Evidence for Special Relativity with de Sitter Space-Time Symmetry

I show the formulation of de Sitter Special Relativity (dS-SR) based on Dirac-Lu-Zou-Guo's discussions. dS-SR quantum mechanics is formulated, and the dS-SR Dirac equation for hydrogen is suggested. The equation in the earth-QSO framework reference is solved by means of the adiabatic approach. It's found that the fine-structure "constant" $\alpha$ in dS-SR varies with time. By means of the $t-z$ relation of the $\Lambda$CDM model, $\alpha$'s time-dependency becomes redshift $z$-dependent. The dS-SR's predictions of $\Delta\alpha/\alpha$ agree with data of spectra of 143 quasar absorption systems, the dS-space-time symmetry is SO(3,2) (i.e., anti-dS group) $\;$ and the universal parameter $R$ (de Sitter ratio) in dS-SR is estimated to be $R\simeq 2.73\times 10^{12}ly$. The effects of dS-SR become visible at the cosmic space-time scale (i.e., the distance $\geq 10^9 ly$). At that scale dS-SR is more reliable than Einstein SR. The $\alpha$-variation with time is an evidence of SR with de Sitter symmetry.Comment: 5 pages, 3 figure

Unstable and Stable Galaxy Models

To determine the stability and instability of a given steady galaxy configuration is one of the fundamental problems in the Vlasov theory for galaxy dynamics. In this article, we study the stability of isotropic spherical symmetric galaxy models $f_{0}(E)$, for which the distribution function $f_{0}$ depends on the particle energy $E$ only. In the first part of the article, we derive the first sufficient criterion for linear instability of $f_{0}(E):$ $f_{0}(E)$ is linearly unstable if the second-order operator $$A_{0}\equiv-\Delta+4\pi\int f_{0}^{\prime}(E)\{I-\mathcal{P}\}dv$$ has a negative direction, where $\mathcal{P}$ is the projection onto the function space $\{g(E,L)\},$ $L$ being the angular momentum [see the explicit formula (\ref{A0-radial})]. In the second part of the article, we prove that for the important King model, the corresponding $A_{0}$ is positive definite. Such a positivity leads to the nonlinear stability of the King model under all spherically symmetric perturbations.Comment: to appear in Comm. Math. Phy