the formalism required for its analysis. Besides, the paper  contains an excellent motivation for applying the apparatus of fibre bundle theory to quantum mechanics.

An attempt to formulate quantum mechanics in terms of a fibre bundle over the phase space is made in [@Reuter]. Regardless of some common features, this paper is quite different from the present investigation. We shall comment on it later. In particular, in [@Reuter] the gauge structure of the arising theory is governed by a non[-]{}dynamical connection related to the symplectic structure of the system’s phase space, while in this work analogous structure (linear transport along paths) is uniquely connected with system’s Hamiltonian, playing here the rôle of a gauge field itself.

The present work is a direct continuation of the considerations in [@bp-BQM-preliminary] which paper, in fact, may be regarded as its preliminary version. Here we suggests a purely fibre bundle formulation of the nonrelativistic quantum mechanics. This new form of the theory is entirely equivalent to the usual one, which is a consequence or our step by step equivalent reformulation of the quantum theory. The bundle description is obtained on the base of the developed by the author theory of transports along paths in 