The Proceedings consists of 6 lectures each from Prof L Takhtajan and Prof F Smirnov which were presented during the workshop. Contents:Lectures on Integrable Massive Models of Quantum Field Theory (F A Smirnov):General Problems of the Quantum Field Theory. Completely Integrable ModelsSpace of States. Form Factors. A Set of Axioms for Form FactorsLocal Commutativity and Asymptotic ConditionsForm Factors in SU(2)-Invariant Thirring ModelNecessary Properties of the Currents Form Factors in SU(2)-Invariant Thirring ModelProperties of Currents in SU(2)-Invariant Thirring ModelLectures on Quantum Groups (L A Takhtajan):Historical Introduction. Algebraic BackgroundPoisson-Lie Groups, CYBE and Modified CYBE. Connection with ISM. Lie-Algebraic Meaning of CYBE and Modified CYBEQuantization Procedure as a Deformation of the Algebra of Classical ObservablesWeyl Quantization. Quantization of Poisson-Lie Groups Associated with CYBEQYBEQuantization of Poisson-Lie Groups Associated with Modified CYBE. Quantum Matrix Algebras. Quantum Determinant and Quantum Groups SL(n) and GL (n)Quantum Vector Spaces for the Quantum Groups SLq(n), GLq(n) and their Real Forms. Quantum Groups Oq(N), SPq(n), Quantum Vector Spaces Associated with them and their Real FormsQuantization of the Universal Enveloping Algebras of the Simple Lie Algebras. Elements of the Representations Theory Readership: Mathematical physicists. keywords:

This volume contains the lectures given by the three speakers, M Jimbo, P P Kulish and E K Sklyanin, who are outstanding experts in their field. It is essential reading to those working in the fields of Quantum Groups, and Integrable Systems.

Proceedings of the June 1992 NATO Advanced Study Institute, conceived as a preparatory school for the XIXth International Colloquium on Group Theoretical Methods in Physics, which was held in Salamanca the following week. This necessitated coverage of a wide range of problems in mathematical physics

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

' 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. Contents:Completely Integrable Models of Quantum Field TheoryThe Space of Physical StatesThe Necessary Properties of Form FactorsThe Local Commutativity TheoremSoliton Form Factors in SG ModelThe Main Properties of the Soliton Form FactorsBreathers Form Factors in SG ModelProperties of the Operators jμ, Tμν, exp(± iβu/2) in SG ModelForm Factors in SU(2)-Invariant Thirring ModelForm Factors in O(3)-Nonlinear σ-modelAsymptotics of Form FactorsCurrent AlgebrasForm Factors in SU(N) — Invariant Thirring Model (SU(N) Chiral Gross-Neveu Model)Phenomenological Reasonings Readership: Mathematical physicists. Keywords:Integrable;Quantum Field Theory in Two Dimensions;S-Matrix;Existence of Completely Integrable Models;Scattering Operator;Many-Particle Scattering;Yang-Baxter Triangle Equation;Soluable Lattice Models of Classical Statistical Mechanics;Form Factors;Zamolodchikov-Faddeev Approach;SU(2)-Invariant Thirring Model;Kinks;O(3)-Invariant σ-Model “It will be of great help to those who look for a reliable source of the numerous detailed calculations that have been performed over the years by many experts.” Mathematics Abstracts '