Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comments on noncommutative quantum mechanical systems associated with
  Lie algebras   We consider quantum mechanics on the noncommutative spaces characterized by
the commutation relations $$ [x_a, x_b] \ =\ i\theta f_{abc} x_c\,, $$ where
$f_{abc}$ are the structure constants of a Lie algebra. We note that this
problem can be reformulated as an ordinary quantum problem in a commuting
momentum space. The coordinates are then represented as linear differential
operators $\hat x_a = -i\hat D_a = -iR_{ab} (p)\, \partial /\partial p_b $.
Generically, the matrix $R_{ab}(p)$ represents a certain infinite series over
the deformation parameter $\theta$: $R_{ab} = \delta_{ab} + \ldots$. The
deformed Hamiltonian, $\hat H = -\frac 12 \hat D_a^2\,,$ describes the motion
along the corresponding group manifolds with the characteristic size of order
$\theta^{-1}$. Their metrics are also expressed into certain infinite series in
$\theta$. For the algebras $su(2)$ and $u(2)$, it has been possible to
represent the operators $\hat x_a$ in a simple finite form. A byproduct of our
study are new nonstandard formulas for the metrics on $SU(2) \equiv S^3$ and on
$SO(3)$.

18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con