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 $A_2^{(1)}$ 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 $A_N^{(1)}$ 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 $A_N^{(1)}$ theory. For $A_N$ theories, existence of the conserved ${\mathbf{Z}}_{N+1}$ charge leads to the division of the set of form factors into $N+1$ decoupled sectors.

20 pages, LaTeX, 1 figure in a uuencoded-gzipcompressed ps file

References in corpus (9)

• On the Operator Content of the Sinh-Gordon Model
• Form Factors for Integrable Lagrangian Field Theories, the Sinh-Gordon Model
• The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at $T=T_c$
• Root Systems and Purely Elastic S-Matrices II
• The space of local operators in perturbed conformal field theories,
• Form Factors of the Elementary Field in the Bullough-Dodd Model
• Two-point Correlation Function in Integrable QFT with Anti-Crossing Symmetry
• Form-Factor Bootstrap and the Operator Content of Perturbed Minimal Models
• A method to determine the operator content of perturbed conformal field theories

Cited by in corpus (13)

• Exact Form Factors in Integrable Quantum Field Theories: the Sine-Gordon Model
• Free Field Construction for the ABF Models in Regime II
• Exact form factors for the scaling Z{N}-Ising and the affine A{N-1}-Toda quantum field theories
• The determinant representation for quantum correlation functions of the sinh-Gordon model
• Higher particle form factors of branch point twist fields in integrable quantum field theories
• Form factors of boundary fields for A(2)-affine Toda field theory
• The Determinant Representation for a Correlation Function in Scaling Lee-Yang Model
• The complex sinh-Gordon model: form factors of descendant operators and current-current perturbations
• The Form Factors in the Sinh-Gordon Model
• Exact two-particle Matrix Elements in S-Matrix Preserving Deformation of Integrable QFTs
• Form Factors in $D_n^{(1)}$ Affine Toda Field Theories
• Two-point correlation functions in perturbed minimal models
• Wave function renormalization constants and one-particle form factors in $D_l^{(1)}$ Toda field theories