Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The gauge freedoms of enlarged Helmholtz theorem and the Neumann ---
  Debye potentials; their manifestation in the multipole expansion of conserved
  current   We discuss gauge freedom within the scope of the enlarged Helmholtz theorem
and Neumann-Debye decomposition and then demonstrate its realization for the
multipole expansion of a electromagnetic current with distinguished toroid
moment family. The exact solution to the latter problem was obtained in 1974,
but answers to some purely mathematical questions raised by I.B.~French and
Y.~Shimamoto~\cite{French} about 40 years ago are given in this paper for the
first time.

9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom