Relativistic potential scattering and phase shift analysis

It is shown that two-body relativistic scattering cross sections can be represented in terms of phase shift analysis in essentially the same form as that of nonrelativistic scattering theory. The representation is covariant; the variable that corresponds to the orbital quantum number (and approaches it in the nonrelativistic limit) is relativistically invariant. The Levinson theorem is valid, and provides a link between the bound states, which have support in an O(2,1) invariant subspace of the full spacelike region of relative coordinates, and the scattering states that contain resonant behavior. These scattering states consequently have support in the same restricted subspace, and the same procedure may be used for the separation of variables. As an example, the resonances of an O(3,1) invariant "square well" are discussed.