Relativistic N-body problem in a separable two-body basis - art. no. 044907

We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of t he relativistic N-body problem in a separable two-body basis in which the p articles interact pairwise through scalar and vector interactions. The resu ltant N-body Hamiltonian is relativistically covariant. It can be easily se parated in terms of the center of mass and the relative motion of any two-b ody subsystem. It can also be separated into an unperturbed Hamiltonian wit h 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 Schrodinge r-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 guaran tees a unique evaluation of the reaction matrix element, independent of the ways of separating the Hamiltonian into unperturbed and residual interacti ons. Since an arbitrary reaction matrix element involves composite particle s in motion, we show explicitly how such matrix elements can be evaluated i n terms of the wave functions of the composite particles and the relevant L orentz transformations.