  The subject of this thesis is a novel construction method for interacting
relativistic quantum field theories on two-dimensional Minkowski space. The
input in this construction is not a classical Lagrangian, but rather a
prescribed factorizing S-matrix, i.e. the inverse scattering problem for such
quantum field theories is studied.
  For a large class of factorizing S-matrices, certain associated quantum
fields, which are localized in wedge-shaped regions of Minkowski space, are
constructed explicitely. With the help of these fields, the local observable
content of the corresponding model is defined and analyzed by employing methods
from the algebraic framework of quantum field theory.
  The abstract problem in this analysis amounts to the question under which
conditions an algebra of wedge-localized observables can be used to generate a
net of local observable algebras with the right physical properties. The answer
given here uses the so-called modular nuclearity condition, which is shown to
imply the existence of local observables and the Reeh-Schlieder property.
  In the analysis of the concrete models, this condition is proven for a large
family of S-matrices, including the scattering operators of the Sinh-Gordon
model and the scaling Ising model as special examples. The so constructed
models are then investigated with respect to their scattering properties. They
are shown to solve the inverse scattering problem for the considered
S-matrices, and a proof of asymptotic completeness is given.
