Hi all, I have a question about the ground state of an interacting quantum field theory. The state space in non-interacting QFT is a space where each field mode (with specified momentum p) has some occupation number n. These modes are interpreted as n particles with momentum p. The vacuum is the state where all occupation numbers are zero. In my understanding, if we add interactions, the ground state of the Hamiltonian is no longer the non-interacting vacuum. This means that the interacting vacuum has n-particle states mixed in (n>0). Shouldn't we then be able to measure these particles, which would show up even without any particle coming in? Or can we perform something like a Bogoliubov transformation, such that the real, measurable particles are actually the quasi-particles of the theory? But does the energy-momentum relation E2 = m2 + p2 then still hold in this case?