bundles that has no analogue in the general theory: a transport along paths is Hermitian if and only if it is unitary. This assertion is implicitly contained in [@bp-BQM-preliminary sect. 3] (see the paragraph after equation (3.6) in it).

In [@bp-normalF-LTP sect. 3] are introduced the so-called *normal* frames for a linear transport along paths as a (local) field of bases in which (on some set) the matrix of the transport is unit. Further in this series [@bp-BQM-pictures+integrals] we shall see that the normal frames realize the Heisenberg picture of motion in the Hilbert bundle formulation of quantum mechanics.

The Hilbert bundle description\
of quantum mechanics {#new-I}
===============================

As we shall see in this investigation, the Hilbert bundles provide a natural mathematical framework for a geometrical formulation of quantum mechanics. In it all quantum[-]{}mechanical quantities, such as Hamiltonians, observables, wavefunctions, etc., have an adequate description. For instance, the evolution of a systems is described as an appropriate (parallel or, more precisely, linear) transport of system’s state sections along some path. We have to emphasize on the fact that the new bundle formulation of quantum mechanics and the conventional one are completely equivalent at the present stage.

Before going on, we 