Integrable Quantum Field Theories

The monograph summarizes recent achievements in the calculation of matrix elements of local operators (form factors) for completely integrable models. Particularly, it deals with sine-Gordon, chiral Gross-Neven and O(3) nonlinear s models. General requirements on form factors are formulated and explicit formulas for form factors of most fundamental local operators are presented for the above mentioned models.

Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

Applications of reflection amplitudes in Toda-type theories / C. Ahn, C. Kim and C. Rim -- Lax pairs and involutive Hamiltonians for CN and BCN Ruijsenaars-Schneider models / Kai Chen, B.-Y. Hou and W.-L. Yang -- Fateev's models and their applications / D. Controzzi and A.M. Tsvelik -- The ODE/IM correspondence / P. Dorey, C. Dunning and R. Tateo -- Integrable sigma models / P. Fendley -- Lorentz lattice gases and spin chains / M.J. Martins -- Quantum Calogero-Moser models for any root system / R. Sasaki -- Quasi-particles in conformal field theories for fractional quantum Hall systems / K. Schoutens and R.A.J. van Elburg -- Towards form factors in finite volume / F.A. Smirnov -- Static and dynamic properties of trapped Bose-Einstein condensates / T. Tsurumi, H. Morise and M. Wadati -- Integrability of the Calogero Model: Conserved quantities, the classical general solution and the quantum orthogonal basis / H. Ujino, A. Nishino and M. Wadati -- Conformal boundary conditions / J.-B. Zuber

In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.

This volume includes several lecture notes on the fundamentals and elementary techniques of integrable field theories and on their applications to low-dimensional physics systems contributed by leading scientists in the respective fields. The main topics covered are various aspects of the thermodynamic Bethe ansatz, form factors, Calogero (and related) models, sigma models, conformal boundary conditions, etc. The volume presents both pedagogical material and a current research trend in the field.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)

Proceedings of a NATO ARW held in Como, Italy, September 14-19, 1992

Integrable Sys Quantum Field Theory

This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.