A General Manifestly Covariant Construction of Partial-Wave Amplitudes in the Rarita-Schwinger Formalism

Abstract

We propose a new set of functions, named Relative Spin Wave Functions (RSWFs), defined via covariant pure boosts to a common rest frame. RSWFs separate spin transport from orbital-spin coupling while preserving the conventional partial-wave angular structure in a manifestly covariant form. Within the Rarita-Schwinger formalism, this approach generates explicit, covariant on-shell partial-wave amplitudes for two-body decays of massive particles of arbitrary spin, with definite orbital angular momentum and total final-state spin. This general framework provides a foundational Lorentz basis for hadronic reaction studies and $LS$-organized operators in theoretical investigations, such as Lattice QCD and QCD sum rules.