Triviality conditions for the $S$-matrix in the Haag–Ruelle scattering theory

In the framework of Hepp's formulation of Haag–Ruelle scattering theory, some conditions for the asymptotic fields to be identical are found. In particular, it is shown that the theory is trivial if an invertible operator relationship (whose boundedness is not assumed) exists between the states of the interpolating field and the states of one of the asymptotic fields.