  Effective field theory requires all observables to be independent of the
representation used for the quantum field operators. It means that off-shell
properties of the interactions should not lead to any observable effects. We
analyse this issue in the context of many-body approaches to nuclear matter,
where it should be possible to shift the contributions of lowest order in
purely off-shell two-body interactions into three-body forces. We show that
none of the commonly used truncations of the two-body scattering amplitude such
as the ladder, Brueckner-Hartree-Fock or parquet approximations respect this
requirement.
