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Hello! I attached a SS of the part of my book that I am confused about. So there they write the initial and final states in term of creation and annihilation operators, acting on the (not free) vacuum i.e. ##|\Omega>##. So first thing, the value of the creation (annihilation) operators at ##\pm\infty## are not the same, right? They evolve in time with the full interaction hamiltonian, so differently from the free case they have different values in time. Second thing, the last line, if I understand it well, and plugging in the values for the initial and final states, would be $$<f|S|i>=<f|i>$$ Is this right? It looks like the S matrix does nothing here. What am I doing wrong? Thank you!