Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Space of Quantum Theory Representations of Natural Numbers, Integers,
  and Rational Numbers   This paper extends earlier work on quantum theory representations of natural
numbers N, integers I, and rational numbers Ra to describe a space of these
representations and transformations on the space. The space is parameterized by
4-tuple points in a parameter set. Each point, (k,m,h,g), labels a specific
representation of X = N, I, Ra as a Fock space F^{X}_{k,m,h} of states of
finite length strings of qukits q and a string state basis B^{X}_{k,m,h,g}. The
pair (m,h) locates the q string in a square integer lattice I \times I, k is
the q base, and the function g fixes the gauge or basis states for each q. Maps
on the parameter set induce transformations on on the representation space.
There are two shifts, a base change operator W_{k',k}, and a basis or gauge
transformation function U_{k}. The invariance of the axioms and theorems for N,
I, and Ra under any transformation is discussed along with the dependence of
the properties of W_{k',k} on the prime factors of k' and k. This suggests that
one consider prime number q's, q_{2}, q_{3}, q_{5}, etc. as elementary and the
base k q's as composites of the prime number q's.

32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys