  The space-time geometry is considered to be a physical geometry, i.e. a
geometry described completely by the world function. All geometrical concepts
and geometric objects are taken from the proper Euclidean geometry. They are
expressed via the Euclidean world function \sigma_E and declared to be concepts
and objects of any physical geometry, provided the Euclidean world function
\sigma_E is replaced by the world function \sigma of the physical geometry in
question. The set of physical geometries is more powerful, than the set of
Riemannian geometries, and one needs to choose a true space-time geometry. In
general, the physical geometry is multivariant (there are many vectors which
are equivalent to a given vector, but are not equivalent between themselves).
The multivariance admits one to describe quantum effects as geometric effects
and to consider existence of elementary particles as a geometrical problem,
when the possibility of the physical existence of an elementary geometric
object in the form of a physical body is determined by the space-time geometry.
Multivariance admits one to describe discrete and continuous geometries, using
the same technique. A use of physical geometry admits one to realize the
geometrical approach to the quantum theory and to the theory of elementary
particles.
