70,012 research outputs found
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" in dS-SR varies with time. By means
of the relation of the CDM model, 's time-dependency
becomes redshift -dependent. The dS-SR's predictions of
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 (de Sitter ratio) in dS-SR is estimated to be
. The effects of dS-SR become visible at the
cosmic space-time scale (i.e., the distance ). At that scale
dS-SR is more reliable than Einstein SR. The -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 , for which the distribution function
depends on the particle energy only. In the first part of the article, we
derive the first sufficient criterion for linear instability of
is linearly unstable if the second-order operator has a
negative direction, where is the projection onto the function
space 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 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
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