Nontrivial scattering amplitudes for some local relativistic quantum field models with indefinite metric

We study models of self-interacting massless spin 1 local relativistic quantum fields with indefinite metric in space-time dimension four. We prove that these models for large times converge to free fields and we derive explicit formulae for their (nontrivial, gauge invariant) scattering amplitudes. These scattering amplitudes have properties expected for S-matrix theory.