Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quaternions, Spinors and the Hopf Fibration: Hidden Variables in
  Classical Mechanics   Rotations in 3 dimensional space are equally described by the SU(2) and SO(3)
groups. These isomorphic groups generate the same 3D kinematics using different
algebraic structures of the unit quaternion. The Hopf Fibration is a projection
between the hypersphere $\mathbb{S}^3$ of the quaternion in 4D space, and the
unit sphere $\mathbb{S}^2$ in 3D space. Great circles in $\mathbb{S}^3$ are
mapped to points in $\mathbb{S}^2$ via the 6 Hopf maps, and are illustrated via
the stereographic projection. The higher and lower dimensional spaces are
connected via the $\mathbb{S}^1$ fibre bundle which consists of the global,
geometric and dynamic phases. The global phase is quantized in integer
multiples of $2\pi$ and presents itself as a natural hidden variable of
Classical Mechanics.

23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex