Harmonic Mappings Twistors And O Models

Harmonic mappings have played in recent years and will likely to play in the future an important role in Differential Geometry and Theoretical Physics, where they are known as s-models. These Proceedings develop both aspects of the theory, with a special attention to the constructive methods, in particular the so-called twistorial approach. It includes expository articles on the twistorial methods, the various appearence of σ-models in Physics, the powerful analytic theory of regularity of SCHOEN-UHLENBECK.

This 1990 collection of review articles covers the considerable progress made in a wide range of applications of twistor theory.

' 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 '

This proceedings on pure and applied differential geometry, discusses several subjects in submanifold theory, such as the Willmore problem, minimal surfaces, submanifolds of finite type, affine differential geometry, indefinite Riemannian geometry, and applications of differential geometry in human and artificial vision.

Since their discovery a mere thirty years ago, solitons have been invoked to explain such diverse phenomena as: The long lived 'giant red spot' in the highly turbulent Jovian atmosphere. The famous Fermi-Pasta-Ulam paradox wherein a nonlinearly coupled lattice of particles does not display the expected equipartition of energy among available modes. Covering ion-acoustic waves in a plasma, energy storage and transfer in proteins via the Davydov soliton, and, the propagation of short laser pulses in optical fibres over long distances with negligible shape change, this volume presents important research from around the globe.

This book provides the first-ever systematic introduction to thetheory of Riemannian submersions, which was initiated by BarrettO''Neill and Alfred Gray less than four decades ago. The authorsfocus their attention on classification theorems when the total spaceand the fibres have nice geometric properties.