  A finite-dimensional pseudo-unitary framework is set up for describing the
dynamics of free elementary particles in a purely relativistic quantum
mechanical way. States of any individual particles or antiparticles are defined
as suitably normalized vectors belonging to the two-complex-dimensional spaces
that occur in local orthogonal decompositions of isomorphic copies of Cartan's
space. The corresponding dynamical variables thus show up as bounded
pseudo-Hermitian operator restrictions that possess real discrete spectra. Any
measurement processes have to be performed locally in orthocronous proper
Lorentz frames, but typical observational correlations are expressed in terms
of symbolic configurations which come from the covariant action on spaces of
state vectors of the Poincar\'e subgroup of an adequate realization of SU(2,2).
The overall approach turns out to supply a supposedly natural description of
the dynamics of free twofold systems in flat spacetime. One of the main
outlooks devised here brings forward the possibility of carrying out
methodically the construction of a background to a new relativistic theory of
quantum information.
