One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry

The de Sitter invariant Special Relativity (dS-SR) is SR with constant curvature, and a natural extension of usual Einstein SR (E-SR). In this paper, we solve the dS-SR Dirac equation of Hydrogen by means of the adiabatic approach and the quasi-stationary perturbation calculations of QM. Hydrogen atom is located in the light cone of the Universe. FRW metric and ΛCDM 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 reveal that: (i) The fundamental physics constants m_e,h,e variate adiabatically along with cosmologic time in dS-SR QM framework. But the fine-structure constant α≡ e²/(hc) keeps to be invariant; (ii) (2s^1/2-2p^1/2)-splitting due to dS-SR QM effects: By means of perturbation theory, that splitting Δ E(z) are calculated analytically, which belongs to O(1/R²)-physics of dS-SR QM. Numerically, we find that when |R|～{10³Gly, 10⁴Gly, 10⁵Gly}, and z～{1,or 2}, the Δ E(z)>>1 (Lamb shift). This indicates 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.