77,222 research outputs found
From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality
By means of Dirac procedure, we re-examine Yang's quantized space-time model,
its relation to Snyder's model, the de Sitter special relativity and their
UV-IR duality. Starting from a dimensionless dS_5-space in a 5+1-d Mink-space a
complete Yang model at both classical and quantum level can be presented and
there really exist Snyder's model, the dS special relativity and the duality.Comment: 7 papge
Global Hilbert Expansion for the Vlasov-Poisson-Boltzmann System
We study the Hilbert expansion for small Knudsen number for the
Vlasov-Boltzmann-Poisson system for an electron gas. The zeroth order term
takes the form of local Maxwellian: $ F_{0}(t,x,v)=\frac{\rho_{0}(t,x)}{(2\pi
\theta_{0}(t,x))^{3/2}} e^{-|v-u_{0}(t,x)|^{2}/2\theta_{0}(t,x)},\text{\
}\theta_{0}(t,x)=K\rho_{0}^{2/3}(t,x).t=0u_00\leq t\leq \varepsilon
^{-{1/2}\frac{2k-3}{2k-2}},\rho_{0}(t,x) u_{0}(t,x)\gamma=5/3$
Geometries for Possible Kinematics
The algebras for all possible Lorentzian and Euclidean kinematics with
isotropy except static ones are re-classified. The geometries
for algebras are presented by contraction approach. The relations among the
geometries are revealed. Almost all geometries fall into pairs. There exists correspondence in each pair. In the viewpoint of
differential geometry, there are only 9 geometries, which have right signature
and geometrical spatial isotropy. They are 3 relativistic geometries, 3
absolute-time geometries, and 3 absolute-space geometries.Comment: 40 pages, 7 figure
A sharp stability criterion for the Vlasov-Maxwell system
We consider the linear stability problem for a 3D cylindrically symmetric
equilibrium of the relativistic Vlasov-Maxwell system that describes a
collisionless plasma. For an equilibrium whose distribution function decreases
monotonically with the particle energy, we obtained a linear stability
criterion in our previous paper. Here we prove that this criterion is sharp;
that is, there would otherwise be an exponentially growing solution to the
linearized system. Therefore for the class of symmetric Vlasov-Maxwell
equilibria, we establish an energy principle for linear stability. We also
treat the considerably simpler periodic 1.5D case. The new formulation
introduced here is applicable as well to the nonrelativistic case, to other
symmetries, and to general equilibria
Newton-Hooke Limit of Beltrami-de Sitter Spacetime, Principles of Galilei-Hooke's Relativity and Postulate on Newton-Hooke Universal Time
Based on the Beltrami-de Sitter spacetime, we present the Newton-Hooke model
under the Newton-Hooke contraction of the spacetime with respect to the
transformation group, algebra and geometry. It is shown that in Newton-Hooke
space-time, there are inertial-type coordinate systems and inertial-type
observers, which move along straight lines with uniform velocity. And they are
invariant under the Newton-Hooke group. In order to determine uniquely the
Newton-Hooke limit, we propose the Galilei-Hooke's relativity principle as well
as the postulate on Newton-Hooke universal time. All results are readily
extended to the Newton-Hooke model as a contraction of Beltrami-anti-de Sitter
spacetime with negative cosmological constant.Comment: 25 pages, 3 figures; some misprints correcte
Snyder's Quantized Space-time and De Sitter Special Relativity
There is a one-to-one correspondence between Snyder's model in de Sitter
space of momenta and the \dS-invariant special relativity. This indicates that
physics at the Planck length and the scale should be
dual to each other and there is in-between gravity of local \dS-invariance
characterized by a dimensionless coupling constant .Comment: 8 page
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