Structure of Relativistic Two-Particle Scattering Theories

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Abstract
The paper deals with two-particle scattering theories possessing both Lorentz invariance and a complete space-time description (i.e., a set of generators of the inhomogeneous Lorentz group describing interactions). We describe how to construct such theories starting, not from some assumed Hamiltonian, but from another operator, namely, the Cayley transform of the wave operator. This has the advantage that the scattering matrix is predetermined (i.e., known before solving any dynamical equations). The simplest possible model within the context of this approach is considered and solved exactly. This class of models contains the class considered by Jordan, Macfarlane, and Sudarshan.