  It is argued that the baryon excitations group to four-dimensional partial
waves described by means of the three Rarita-Schwinger (RS) fields [(\sigma -1
)/2 ,(\sigma -1)/2]* [(1/2, 0)+(0,1/2)] with \sigma =2,4 and 6, where all
components happen to be occupied. In the O(4) decomposition of the \pi N
scattering amplitudes, the RS spin- and parity clusters appear as poles on the
complex energy plane, socalled H"ohler poles. This phenomenon indicates that
the symmetry of the \pi N scattering amplitude is O(4) and thereby the
space-time version of chiral symmetry, rather than O(3). Accordingly, the
baryon spectrum generating algebra is su(2)_I*su(3)_c*o(1,3)_{ls} rather than
su(6)_{sf} * su(3)_c * o(3)_l. The nucleon and \Delta spectra below \sim 2500
MeV are complete up to only 5 `missing' resonances. The three O(4) poles are
distributed over two distinct Fock spaces of opposite vacuum parities thus
defining the energy scale of the chiral phase transition for baryons. Within
this new symmetry scenario, the covariant description of the RS baryon clusters
is straightforward and their averaged masses are fitted by a Balmer-series like
formula emerging from a simple quark-diquark model in the O(4) basis with
Coulomb potential and a four-dimensional rigid rotator.
