Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operad Structures in Geometric Quantization of the Moduli Space of
  Spatial Polygons   The moduli space of spatial polygons is known as a symplectic manifold
equipped with both K\"ahler and real polarizations. In this paper, associated
to the K\"ahler and real polarizations, morphisms of operads
$\mathsf{f}_{\mathsf{K}\ddot{\mathsf{a}}\mathsf{h}}$ and
$\mathsf{f}_{\mathsf{re}}$ are constructed by using the quantum Hilbert spaces
$\mathscr{H}_{\mathrm{K}\ddot{\mathrm{a}}\mathrm{h}}$ and
$\mathscr{H}_\mathrm{re}$, respectively. Moreover, the relationship between the
two morphisms of operads $\mathsf{f}_{\mathsf{K}\ddot{\mathsf{a}}\mathsf{h}}$
and $\mathsf{f}_{\mathsf{re}}$ is studied and then the equality $\dim
\mathscr{H} _{\mathrm{K}\ddot{\mathrm{a}}\mathrm{h}}=\dim
\mathscr{H}_\mathrm{re}$ is proved in general setting. This operadic framework
is regarded as a development of the recurrence relation method by Kamiyama for
proving $\dim \mathscr{H}_{\mathrm{K}\ddot{\mathrm{a}}\mathrm{h}}=\dim
\mathscr{H}_\mathrm{re}$ in a special case.

13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex