Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Mechanics on Manifolds   A definition of quantum mechanics on a manifold $ M $ is proposed and a
method to realize the definition is presented. This scheme is applicable to a
homogeneous space $ M = G / H $. The realization is a unitary representation of
the transformation group $ G $ on the space of vector bundle-valued functions.
When $ H \ne \{ e \} $, there exist a number of inequivalent realizations. As
examples, quantum mechanics on a sphere $ S^n $, a torus $ T^n $ and a
projective space $ \RP $ are studied. In any case, it is shown that there are
an infinite number of inequivalent realizations.

19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat