Form Factors in Higher Spin XXZ Model

Abstract

A free field realization of the type II q-vertex operator of quantum affine algebra U_q(<sl>^^^^_2) of arbitrary level is presented. This vertex operator describes creation and annihilation of physical particles in higher spin XXZ model. We also derive an integral formula for the form factor in this model by taking a trace of the type I and II q-vertex operators over the irreducible highest weight representation space of U_q(<sl>^^^^_2). Investigating the structure of poles, we obtain a residue formula for the form factor. This turns out to be a higher spin extension of the lattice analog of 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.