Discrimination of particle masses in multivariant space-time geometry

Abstract

Multivariance of geometry means that at the point $P_{0}$ there exist many vectors $P_{0}P_{1}$, $\P_{0}P_{2}$,... which are equivalent (equal) to the vector $\Q_{0}Q_{1}$ at the point $Q_{0}$, but they are not equivalent between themselves. The discrimination capacity (zero-variance) of geometry appears, when at the point $P_{0}$ there are no vectors, which are equivalent to the vector $Q_{0}Q_{1}$ at the point $Q_{0}$. It is shown, that in some multivariant space-time geometries some particles of small mass may be discriminated (i.e. either they do not exist, or their evolution is impossible). The possibility of some particle discrimination may appear to be important for explanation of the discrete character of mass spectrum of elementary particles.