Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Does the Helmholtz theorem of vector decomposition apply to the wave
  fields of electromagnetic radiation?   The derivation of the Helmholtz theorem of vector decomposition of a 3-vector
field requires that the field satisfy certain convergence properties at spatial
infinity. This paper investigates if time-dependent electromagnetic radiation
wave fields, which are of long range, satisfy these requirements. It is found
that the requirements are satisfied because the fields give rise to integrals
over the radial distance r of integrands of the form sin(kr)/r and cos(kr)/r.
These Dirichlet integrals converge at infinity as required.

22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org