19,719 research outputs found
Renormalization Group Flow and Fragmentation in the Self-Gravitating Thermal Gas
The self-gravitating thermal gas (non-relativistic particles of mass m at
temperature T) is exactly equivalent to a field theory with a single scalar
field phi(x) and exponential self-interaction. We build up perturbation theory
around a space dependent stationary point phi_0(r) in a finite size domain
delta \leq r \leq R ,(delta << R), which is relevant for astrophysical applica-
tions (interstellar medium,galaxy distributions).We compute the correlations of
the gravitational potential (phi) and of the density and find that they scale;
the latter scales as 1/r^2. A rich structure emerges in the two-point correl-
tors from the phi fluctuations around phi_0(r). The n-point correlators are
explicitly computed to the one-loop level.The relevant effective coupling turns
out to be lambda=4 pi G m^2 / (T R). The renormalization group equations (RGE)
for the n-point correlator are derived and the RG flow for the effective
coupling lambda(tau) [tau = ln(R/delta), explicitly obtained.A novel dependence
on tau emerges here.lambda(tau) vanishes each time tau approaches discrete
values tau=tau_n = 2 pi n/sqrt7-0, n=0,1,2, ...Such RG infrared stable behavior
[lambda(tau) decreasing with increasing tau] is here connected with low density
self-similar fractal structures fitting one into another.For scales smaller
than the points tau_n, ultraviolet unstable behaviour appears which we connect
to Jeans' unstable behaviour, growing density and fragmentation. Remarkably, we
get a hierarchy of scales and Jeans lengths following the geometric progression
R_n=R_0 e^{2 pi n /sqrt7} = R_0 [10.749087...]^n . A hierarchy of this type is
expected for non-spherical geometries,with a rate different from e^{2 n/sqrt7}.Comment: LaTex, 31 pages, 11 .ps figure
Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes
The string propagation equations in axisymmetric spacetimes are exactly
solved by quadratures for a planetoid Ansatz. This is a straight
non-oscillating string, radially disposed, which rotates uniformly around the
symmetry axis of the spacetime. In Schwarzschild black holes, the string stays
outside the horizon pointing towards the origin. In de Sitter spacetime the
planetoid rotates around its center. We quantize semiclassically these
solutions and analyze the spin/(mass) (Regge) relation for the planetoids,
which turns out to be non-linear.Comment: Latex file, 14 pages, two figures in .ps files available from the
author
String dynamics in cosmological and black hole backgrounds: The null string expansion
We study the classical dynamics of a bosonic string in the --dimensional
flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a
perturbative development in the string coordinates around a {\it null} string
configuration; the background geometry is taken into account exactly. In the
cosmological case we uncouple and solve the first order fluctuations; the
string time evolution with the conformal gauge world-sheet --coordinate
is given by , where
are given by Eqs.\ (3.15), and is the exponent of the conformal factor
in the Friedmann--Robertson--Walker metric, i.e. . The string
proper size, at first order in the fluctuations, grows like the conformal
factor and the string energy--momentum tensor corresponds to that of
a null fluid. For a string in the black hole background, we study the planar
case, but keep the dimensionality of the spacetime generic. In the null
string expansion, the radial, azimuthal, and time coordinates are
and The first terms of the series represent a
{\it generic} approach to the Schwarzschild singularity at . First and
higher order string perturbations contribute with higher powers of . The
integrated string energy-momentum tensor corresponds to that of a null fluid in
dimensions. As the string approaches the singularity its proper
size grows indefinitely like . We end the paper
giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure
Multi-String Solutions by Soliton Methods in De Sitter Spacetime
{\bf Exact} solutions of the string equations of motion and constraints are
{\bf systematically} constructed in de Sitter spacetime using the dressing
method of soliton theory. The string dynamics in de Sitter spacetime is
integrable due to the associated linear system. We start from an exact string
solution and the associated solution of the linear system , and we construct a new solution differing from
by a rational matrix in with at least four
poles . The periodi-
city condition for closed strings restrict to discrete values
expressed in terms of Pythagorean numbers. Here we explicitly construct solu-
tions depending on -spacetime coordinates, two arbitrary complex numbers
(the 'polarization vector') and two integers which determine the string
windings in the space. The solutions are depicted in the hyperboloid coor-
dinates and in comoving coordinates with the cosmic time . Despite of
the fact that we have a single world sheet, our solutions describe {\bf multi-
ple}(here five) different and independent strings; the world sheet time
turns to be a multivalued function of .(This has no analogue in flat space-
time).One string is stable (its proper size tends to a constant for , and its comoving size contracts); the other strings are unstable (their
proper sizes blow up for , while their comoving sizes tend to cons-
tants). These solutions (even the stable strings) do not oscillate in time. The
interpretation of these solutions and their dynamics in terms of the sinh-
Gordon model is particularly enlighting.Comment: 25 pages, latex. LPTHE 93-44. Figures available from the auhors under
reques
Strings in Cosmological and Black Hole Backgrounds: Ring Solutions
The string equations of motion and constraints are solved for a ring shaped
Ansatz in cosmological and black hole spacetimes. In FRW universes with
arbitrary power behavior [R(X^0) = a\;|X^0|^{\a}\, ], the asymptotic form of
the solution is found for both and and we plot the
numerical solution for all times. Right after the big bang (), the
string energy decreasess as and the string size grows as for . Very
soon [ ] , the ring reaches its oscillatory regime with frequency
equal to the winding and constant size and energy. This picture holds for all
values of \a including string vacua (for which, asymptotically, \a = 1).
In addition, an exact non-oscillatory ring solution is found. For black hole
spacetimes (Schwarzschild, Reissner-Nordstr\oo m and stringy), we solve for
ring strings moving towards the center. Depending on their initial conditions
(essentially the oscillation phase), they are are absorbed or not by
Schwarzschild black holes. The phenomenon of particle transmutation is
explicitly observed (for rings not swallowed by the hole). An effective horizon
is noticed for the rings. Exact and explicit ring solutions inside the
horizon(s) are found. They may be interpreted as strings propagating between
the different universes described by the full black hole manifold.Comment: Paris preprint PAR-LPTHE-93/43. Uses phyzzx. Includes figures. Text
and figures compressed using uufile
Real Time Nonequilibrium Dynamics of Quantum Plasmas. Quantum Kinetics and the Dynamical Renormalization Group
We implement the dynamical renormalization group (DRG) using the hard thermal
loop (HTL) approximation for the real-time nonequilibrium dynamics in hot
plasmas. The focus is on the study of the relaxation of gauge and fermionic
mean fields and on the quantum kinetics of the photon and fermion distribution
functions. As a concrete physical prediction, we find that for a QGP of
temperature T sim 200 MeV and lifetime 10 < t < 50 fm/c there is a new
contribution to the hard (k \sim T) photon production from off-shell
bremsstrahlung (q rightarrow q gamma and bar{q} rightarrow bar{q} gamma) at
just O (alpha) that grows logarithmically in time and is comparable to the
known on-shell Compton scattering and pair annihilation at O(alpha alpha_s).Comment: LaTex, 5 pages, one .ps figure, lecture given at the DPF 2000
Conference, August 9-12, Columbus, Ohi
The Effective Theory of Inflation and the Dark Matter Status in the Standard Model of the Universe
We present here the effective theory of inflation `a la Ginsburg-Landau in
which the inflaton potential is a polynomial. The slow-roll expansion becomes a
systematic 1/N expansion where N ~ 60. The spectral index and the ratio of
tensor/scalar fluctuations are n_s - 1 = O(1/N), r = O(1/N) while the running
turns to be d n_s/d \ln k = O(1/N^2) and can be neglected. The energy scale of
inflation M ~ 0.7 10^{16} GeV is completely determined by the amplitude of the
scalar adiabatic fluctuations. A complete analytic study plus the Monte Carlo
Markov Chains (MCMC) analysis of the available CMB+LSS data showed: (a) the
spontaneous breaking of the phi -> - phi symmetry of the inflaton potential.
(b) a lower bound for r: r > 0.023 (95% CL) and r > 0.046 (68% CL). (c) The
preferred inflation potential is a double well, even function of the field with
a moderate quartic coupling yielding as most probable values: n_s = 0.964, r =
0.051. This value for r is within reach of forthcoming CMB observations. We
investigate the DM properties using cosmological theory and the galaxy
observations. Our DM analysis is independent of the particle physics model for
DM and it is based on the DM phase-space density rho_{DM}/sigma^3_{DM}. We
derive explicit formulas for the DM particle mass m and for the number of
ultrarelativistic degrees of freedom g_d (hence the temperature) at decoupling.
We find that m turns to be at the keV scale. The keV scale DM is
non-relativistic during structure formation, reproduces the small and large
scale structure but it cannot be responsible of the e^+ and pbar excess in
cosmic rays which can be explained by astrophysical mechanisms (Abridged).Comment: 28 pages; to be published in the Lev Lipatov Festschrift on the
occasion of Lev's 70th birthday, `Subtleties in Quantum Field Theories', D.
Diakonov, Editor, Gatchina, Russia, 201
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