Multiparticle Partial-Wave Amplitudes and Inelastic Unitarity. I. General Formalism; Racah Coefficients for the Poincaré Group

Abstract

Multiparticle partial-wave amplitudes are defined for arbitrary scattering processes. Unitarity conditions are then imposed at arbitrary energies, resulting in nonlinear relations between the multiparticle partial-wave amplitudes. It is pointed out that the derivation of such unitarity relations is equivalent to finding the Racah coefficients for the Poincaré group. These coefficients, as with other quantities of interest in the paper, are derived for particles with arbitrary spins, masses, and boosting operations. Complications due to identical particles are also discussed.