On the Free Field Realization of Form Factors

A method to construct free field realizations for the form factors of diagonal factorized scattering theories is described. Form factors are constructed from linear functionals over an associative `form factor algebra', which in particular generate solutions of the deformed Knizhnik-Zamolodchikov equations with parameter $2\pi$. We show that there exists a unique deformation off the (`Rindler') value $2\pi$ that preserves the original $S$-matrix and which allows one to realize form factors as vector functionals over an algebra of generalized vertex operators.