78,067 research outputs found

    From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality

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    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

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    We study the Hilbert expansion for small Knudsen number ε\varepsilon 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).OurmainresultstatesthatiftheHilbertexpansionisvalidat Our main result states that if the Hilbert expansion is valid at t=0forwell−preparedsmallinitialdatawithirrotationalvelocity for well-prepared small initial data with irrotational velocity u_0,thenitisvalidfor, then it is valid for 0\leq t\leq \varepsilon ^{-{1/2}\frac{2k-3}{2k-2}},where where \rho_{0}(t,x)and and u_{0}(t,x)satisfytheEuler−Poissonsystemformonatomicgas satisfy the Euler-Poisson system for monatomic gas \gamma=5/3$

    Geometries for Possible Kinematics

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    The algebras for all possible Lorentzian and Euclidean kinematics with so(3)\frak{so}(3) 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 t↔1/(ν2t)t \leftrightarrow 1/(\nu^2t) 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

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    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

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    Based on the Beltrami-de Sitter spacetime, we present the Newton-Hooke model under the Newton-Hooke contraction of the BdSBdS 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

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    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 ℓP\ell_P and the scale R=3/ΛR=3/\Lambda should be dual to each other and there is in-between gravity of local \dS-invariance characterized by a dimensionless coupling constant g=ℓP/R∼10−61g=\ell_P/R\sim 10^{-61}.Comment: 8 page
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