Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One Electron Atom in Special Relativity with de Sitter Space-Time
  Symmetry   The de Sitter invariant Special Relativity (dS-SR) is a SR with constant
curvature, and a natural extension of usual Einstein SR (E-SR). In this paper,
we solved the dS-SR Dirac equation of Hydrogen by means of the adiabatic
approach and the quasi-stationary perturbation calculations of QM. Hydrogen
atoms are located on the light cone of the Universe. FRW metric and
$\Lambda$CDM cosmological model are used to discuss this issue. To the atom,
effects of de Sitter space-time geometry described by Beltrami metric are taken
into account. The dS-SR Dirac equation turns out to be a time dependent quantum
Hamiltonian system. We revealed that: 1,The fundamental physics constants
$m_e,\;\hbar,\;e$ variate adiabatically along with cosmologic time in dS-SR QM
framework. But the fine-structure constant $\alpha\equiv e^2/(\hbar c)$ keeps
to be invariant; 2,$(2s^{1/2}-2p^{1/2})$-splitting due to dS-SR QM effects: By
means of perturbation theory, that splitting $\Delta E(z)$ were calculated
analytically, which belongs to $\mathcal{O}(1/R^2)$-physics of dS-SR QM.
Numerically, we found that when $|R|\simeq \{10^3 Gly,\;10^4 Gly,\;10^5
Gly\;\}$, and $z\simeq \{1,\;{\rm or}\;2\}$, the $\Delta E(z)>> 1{\rm (Lamb\;
shift)}$. This indicate that for these cases the hyperfine structure effects
due to QED could be ignored, and the dS-SR fine structure effects are dominant.
This effect could be used to determine the universal constant $R$ in dS-SR, and
be thought as a new physics beyond E-SR.

6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio