Correlation functions of integrable lattice models and quantum field theories

该项目的主要目标是推进可积晶格模型和量子场论的相关函数的精确和有效计算方法。 在以前的工作中，我们已经表明，自旋为1/2的海森堡链和相关的可积模型的相关函数的特征在于一个特定的结构，我们称之为因式分解：长程相关函数是多项式的一点函数和邻居，其系数是由潜在的无限维对称代数。在这里，我们想证明其他可积模型的相关函数也可以因式分解，并且我们想将因式分解的概念扩展到相关函数的谱表示中出现的矩阵元素。对于海森堡链的因式分解依赖于存在一个特殊的“费米"基础的空间的本地运营商的空间的状态空间的自旋链。在标度极限中，它变成了相应的量子场论的基础。该项目的另一个目标是研究确定其紫外行为的共形场论的Verma模基础与场论的费米基础之间的关系。

The main objective of this project is the advancement of methods for the exact and efficient calculation of correlation functions of integrable lattice models and quantum field theories . In previous work we have shown that the correlation functions of the spin-1/2 Heisenberg chain and of related integrable models are characterized by a specific structure which we have called factorization: longer-range correlation functions are polynomials in one-point functions and neighbour-correlators, whose coefficients are determined by the underlying infinite-dimensional symmetry algebra. Here we want to show that the correlation functions of other integrable models factorize as well, and we want to extend the notion of factorization to the matrix elements occuring in the spectral representations of correlation functions. For the Heisenberg chain the factorization relied on the existence of a special 'Fermionic' basis of the space of local operators acting on the space of states of the spin chain. In the scaling limit it turns into a basis of the corresponding quantum field theory. Another goal of this project is to study the relation of the Fermionic basis of the field theory with the Verma module basis of the conformal field theory that determines its ultraviolet behaviour.