Vertex operators, semiclassical limit for soliton S-matrices and the number of bound states in affine Toda field theories

Abstract

Soliton time delays and the semiclassical limit for soliton S-matrices are calculated for non-simply laced affine Toda field theories. The phase shift is written as a sum over bilinears on the soliton conserved charges. The results apply to any two solitons of any affine Toda field theory. As a by-product, a general expression for the number of bound states and the values of the coupling in which the soliton S-matrix can be diagonal are obtained. In order to arrive at these results, a vertex operator is constructed, in the principal gradation, for non-simply laced affine Lie algebras, extending the previous constructions for simply laced and twisted affine Lie algebras.