In relativistic Schrodinger theory, additional conservation laws arise
of topological origin. These are due to the existence of topological
currents which are built up by the exclusive use of operators, whereas
the matter currents are composed of the densities. The general concep
ts and results are exemplified by considering a specific (Dirac) spino
r held over the Robertson-Walker universes. The invariant, associated
to the topological current, can be explicitly determined for SU(2)-bun
dles.