We consider the reaction dynamics of bosons with negative parity and spin 0
or 1 and fermions with positive parity and spin 21​ or
23​. Such systems are of central importance for the computation of
the baryon resonance spectrum in the hadrogenesis conjecture. Based on a chiral
Lagrangian the coupled-channel partial-wave scattering amplitudes have to be
computed. We study the generic properties of such amplitudes. A decomposition
of the various scattering amplitudes into suitable sets of invariant functions
expected to satisfy Mandelstam's dispersion-integral representation is
presented. Sets are identified that are free from kinematical constraints and
that can be computed efficiently in terms of a novel projection algebra. From
such a representation one can deduce the analytic structure of the partial-wave
amplitudes. The helicity and the conventional angular-momentum partial-wave
amplitudes are kinematically constrained at the Kibble conditions. Therefore an
application of a dispersion-integral representation is prohibitively
cumbersome. We derive covariant partial-wave amplitudes that are free from
kinematical constraints at the Kibble conditions. They correspond to specific
polynomials in the 4-momenta and Dirac matrices that solve the various
Bethe-Salpeter equations in the presence of short-range interactions
analytically.Comment: 18 page