Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirac quantisation condition: a comprehensive review   In most introductory courses on electrodynamics, one is taught the electric
charge is quantised but no theoretical explanation related to this law of
nature is offered. Such an explanation is postponed to graduate courses on
electrodynamics, quantum mechanics and quantum field theory, where the famous
Dirac quantisation condition is introduced, which states that a single magnetic
monopole in the Universe would explain the electric charge quantisation. Even
when this condition assumes the existence of a not-yet-detected magnetic
monopole, it provides the most accepted explanation for the observed
quantisation of the electric charge. However, the usual derivation of the Dirac
quantisation condition involves the subtle concept of an "unobservable"
semi-infinite magnetised line, the so-called "Dirac string," which may be
difficult to grasp in a first view of the subject. The purpose of this review
is to survey the concepts underlying the Dirac quantisation condition, in a way
that may be accessible to advanced undergraduate and graduate students. Some of
the discussed concepts are gauge invariance, singular potentials,
single-valuedness of the wave function, undetectability of the Dirac string and
quantisation of the electromagnetic angular momentum. Five quantum-mechanical
and three semi-classical derivations of the Dirac quantisation condition are
reviewed. In addition, a simple derivation of this condition involving
heuristic and formal arguments is presented.

14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph