标题： 量子仿射代数$U_q\widehat{sl_2}$的自由场表示以及高自旋 XXZ 模型中的形式因子 显示英文标题

标题： Free Field Representation of Quantum Affine Algebra $U_q\widehat{sl_2}$ and Form Factors in Higher Spin XXZ Model

摘要： 我们考虑在反铁磁区域中的自旋$k/2$XXZ 模型，使用量子仿射代数$\uqa$在级别$k$的自由场实现。 我们给出了类型 II$q$-顶点算子的自由场实现，该算子描述了模型中物理粒子的产生和湮灭。 通过在不可约最高权表示$\uqa$上对类型 I 和类型 II$q$-顶点算子取迹，我们也推导出了该模型中形式因子的积分公式。 通过研究极点结构，我们得到了形式因子的残差公式，这是质量可积量子场论中 Smirnov 公式高自旋扩展的晶格类似物。 这一结果以及形式因子的 Knizhnik-Zamolodchikov 方程的量子变形显示了可积晶格模型与质量可积量子场论在数学结构上的深刻联系。 显示英文摘要

摘要： We consider the spin $k/2$ XXZ model in the antiferomagnetic regime using the free field realization of the quantum affine algebra $\uqa$ of level $k$. We give a free field realization of the type II $q$-vertex operator, which describes creation and annihilation of physical particles in the model. By taking a trace of the type I and the type II $q$-vertex operators over the irreducible highest weight representation of $\uqa$, we also derive an integral formula for form factors in this model. Investigating the structure of poles, we obtain a residue formula for form factors, which is a lattice analog of the higher spin extension of the Smirnov's formula in the massive integrable quantum field theory. This result as well as the quantum deformation of the Knizhnik-Zamolodchikov equation for form factors shows a deep connection in the mathematical structure of the integrable lattice models and the massive integrable quantum field theory.