is essentially different. For instance, in both cases the quantum evolution from point to point (in space-time) is described via a kind of (parallel or generic linear) transport (along paths) in a suitable Hilbert fibre bundle. But the notion of a ‘Hilbert bundle’ in our and Prugovečki’s approach is different nevertheless that in both case the typical (standard) fibre is practically the same (when one and the same theory is concerned). Besides, we need not even to introduce the Poincaré (principal) fibre bundle over the space-time or the phase space which play an important rôle in Prugovečki’s theory. Also we have to notice that the used in it concepts of quantum and parallel transport are special cases of the notion of a ‘linear transport along paths’ introduced in [@bp-normalF-LTP; @bp-LTP-general]. The application of the last concept, which is accepted in the present investigation, has a lot of advantages, significantly simplifies some proofs and makes certain results ‘evident’ or trivial (e.g. the last part of section 2 and the whole section 4 of [@Drechsler/Tuckey-96]). At last, at the present level (nonrelativistic quantum mechanics) our bundle formulation of the quantum theory is insensitive with respect to the space-time curvature. A detail comparison 