Towards the Construction of Wightman Functions of Integrable Quantum Field Theories

Abstract

The purpose of the "bootstrap program" for integrable quantum field theories in 1+1 dimensions is to construct a model in terms of its Wightman functions explicitly. In this article, this program is mainly illustrated in terms of the sineGordon and the sinh-Gordon model and (as an exercise) the scaling Ising model. We review some previous results on sine-Gordon breather form factors and quantum operator equations. The problem to sum over intermediate states is attacked in the short distance limit of the two point Wightman function for the sinh-Gordon and the scaling Ising model.

Construction of Quantum Field Theories with Factorizing S-Matrices

“…There also exist many integrable quantum field theories with richer particle spectra, containing bound states and solitons. The generalization of the construction procedure presented here to this larger class of models is currently under investigation 6 . Before a generalization to models with bound states can be realized, one probably needs to develop an operator-algebraic understanding of the singularity structure of the corresponding S-matrices [1,6], just as the crossing symmetry of factorizing S-matrices is now known to be linked to the wedge-locality of its associated polarization-free generators [57].…”

“…This feature is typical for completely integrable models, which provide a rich class of examples for such scattering operators [1]. Basic properties of S, like unitarity, crossing symmetry and its analytic properties, imply corresponding properties of the scattering function S 2 [1,25,6], which we take as a definition. Here and in the following, we write S(a, b) := {ζ ∈ C : a < Im ζ < b} (3.23) for strips in the complex plane.…”

Master equation for spin–spin correlation functions of the chain

“…For these models the approach (i) usually leads to short distance expansions for the correlation functions, while the approach (ii) gives their long distance expansion. The problem of putting into explicit (analytic) correspondence these two regimes has been the subject of several works along the last fifteen years (see e.g., [40,41,42,43]), remaining however up to now an open problem. We hope that the method presented here could ultimately shed some new light on these topics.…”

Формфакторная Программа. Обзор И Новые Результаты: Рекурсивный $SU(N)$-анзац Бете Вне Массовой Оболочки И $1/N$-Разложение

“…Тогда функции h n (θ) зависят только от разно-стей быстрот. Выполняя одно интегрирование, получим соотношение для малых τ [37], [38]. Поэтому двухточечная функция Вайтмана имеет степенное поведение на малых расстояниях:…”