  There were many attempts to geometrize electromagnetic field and find out new
interpretation for quantum mechanics formalism. The distinctive feature of this
work is that it combines geometrization of electromagnetic field and
geometrization of material field within the unique topological idea. According
to the suggested topological interpretation, the Dirac equations for a free
particle and for a hydrogen atom prove to be the group--theoretical relations
that account for the symmetry properties of localized microscopic deviations of
the space--time geometry from the pseudoeuclidean one (closed topological
4-manifolds). These equations happen to be written in universal covering spaces
of the above manifolds. It is shown that "long derivatives" in Dirac equation
for a hydrogen atom can be considered as covariant derivatives of spinors in
the Weyl noneuclidean 4-space and that electromagnetic potentials can be
considered as connectivities in this space. The gauge invariance of
electromagnetic field proves to be a natural consequence of the basic
principles of the proposed geometrical interpretation. Within the suggested
concept, atoms have no inside any point-like particles (electrons) and this can
give an opportunity to overcome the difficulties of atomic physics connected
with the many-body problem.
