  The relativistic two-particle quantum mixtures are studied from the
topological point of view. The mixture field variables can be transformed in
such a way that a kinematical decoupling of both particle degrees of freedom
takes place with a residual coupling of purely algebraic nature ("exchange
coupling"). Both separated sets of particle variables induce a certain map of
space-time onto the corresponding "exchange groups", i.e. SU(2) and SU(1,1), so
that for the compact case (SU(2)) there arises a pair of winding numbers,
either odd or even, which are a topological characteristic of the two-particle
Hamiltonian.
