When talking about QFT, I have in mind mainly QED, which is a very successful example of a physical theory. QED is both relativistic and interacting. It can be formulated as a theory with a fixed Fock space structure.But there are many examples of QFTs (e.g., conformal field theories in 1+1 dimension) whose Hilbert space does not have such a Fock space structure. The latter is specific to the nonrelativistic case and to free relativistic theories.

Eugene.