Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conformal bridge in a cosmic string background   Hidden symmetries of non-relativistic $\mathfrak{so} (2,1)\cong
\mathfrak{sl}(2, {\mathbb R})$ invariant systems in a cosmic string background
are studied using the conformal bridge transformation. Geometric properties of
this background are analogous to those of a conical surface with a
deficiency/excess angle encoded in the "geometrical parameter" $\alpha$,
determined by the linear positive/negative mass density of the string. The free
particle and the harmonic oscillator on this background are shown to be related
by the conformal bridge transformation. To identify the integrals of the free
system, we employ a local canonical transformation that relates the model with
its planar version. The conformal bridge transformation is then used to map the
obtained integrals to those of the harmonic oscillator on the cone.
Well-defined classical integrals in both models exist only at $\alpha=q/k$ with
$q,k=1,2,\ldots,$ which for $q>1$ are higher-order generators of finite
nonlinear algebras. The systems are quantized for arbitrary values of $\alpha$;
however, the well-defined hidden symmetry operators associated with spectral
degeneracies only exist when $\alpha$ is an integer, that reveals a quantum
anomaly.

25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th