Functional Equations of Form Factors for Diagonal Scattering Theories

Abstract

Form factor bootstrap approach is applied for diagonal scattering theories. We consider the ADE theories and determine the functional equations satisfied by the minimal two-particle form factors. We also determine the parameterization of the singularities in two particle form factors. For $A^{(1)}_{2}$ Affine Toda field theory which is the simplest non-self conjugate theory, form factors are derived up to four-body and identification of operator is done. Generalizing this identification to the $A^{(1)}_N$ Affine Toda cases, we fix the two particle form factors. We also determine the additional pole structure of form factors which comes from the double pole of the $S$-matrices of the $A^{(1)}_N$ theory. For $A_N$ theories, existence of the conserved ${\bf Z}_{N+1}$ charge leads to the division of the set of form factors into $N+1$ decoupled sectors.