Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spinors in $\mathbb{K}$-Hilbert Spaces   We consider a structure of the $\mathbb{K}$-Hilbert space, where
$\mathbb{K}\simeq\mathbb{R}$ is a field of real numbers,
$\mathbb{K}\simeq\mathbb{C}$ is a field of complex numbers,
$\mathbb{K}\simeq\mathbb{H}$ is a quaternion algebra, within the framework of
division rings of Clifford algebras. The $\mathbb{K}$-Hilbert space is
generated by the Gelfand-Naimark-Segal construction, while the generating
$C^\ast$-algebra consists of the energy operator $H$ and the generators of the
group $SU(2,2)$ attached to $H$. The cyclic vectors of the $\mathbb{K}$-Hilbert
space corresponding to the tensor products of quaternionic algebras define the
pure separable states of the operator algebra. Depending on the division ring
$\mathbb{K}$, all states of the operator algebra are divided into three
classes: 1) charged states with $\mathbb{K}\simeq\mathbb{C}$; 2) neutral states
with $\mathbb{K}\simeq\mathbb{H}$; 3) truly neutral states with
$\mathbb{K}\simeq\mathbb{R}$. For pure separable states that define the
fermionic and bosonic states of the energy spectrum, the fusion, doubling
(complexification) and annihilation operations are determined.

32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph