In quantum field theory with a mass gap, why do states in the asymptotic future/past turn out to have a Fock space structure? For a free quantum field theory, that's trivial, but why is that the case for interacting theories? In fact, the more one thinks about it, the less clear it becomes. If the quanta of the "fundamental" field is unstable, it doesn't show up in the asymptotic Fock space. If the quanta is confined, it also doesn't show up. If there is a stable bound state, it does show up. If there is a stable solitonic particle, it also shows up.
I am very aware of the LSZ formalism, but that presupposes the existence of an asymptotic Fock space structure as a starting point. Besides, it doesn't handle stable solitons.
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