406 research outputs found
Mass Spectrum of Strings in Anti de Sitter Spacetime
We perform string quantization in anti de Sitter (AdS) spacetime. The string
motion is stable, oscillatory in time with real frequencies and the string size and energy are bounded. The
string fluctuations around the center of mass are well behaved. We find the
mass formula which is also well behaved in all regimes. There is an {\it
infinite} number of states with arbitrarily high mass in AdS (in de Sitter (dS)
there is a {\it finite} number of states only). The critical dimension at which
the graviton appears is as in de Sitter space. A cosmological constant
(whatever its sign) introduces a {\it fine structure} effect
(splitting of levels) in the mass spectrum at all states beyond the graviton.
The high mass spectrum changes drastically with respect to flat Minkowski
spacetime. For {\it
independent} of and the level spacing {\it grows} with the
eigenvalue of the number operator, The density of states grows
like \mbox{Exp}[(m/\sqrt{\mid\Lambda\mid}\;)^{1/2}] (instead of
\rho(m)\sim\mbox{Exp}[m\sqrt{\alpha'}] as in Minkowski space), thus {\it
discarding} the existence of a critical string temperature.
For the sake of completeness, we also study the quantum strings in the black
string background, where strings behave, in many respects, as in the ordinary
black hole backgrounds. The mass spectrum is equal to the mass spectrum in flat
Minkowski space.Comment: 31 pages, Latex, DEMIRM-Paris-9404
Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes
We compute the {\it exact} equation of state of circular strings in the (2+1)
dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its
properties for the different (oscillating, contracting and expanding) strings.
The string equation of state has the perfect fluid form with
the pressure and energy expressed closely and completely in terms of elliptic
functions, the instantaneous coefficient depending on the elliptic
modulus. We semi-classically quantize the oscillating circular strings. The
string mass is being the Casimir operator,
of the -dS [-AdS] group, and is
the Hubble constant. We find \alpha'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0),
and a {\it finite} number of states N_{\mbox{dS}}\approx 0.17/(H^2\alpha') in
de Sitter spacetime; m^2_{\mbox{AdS}}\approx 4H^2n^2 (large ) and
N_{\mbox{AdS}}=\infty in anti de Sitter spacetime. The level spacing grows
with in AdS spacetime, while is approximately constant (although larger
than in Minkowski spacetime) in dS spacetime. The massive states in dS
spacetime decay through tunnel effect and the semi-classical decay probability
is computed. The semi-classical quantization of {\it exact} (circular) strings
and the canonical quantization of generic string perturbations around the
string center of mass strongly agree.Comment: Latex, 26 pages + 2 tables and 5 figures that can be obtained from
the authors on request. DEMIRM-Obs de Paris-9404
QFT, String Temperature and the String Phase of De Sitter Space-time
The density of mass levels \rho(m) and the critical temperature for strings
in de Sitter space-time are found. QFT and string theory in de Sitter space are
compared. A `Dual'-transform is introduced which relates classical to quantum
string lengths, and more generally, QFT and string domains. Interestingly, the
string temperature in De Sitter space turns out to be the Dual transform of the
QFT-Hawking-Gibbons temperature. The back reaction problem for strings in de
Sitter space is addressed selfconsistently in the framework of the `string
analogue' model (or thermodynamical approach), which is well suited to combine
QFT and string study.We find de Sitter space-time is a self-consistent solution
of the semiclassical Einstein equations in this framework. Two branches for the
scalar curvature R(\pm) show up: a classical, low curvature solution (-), and a
quantum high curvature solution (+), enterely sustained by the strings. There
is a maximal value for the curvature R_{\max} due to the string back reaction.
Interestingly, our Dual relation manifests itself in the back reaction
solutions: the (-) branch is a classical phase for the geometry with intrinsic
temperature given by the QFT-Hawking-Gibbons temperature.The (+) is a stringy
phase for the geometry with temperature given by the intrinsic string de Sitter
temperature. 2 + 1 dimensions are considered, but conclusions hold generically
in D dimensions.Comment: LaTex, 24 pages, no figure
Sinh-Gordon, Cosh-Gordon and Liouville Equations for Strings and Multi-Strings in Constant Curvature Spacetimes
We find that the fundamental quadratic form of classical string propagation
in dimensional constant curvature spacetimes solves the Sinh-Gordon
equation, the Cosh-Gordon equation or the Liouville equation. We show that in
both de Sitter and anti de Sitter spacetimes (as well as in the black
hole anti de Sitter spacetime), {\it all} three equations must be included to
cover the generic string dynamics. The generic properties of the string
dynamics are directly extracted from the properties of these three equations
and their associated potentials (irrespective of any solution). These results
complete and generalize earlier discussions on this topic (until now, only the
Sinh-Gordon sector in de Sitter spacetime was known). We also construct new
classes of multi-string solutions, in terms of elliptic functions, to all three
equations in both de Sitter and anti de Sitter spacetimes. Our results can be
straightforwardly generalized to constant curvature spacetimes of arbitrary
dimension, by replacing the Sinh-Gordon equation, the Cosh-Gordon equation and
the Liouville equation by higher dimensional generalizations.Comment: Latex, 19 pages + 1 figure (not included
Infinitely Many Strings in De Sitter Spacetime: Expanding and Oscillating Elliptic Function Solutions
The exact general evolution of circular strings in dimensional de
Sitter spacetime is described closely and completely in terms of elliptic
functions. The evolution depends on a constant parameter , related to the
string energy, and falls into three classes depending on whether
(oscillatory motion), (degenerated, hyperbolic motion) or
(unbounded motion). The novel feature here is that one single world-sheet
generically describes {\it infinitely many} (different and independent)
strings. The world-sheet time is an infinite-valued function of the
string physical time, each branch yields a different string. This has no
analogue in flat spacetime. We compute the string energy as a function of
the string proper size , and analyze it for the expanding and oscillating
strings. For expanding strings : even at ,
decreases for small and increases for large .
For an oscillating string , the average energy
over one oscillation period is expressed as a function of as a
complete elliptic integral of the third kind.Comment: 32 pages, Latex file, figures available from the authors under
request. LPTHE-PAR 93-5
Recovery of 3D footwear impressions using a range of different techniques.
Three-dimensional (plastic) footwear impressions are frequently found at, or in the vicinity of a crime scene, and may provide a valuable form of evidence or intelligence. This paper compares the traditional methods of casting and/or two-dimensional photography with Structure from Motion (SfM) photogrammetry. We focus both on the recovery of class characteristics (sole pattern) and randomly acquired characteristics caused by damage. We examine how different recovery techniques influence visualization of outsole features and discuss what effect this may have on evidential value. Five shoes and their associated three-dimensional impressions made in both sand and soil were compared using a grid system and tread descriptors commonly used in the UK. We conclude that within the limitations of this study SfM photogrammetry allows superior levels of visualization of both class and randomly acquired characteristics, giving a better definition in detail in some instances. The use of SfM as a complementary approach can therefore lead to a potential increase in evidential value
Open Cosmic Strings in Black Hole Space-Times
We construct open cosmic string solutions in Schwarzschild black hole and
non-dilatonic black p-brane backgrounds. These strings can be thought to
stretch between two D-branes or between a D-brane and the horizon in curved
space-time. We study small fluctuations around these solutions and discuss
their basic properties.Comment: 11 pages, REVTex, 5 figures, a reference adde
Open String Fluctuations in AdS with and without Torsion
The equations of motion and boundary conditions for the fluctuations around a
classical open string, in a curved space-time with torsion, are considered in
compact and world-sheet covariant form. The rigidly rotating open strings in
Anti de Sitter space with and without torsion are investigated in detail. By
carefully analyzing the tangential fluctuations at the boundary, we show
explicitly that the physical fluctuations (which at the boundary are
combinations of normal and tangential fluctuations) are finite, even though the
world-sheet is singular there. The divergent 2-curvature thus seems less
dangerous than expected, in these cases. The general formalism can be
straightforwardly used also to study the (bosonic part of the) fluctuations
around the closed strings, recently considered in connection with the AdS/CFT
duality, on AdS_5 \times S^5 and AdS_3 \times S^3 \times T^4.Comment: 19 pages, Late
Spinning Pulsating String Solitons in AdS_5 x S^5
We point out the existence of some simple string solitons in AdS_5 x S^5,
which at the same time are spinning in AdS_5 and pulsating in S^5, or
vice-versa. This introduces an additional arbitrary constant into the scaling
relations between energy and spin or R-charge. The arbitrary constant is not an
angular momentum, but can be related to the amplitude of the pulsation. We
discuss the solutions in detail and consider the scaling relations. Pulsating
multi spin or multi R-charge solutions can also be constructed.Comment: 15 pages, Late
Strings in Homogeneous Background Spacetimes
The string equations of motion for some homogeneous (Kantowski-Sachs, Bianchi
I and Bianchi IX) background spacetimes are given, and solved explicitly in
some simple cases. This is motivated by the recent developments in string
cosmology, where it has been shown that, under certain circumstances, such
spacetimes appear as string-vacua.
Both tensile and null strings are considered. Generally, it is much simpler
to solve for the null strings since then we deal with the null geodesic
equations of General Relativity plus some additional constraints.
We consider in detail an ansatz corresponding to circular strings, and we
discuss the possibility of using an elliptic-shape string ansatz in the case of
homogeneous (but anisotropic) backgrounds.Comment: 25 pages, REVTE
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