  Starting from a unitary, Lorentz invariant two-particle scattering amplitude
, we show how to use an identification and replacement process to construct a
unique, unitary particle-antiparticle amplitude. This process differs from
conventional on-shell Mandelstam s,t,u crossing in that the input and
constructed amplitudes can be off-diagonal and off-energy shell. Further,
amplitudes are constructed using the invariant parameters which are appropriate
to use as driving terms in the multi-particle, multichannel non-perturbative,
cluster decomposable, relativistic scattering equations of the Faddeev-type
integral equations recently presented by Alfred, Kwizera, Lindesay and Noyes.
It is therefore anticipated that when so employed, the resulting multi-channel
solutions will also be unitary. The process preserves the usual
particle-antiparticle symmetries. To illustrate this process, we construct a
J=0 scattering length model chosen for simplicity. We also exhibit a class of
physical models which contain a finite quantum mass parameter and are Lorentz
invariant. These are constructed to reduce in the appropriate limits, and with
the proper choice of value and sign of the interaction parameter, to the
asymptotic solution of the non-relativistic Coulomb problem, including the
forward scattering singularity, the essential singularity in the phase, and the
Bohr bound-state spectrum.
