobel Prize winner (1979) and professor at the University of Texas at Austin. The volume also contains translations of some of Klein's original papers, one on intermediate charged fields (original in French, 1938), another on five-dimensional quantum theory (”Kaluza-Klein theory,” original in German, 1926). A scientific biography of Klein, written by Professors I. Fischer- Hjalmars and B Laurent, who both knew Klein well, is included as well as an autobiography by Klein.
With Translated Reprints by O KleinThe Oskar Klein Memorial Lectures, instituted in 1988 and supported by the Royal Swedish Academy of Sciences through its Nobel Committee for Physics, are given at Stockholm University in Sweden, where Oskar Klein was professor in Theoretical Physics 1930-1962.Volume 1 contains the 1988 lectures on ?Symmetry and Physics? and ?From the Bethe-Hulthn Hypothesis to the Yang-Baxter Equation,? given by C N Yang, Nobel Prize winner (1957) and professor at the State University of New York at Stony Brook. The 1989 lectures on ?Beyond the Standard Models,? referring to models for cosmology and elementary particles, and on ?Precision Tests of Quantum Mechanics? were given by Steven Weinberg, Nobel Prize winner (1979) and professor at the University of Texas at Austin. The volume also contains translations of some of Klein's original papers, one on intermediate charged fields (original in French, 1938), another on five-dimensional quantum theory (?Kaluza-Klein theory,? original in German, 1926). A scientific biography of Klein, written by Professors I. Fischer- Hjalmars and B Laurent, who both knew Klein well, is included as well as an autobiography by Klein.
The last twenty years have seen an active interaction between mathematics and physics. This book is devoted to one of the new areas which deals with mathematical structures related to conformal field theory and its sqs-deformations. In the book, the author discusses the interplay between Knizhnik-Zamolodchikov type equations, the Bethe ansatz method, representation theory, and geometry of multi-dimensional hypergeometric functions. This book aims to provide an introduction to the area and expose different facets of the subject. It contains constructions, discussions of notions, statements of main results, and illustrative examples. The exposition is restricted to the simplest case of the theory associated with the Lie algebra s\mathfrak{sl 2s. This book is intended for researchers and graduate students in mathematics and in mathematical physics, in particular to those interested in applications of special functions.
Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory, and has thrown new light on many different topics, notably low-dimensional topology and conformal field theory. The goal of this book is to give a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Thus this book can serve both as an introduction for the newcomer, and as a guide for the more experienced reader. All who have an interest in the subject will welcome this unique treatment of quantum groups.
Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.
In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.