  We present a solution method for the inverse scattering problem for
integrable two-dimensional relativistic quantum field theories, specified in
terms of a given massive single particle spectrum and a factorizing S-matrix.
An arbitrary number of massive particles transforming under an arbitrary
compact global gauge group is allowed, thereby generalizing previous
constructions of scalar theories. The two-particle S-matrix $S$ is assumed to
be an analytic solution of the Yang-Baxter equation with standard properties,
including unitarity, TCP invariance, and crossing symmetry. Using methods from
operator algebras and complex analysis, we identify sufficient criteria on $S$
that imply the solution of the inverse scattering problem. These conditions are
shown to be satisfied in particular by so-called diagonal S-matrices, but
presumably also in other cases such as the $O(N)$-invariant nonlinear
$\sigma$-models.
