Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirac oscillator with nonzero minimal uncertainty in position   In the context of some deformed canonical commutation relations leading to
isotropic nonzero minimal uncertainties in the position coordinates, a Dirac
equation is exactly solved for the first time, namely that corresponding to the
Dirac oscillator. Supersymmetric quantum mechanical and shape-invariance
methods are used to derive both the energy spectrum and wavefunctions in the
momentum representation. As for the conventional Dirac oscillator, there are
neither negative-energy states for $E=-1$, nor symmetry between the $l = j -
{1/2}$ and $l = j + {1/2}$ cases, both features being connected with
supersymmetry or, equivalently, the $\omega \to - \omega$ transformation. In
contrast with the conventional case, however, the energy spectrum does not
present any degeneracy pattern apart from that associated with the rotational
symmetry. More unexpectedly, deformation leads to a difference in behaviour
between the $l = j - {1/2}$ states corresponding to small, intermediate and
very large $j$ values in the sense that only for the first ones supersymmetry
remains unbroken, while for the second ones no bound state does exist.

8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys