Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Central extensions and quantum physics   The unitary implementation of a symmetry group $G$ of a classical system in
the corresponding quantum theory entails unavoidable deformations $\TG$ of $G$,
namely, central extensions by the typical phase invariance group U(1). The
appearance of central charges in the corresponding Lie-algebra quantum
commutators, as a consequence of non-trivial responses of the phase of the wave
function under symmetry transformations, lead to a quantum generation of extra
degrees of freedom with regard to the classical counterpart. In particular,
symmetries of the Hall effect, Yang-Mills and conformally invariant classical
field theories are affected when passing to the quantum realm.

12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess