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Do you mean to say that although the LSZ reduction formula cannot handle bound states, massless particles and topological solitons, it can be generalized to cover bound states, by use of composite fields which are often nonlocal. Furthermore, the method, or variants thereof, have turned out to be also fruitful in other fields of theoretical physics. For example in statistical physics they can be used to get a particularly general formulation of the fluctuation-dissipation theorem.
Or did I miss the point?