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.
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.
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.
This book is devoted to a topic that has undergone rapid and fruitful development over the last few years: symmetries and integrability of difference equations and q-difference equations and the theory of special functions that occur as solutions of such equations. Techniques that have been traditionally applied to solve linear and nonlinear differential equations are now being successfully adapted and applied to discrete equations. This volume is based on contributions made by leading experts in the field during the workshop on Symmetries and Integrability of Difference Equations held Estérel, Québec, in May 1994. Giving an up-to-date review of the current status of the field, the book treats these specific topics: Lie group and quantum group symmetries of difference and q-difference equations, integrable and nonintegrable discretizations of continuous integrable systems, integrability of difference equations, discrete Painlevé property and singularity confinement, integrable mappings, applications in statistical mechanics and field theories, Yang-Baxter equations, q-special functions and discrete polynomials, and q-difference integrable systems.