Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-dimensional superintegrable systems in a static electromagnetic
  field   We consider a charged particle moving in a static electromagnetic field
described by the vector potential $\vec A(\vec x)$ and the electrostatic
potential $V(\vec x)$. We study the conditions on the structure of the
integrals of motion of the first and second order in momenta, in particular how
they are influenced by the gauge invariance of the problem. Next, we
concentrate on the three possibilities for integrability arising from the first
order integrals corresponding to three nonequivalent subalgebras of the
Euclidean algebra, namely $(P_1,P_2)$, $(L_3,P_3)$ and $(L_1,L_2,L_3)$. For
these cases we look for additional independent integrals of first or second
order in the momenta. These would make the system superintegrable (minimally or
maximally). We study their quantum spectra and classical equations of motion.
In some cases nonpolynomial integrals of motion occur and ensure maximal
superintegrability.

35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom