Elastic S-Matrices in (1 + 1) Dimensions and Toda Field Theories

Abstract

Particular deformations of 2-D conformal field theory lead to integrable massive quantum field theories. These can be characterized by the relativistic scattering data. We propose a general scheme for classifying the elastic nondegenerate S-matrix in (1 + 1) dimensions starting from the possible boot-strap processes and the spins of the conserved currents. Their identification with the S-matrix coming from the Toda field theory is analyzed. We discuss both cases of Toda field theory constructed with the simply-laced Dynkin diagrams and the nonsimply-laced ones. We present the results of the perturbative analysis and their geometrical interpretations.

FORM FACTORS AND CORRELATION FUNCTIONS OF THE STRESS-ENERGY TENSOR IN MASSIVE DEFORMATION OF THE MINIMAL MODELS (En)1⊗ (En)1/(En)2

“…The two-particle elastic S-matrices considered in this paper present quite a rich pattern of poles in the complex θ plane. According to the analysis carried out by several groups [31,38,39,40], the simple and higher odd-order poles are associated to the presence of bound states appearing as intermediate virtual particles in the scattering processes. Viceversa, all even-order poles are simply due to intermediate multi-scattering processes with no one-particle singularities.…”

Affine Toda solitons and vertex operators

“…Thus 13) where the right hand side denotes the highest weight state of V ( j p j Λ j >. Thus, in principle, all irreducible representations ofĝ can be found by the decomposition of products of its fundamental representations.…”

Affine Toda field theory in the presence of reflecting boundaries

“…As the result of a sequence of investigations [15,16,17,18,19,20,21,22] the S-matrix of affine Toda field theories related to simply laced Lie algebras has been found to take on a very compact form [21,22] † . Adopting the notation of [24,22] it reads…”