Institute for Problems in Mechanics, Russian
Academy of Sciences
101-1 ,Vernadskii Ave., Moscow, 119526, Russia
email: rylov@ipmnet.ru
Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm
or mirror Web site: http://www.ipmnet.ru/~rylov/yrylov.htm
Updated
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.
There is
text of the paper in English (pdf, ps) and in Russian (ps, pdf)