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In the context of constructing interacting quantum field theories in theoperator-algebraic approach, wedge-local fields play an important role. Afterthe work of Lechner to construct factorizing scattering matrix models withscalar S-matrices without bound states, we recently extended this constructionto a class of models with a richer particle spectrum and which are believed tohave bound states. These include the Z(N)-Ising model and the affine-Toda fieldtheories. This construction is done by exhibiting wedge-local fields whicharise as a deformation of Lechner's fields with the so called "bound stateoperator". I will review the main passages of this construction and explain theopen problems.

Wedge-local fields in interacting quantum field theories with bound states