I was going through Rudolf Haag's memoir http://link.springer.com/article/10.1140%2Fepjh%2Fe2010-10032-4 and came across these lines:
'..in quantum ﬁeld theory (or for any system of interacting particles) the equivalence class of the representation of the Poincare group is independent of the interaction. It depends only on the types of stable particles described and is explicitly known. This result was at ﬁrst sight rather counterintuitive since the Hamiltonian –which is one of the generators of the group – contains a term characterizing the interaction. But this is due to the choice of variables in terms of which the Hamiltonian is written. It is not a purely group theoretical feature.'
It will be helpful for me if anyone can explain what exactly he is talking about or can give any references to where this result is proved/ discussed.Haag refers to his notes from 1954 - 'Lecture Notes Copenhagen CERNT/RH1 53/54'. But this does not seem available online.
To me the first statement seems to be saying that representations of Poincare group are labelled by mass and spin, so if I know the particle content of an interacting theory including bound states, I basically know the representation. Is that correct? It is the second part which I can't make much sense of . why is there an apparent contradiction? Different interaction Hamiltonians do contain the information about what bound states can exist and thereby determine the representation, no? What is the role of 'the choice of variables in terms of which the Hamiltonian is written'?