Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Topological Structure in the Set of Classical Free Radiation
  Electromagnetic Fields   The aim of this work is to proceed with the development of a model of
topological electromagnetism in empty space, proposed by one of us some time
ago and based on the existence of a topological structure associated with the
radiation fields in standard Maxwell's theory. This structure consists in pairs
of complex scalar fields, say $\phi$ and $\theta$, that can be interpreted as
maps $\phi,\theta: S^3\mapsto S^2$, the level lines of which are orthogonal to
one another, where $S^3$ is the compactified physical 3-space $R^3$, with only
one point at infinity, and $S^2$ is the 2-sphere identified with the complete
complex plane. These maps were discovered and studied in 1931 by the German
mathematician H. Hopf, who showed that the set of all of them can be ordered in
homotopy classes, labeled by the so called Hopf index, equal to $\gamma=\pm
1,\,\pm 2,\,\cdots ,\, \pm k,...$ but without $\gamma=0$. In the model
presented here and at the level of the scalars $\phi$ and $\theta$, the
equations of motion are highly nonlinear; however there is a transformation of
variables that converts exactly these equations (not by truncation!) into the
linear Maxwell's ones for the magnetic and electric fields $\B$ and $\E$.

6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ