Interacting Fock space versus full Fock module

We present several examples where moments of creators and annihilators on an interacting Fock space may be realized as moments of creators and annihilators on a full Fock module.Motivated by this experience we answer the question, whether such a possibility exists for arbitrary interacting Fock spaces, in the affirmative sense.We treat the problem in full algebraic generality.As a by-product, we find a new notion of positivity for * -algebras which allows to construct tensor products of Hilbert modules over * -algebras.Finally, we consider a subcategory of interacting Fock spaces which are embeddable into a usual full Fock space.We see that a creator a * (f ) on the interacting Fock space is represented by an operator κℓ * (f ), where ℓ * (f ) is a usual creator on the full Fock space and κ is an operator which does not change the number of particles.In the picture of Hilbert modules the one-particle sector is replaced by a two-sided module over an algebra which contains κ.Therefore, κ may be absorbed into the creator, so that we are concerned with a usual creator.However, this creator does not act on a Fock space, but rather on a Fock module.