  We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the
relativistic N-body problem in a separable two-body basis in which the
particles interact pair-wise through scalar and vector interactions. The
resultant N-body Hamiltonian is relativistically covariant. It can be easily
separated in terms of the center-of-mass and the relative motion of any
two-body subsystem. It can also be separated into an unperturbed Hamiltonian
with a residual interaction. In a system of two-body composite particles, the
solutions of the unperturbed Hamiltonian are relativistic two-body internal
states, each of which can be obtained by solving a relativistic
Schr\"odinger-like equation. The resultant two-body wave functions can be used
as basis states to evaluate reaction matrix elements in the general N-body
problem. We prove a relativistic version of the post-prior equivalence which
guarantees a unique evaluation of the reaction matrix element, independent of
the ways of separating the Hamiltonian into unperturbed and residual
interactions. Since an arbitrary reaction matrix element involves composite
particles in motion, we show explicitly how such matrix elements can be
evaluated in terms of the wave functions of the composite particles and the
relevant Lorentz transformations.
