  We consider a Haag-Kastler net in a positive energy representation, admitting
massive Wigner particles and asymptotic fields of massless bosons. We show that
states of the massive particles are always vacua of the massless asymptotic
fields. Our argument is based on the Mean Ergodic Theorem in a certain extended
Hilbert space. As an application of this result we construct the outgoing
isometric wave operator for Compton scattering in QED in a class of
representations recently proposed by Buchholz and Roberts. In the course of
this analysis we use our new technique to further simplify scattering theory of
massless bosons in the vacuum sector. A general discussion of the status of the
infrared problem in the setting of Buchholz and Roberts is given.
