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Abstract: The space-time geometry is considered to be a physical geometry, i.e. ageometry described completely by the world function. All geometrical conceptsand geometric objects are taken from the proper Euclidean geometry. They areexpressed via the Euclidean world function \sigma E and declared to be conceptsand objects of any physical geometry, provided the Euclidean world function\sigma E is replaced by the world function \sigma of the physical geometry inquestion. The set of physical geometries is more powerful, than the set ofRiemannian geometries, and one needs to choose a true space-time geometry. Ingeneral, the physical geometry is multivariant there are many vectors whichare equivalent to a given vector, but are not equivalent between themselves.The multivariance admits one to describe quantum effects as geometric effectsand to consider existence of elementary particles as a geometrical problem,when the possibility of the physical existence of an elementary geometricobject in the form of a physical body is determined by the space-time geometry.Multivariance admits one to describe discrete and continuous geometries, usingthe same technique. A use of physical geometry admits one to realize thegeometrical approach to the quantum theory and to the theory of elementaryparticles.



Author: Yuri A. Rylov

Source: https://arxiv.org/



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