  Within the framework of Relativistic Schroedinger Theory (an alternative form
of quantum mechanics for relativistic many-particle systems) it is shown that a
general N-particle system must occur in one of two forms: either as a
``positive'' or as a ``negative'' mixture, in analogy to the fermion-boson
dichotomy of matter in the conventional theory. The pure states represent a
limiting case between the two types of mixtures which themselves are considered
as the RST counterparts of the entangled (fermionic or bosonic) states of the
conventional quantum theory. Both kinds of mixtures are kept separated from
dynamical as well as from topological reasons. The 2-particle configurations
(N=2) are studied in great detail with respect to their geometric and
topological properties which are described in terms of the Euler class of an
appropriate bundle connection. If the underlying space-time manifold (as the
base space of the fibre bundles applied) is parallelisable, the 2-particle
configurations can be thought to be generated geometrically by an appropriate
(2+2) splitting of the local tangent space.
