Isnt an interacting Dirac field different from the free Dirac field?
Yes, an interacting field could be different from a free field. However, in practice, we do NOT solve the interacting Dirac equations, but rely on the free Dirac equations assuming the locality of interactions, i.e. asymptotic completeness. Therefore, the inconsistencies arise from the basic assumption of QFT and we cannot dismiss my argument as inconsistent as long as QFT is established on the same view. As a matter of fact, this conventional approach of quantum field theory brings the interacting field back to the free field, which is at least practical way to evaluate interactions. This is exactly where the fundamentality of symmetry fails and is limited by our practical calculation.
