Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multivariance as a crucial property of microcosm   The conventional method of a generalized geometry construction, based on
deduction of all propositions of the geometry from axioms, appears to be
imperfect in the sense, that multivariant geometries cannot be constructed by
means of this method. Multivariant geometry is such a geometry, where at the
point P there are many vectors PP', PP'',... which are equivalent to the vector
QQ' at the point Q, but they are not equivalent between themselves. In the
conventional (Euclidean) method the equivalence relation is transitive, whereas
in a multivariant geometry the equivalence relation is intransitive, in
general. It is a reason, why the multivariant geometries cannot be deduced from
a system of axioms. The space-time geometry in microcosm is multivariant.
Multivariant geometry is a grainy geometry, i.e. the geometry, which is partly
continuous and partly discrete. Multivariance is a mathematical method of the
graininess description. The graininess (and multivariance) of the space-time
geometry generates a multivariant (quantum) motion of particles in microcosm.
Besides, the grainy space-time generates some discrimination mechanism,
responsible for discrete parameters (mass, charge, spin) of elementary
particles. Dynamics of particles appears to be determined completely by
properties of the grainy space-time geometry. The quantum principles appear to
be needless.

16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc