  Relativistic quantum dynamics requires a unitary representation of the
Poincare group on the Hilbert space of states. The dynamics of many-body
systems must satisfy cluster separability requirements. In this paper we
formulate an abstract framework of four dimensional Euclidean Green functions
that can be used to construct relativistic quantum dynamics of N-particle
systems consistent with these requirements. This approach should be useful in
bridging the gap between few-body dynamics based on phenomenological mass
operators and on quantum field theory.
