Multiparticle scattering amplitudes with spin - independent Poincaré - transformation properties

Abstract

For systems of massive particles with arbitrary spins, we define new classes of invariant scattering amplitudes. No auxiliary spin group is used, and the amplitudes are parametrized by the eigenvalues of Poincar\'e-invariant operator-valued functions of single-particle observables alone. We construct frame-independent partial-wave decomposition formulas for these amplitudes, and give a detailed derivation of the constraint equations which they must satisfy if scattering processes are to be invariant under space-time translations and proper homogeneous Lorentz transformations. In appendixes we collect together the definitions and transformation properties of many multiparticle states and scattering amplitudes, and derive some useful kinematical transformation formulas.