  The problem of quantizing a class of two-dimensional integrable quantum field
theories is considered. The classical equations of the theory are the complex
$sl(n)$ affine Toda equations which admit soliton solutions with real masses.
The classical scattering theory of the solitons is developed using Hirota's
solution techniques. A form for the soliton $S$-matrix is proposed based on the
constraints of $S$-matrix theory, integrability and the requirement that the
semi-classical limit is consistent with the semi-classical WKB quantization of
the classical scattering theory. The proposed $S$-matrix is an intertwiner of
the quantum group associated to $sl(n)$, where the deformation parameter is a
function of the coupling constant. It is further shown that the $S$-matrix
describes a non-unitary theory, which reflects the fact that the classical
Hamiltonian is complex. The spectrum of the theory is found to consist of the
basic solitons, scalar states (or breathers) and excited (or `breathing')
solitons. It is also noted that the construction of the $S$-matrix is valid for
any representation of the Hecke algebra, allowing the definition of restricted
$S$-matrices, in which case the theory is unitary.
