2010/04/30 by Mu-Lin Yan
Physics and Astronomy · #physics.gen-ph
published as Commun. Theor. Phys. 57 (2012) 930-952 · 37 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:0909.4829
arxiv created 2012/02/17 · arxiv updated 2012/05/23
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 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 revealed that: 1,The fundamental physics constants me, ℏ, e variate adiabatically along with cosmologic time in dS-SR QM framework. But the fine-structure constant α≡ e2/(ℏ c) keeps to be invariant; 2,(2s1/2-2p1/2)-splitting due to dS-SR QM effects: By means of perturbation theory, that splitting ΔE(z) were calculated analytically, which belongs to O(1/R2)-physics of dS-SR QM. Numerically, we found that when |R|≃ \103 Gly, 104 Gly, 105 Gly \, and z≃ \1, \rm or 2\, the ΔE(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.