  Geometrical model for material Dirac wave field and for Maxwell
electromagnetic field is suggested where above fields are considered as
propagating regions of the space itself with distorted euclidean geometry. It
is shown that equations for these fields can be considered as relations
describing the space topological defects. These defects, being closed
topological manifolds, are embedded in the outer five-dimensional space, and
observable objects appear to be intersections of above defects with the
physical space. This interpretation explains irrational properties of quantum
objects such as wave-corpuscular duality, stochastic behavior, instantaneous
nonlocal correlation in EPR-paradox, the light velocity invariance and so on.
Wave-corpuscular properties arise as a result of the defect periodical movement
in the outer space relative to its intersection with the physical space, and
just this periodical movement attributes phase to the propagating object.
Appearance of probabilities within the formalism is a consequence of
uncertainty of the closed topological manifold shape, and ensemble of all
possible shapes for the same object can be considered as an ensemble of hidden
variables that leads to probabilistic description. Embedded in the outer space
topological defects provide channels for nonlocal correlations between their
intersections-- noninteracting particles in EPR-experiments, and this means
that the proposed approach can be considered as a nonlocal model with hidden
variables.
