Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Linear Spaces, Plane Geometries, Hilbert spaces and Finite Phase
  Space   Finite plane geometry is associated with finite dimensional Hilbert space.
The association allows mapping of q-number Hilbert space observables to the
c-number formalism of quantum mechanics in phase space. The mapped entities
reflect geometrically based line-point interrelation. Particularly simple
formulas are involved when use is made of mutually unbiased bases (MUB)
representations for the Hilbert space entries. The geometry specifies a
point-line interrelation. Thus underpinning d-dimensional Hilbert space
operators (resp. states) with geometrical points leads to operators termed
"line operators" underpinned by the geometrical lines. These "line operators",
$\hat{L}_j;$ (j designates the line) form a complete orthogonal basis for
Hilbert space operators. The representation of Hilbert space operators in terms
of these operators form the phase space representation of the d-dimensional
Hilbert space. The "line operators" (resp. "line states") are studied in
detail. The paper aims at self sufficiency and to this end all relevant notions
are explained herewith.

12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an