Representations of the CCR in the (φ4)3 model: Independence of space cutoff

The algebra of observables for the renormalized ⁴ interaction in 3-dimensional space-time is constructed. It is shown that the von Neumann algebras associated with observables in a bounded regionB are independent of the space cutoff which is used in the construction of a Hamiltonian for this interaction. This result is shown to be useful in the construction of a translation invariant ⁴ theory in three dimensions. It also gives a physical criterion for the equivalence of non-Fock representations of the canonical commutation relations.