Correlation functions of integrable lattice models and quantum field theories

本项目的主要目标是为精确和有效地计算可积晶格模型和量子场理论的相关函数的方法的进步。在以前的工作中，我们已经证明了自旋1/2海森堡链和相关可积模型的相关函数具有一种特殊的结构特征，我们称之为因式分解：较长距离的相关函数是单点函数和邻近相关器中的多项式，其系数由潜在的无限维对称代数决定。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，分解依赖于作用于自旋链状态空间的局部算符空间的特殊“费米子”基的存在。在尺度极限下，它变成了相应量子场论的基础。该项目的另一个目标是研究场论的费米子基与确定其紫外行为的共形场论的Verma模基之间的关系。

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.