Daughters, Conspiracies, and Lorentz Symmetry

The Freedman-Wang prescription for the introduction of daughter trajectories is generalized to the arbitrary-spin case. The daughter problem is then investigated, within the framework of Lorentz symmetry, and a Regge-type representation for the asymptotic $S$ matrix is obtained which satisfies all kinematic constraints. The representation is found to be equivalent to a Lorentz pole expansion in the case of elastic scattering. Some properties of the representations of the covering groups of the homogeneous Lorentz group and rotation group are also investigated.