Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Euclidean geometry deformations and capacities of their application
  to microcosm space-time geometry   Usually a Riemannian geometry is considered to be the most general geometry,
which could be used as a space-time geometry. In fact, any Riemannian geometry
is a result of some deformation of the Euclidean geometry. Class of these
Riemannian deformations is restricted by a series of unfounded constraints.
Eliminating these constraints, one obtains a more wide class of possible
space-time geometries (T-geometries). Any T-geometry is described by the world
function completely. T-geometry is a powerful tool for the microcosm
investigations due to three its characteristic features: (1) Any geometric
object is defined in all T-geometries at once, because its definition does not
depend on the form of world function. (2) Language of T-geometry does not use
external means of description such as coordinates and curves; it uses only
primordially geometrical concepts: subspaces and world function. (3) There is
no necessity to construct the complete axiomatics of T-geometry, because it
uses deformed Euclidean axiomatics, and one can investigate only interesting
geometric relations. Capacities of T-geometries for the microcosm description
are discussed in the paper. When the world function is symmetric and T-geometry
is nondegenerate, the particle mass is geometrized, and nonrelativistic quantum
effects are described as geometric ones, i.e. without a reference to principles
of quantum theory. When world function is asymmetric, the future is not
geometrically equivalent to the past, and capacities of T-geometry increase
multiply. Antisymmetric component of the world function generates some metric
fields, whose influence on geometry properties is especially strong in the
microcosm.

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The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: econ
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math