Poincaré invariant potential model

A general Poincaré invariant potential model for two-particle systems is constructed within the framework of light front dynamics. The model specifies all ten of the generators that are necessary to satisfy the Poincaré algebra. Formal expressions for the scattering states are constructed, and it is verified explicitly that they transform correctly under Lorentz transformations. The S-matrix elements are shown to be Lorentz invariant functions of the initial and final four-momenta of a scattering process. The T matrix is found to satisfy an integral equation that has the mathematical simplicity of its nonrelativistic counterpart.