For an arbitrary number of particles an explicit construction is given for direct interactions satisfying cluster separability (macrolocality). The Hamiltonian is in many ways similar to the nonrelativistic many-body Hamiltonian. Under conditions of physical interest the strength of the $N$-body interaction decreases rapidly with increasing $N$.

• Received 25 May 1982

DOI:https://doi.org/10.1103/PhysRevD.26.1348