  The subject of this thesis is the rigorous construction of QFT models with
nontrivial interaction. Two different approaches in the framework of AQFT are
discussed. On the one hand, an inverse scattering problem is considered. A
given factorizing S-matrix is thereby taken as the starting point of the
construction. The particle spectrum taken into account involves an arbitrary
number of massive particle species, transforming under a global gauge group.
Starting from known wedge-local auxiliary fields, the transition to local
theories is shown. To his end, we make use of the modular nuclearity condition
and investigate certain maps from the wedge algebras, generated by the
auxiliary fields, to the considered Hilbert space. Under a very plausible
conjecture it is shown that these maps are nuclear, which implies the
nontriviality of algebras associated with bounded regions in the sense that the
Reeh-Schlieder property holds. A large class of integrable models with
factorizing S-matrices in 1+1 dimensions can be constructed in this way. Among
them are the O(N)-invariant nonlinear sigma-models. Deformation techniques, on
the other hand, constitute a method of construction which may be applied in
arbitrary spacetime dimensions. This approach starts from a known quantum field
theoretic model which is subjected to a certain modification. Here, concretely,
the model of a scalar massive Fermion was deformed. The emerging models are
based on wedge-local fields, allowing for the computation of the two-particle
S-matrix. The resulting scattering matrix depends on the deformation and
differs from the one of the initial model. By restricting to 1+1 dimensions,
the deformation method yields a large class of integrable models with
factorizing S-matrices, including the Sinh-Gordon model.
