Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical magnetic field for 2d magnetic Dirac-Coulomb operators and
  Hardy inequalities   This paper is devoted to the study of the two-dimensional Dirac-Coulomb
operator in presence of an Aharonov-Bohm external magnetic potential. We
characterize the highest intensity of the magnetic field for which a
two-dimensional magnetic Hardy inequality holds. Up to this critical magnetic
field, the operator admits a distinguished self-adjoint extension and there is
a notion of ground state energy, defined as the lowest eigenvalue in the gap of
the continuous spectrum.

25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas