336 research outputs found
Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models
This is the third paper in our series of five in which we test the Master
Constraint Programme for solving the Hamiltonian constraint in Loop Quantum
Gravity. In this work we analyze models which, despite the fact that the phase
space is finite dimensional, are much more complicated than in the second
paper: These are systems with an SL(2,\Rl) gauge symmetry and the
complications arise because non -- compact semisimple Lie groups are not
amenable (have no finite translation invariant measure). This leads to severe
obstacles in the refined algebraic quantization programme (group averaging) and
we see a trace of that in the fact that the spectrum of the Master Constraint
does not contain the point zero. However, the minimum of the spectrum is of
order which can be interpreted as a normal ordering constant arising
from first class constraints (while second class systems lead to normal
ordering constants). The physical Hilbert space can then be be obtained after
subtracting this normal ordering correction.Comment: 33 pages, no figure
Gaia's potential for the discovery of circumbinary planets
The abundance and properties of planets orbiting binary stars - circumbinary
planets - are largely unknown because they are difficult to detect with
currently available techniques. Results from the Kepler satellite and other
studies indicate a minimum occurrence rate of circumbinary giant planets of ~10
%, yet only a handful are presently known. Here, we study the potential of
ESA's Gaia mission to discover and characterise extrasolar planets orbiting
nearby binary stars by detecting the binary's periodic astrometric motion
caused by the orbiting planet. We expect that Gaia will discover hundreds of
giant planets around binaries with FGK dwarf primaries within 200 pc of the
Sun, if we assume that the giant planet mass distribution and abundance are
similar around binaries and single stars. If on the other hand all circumbinary
gas giants have masses lower than two Jupiter masses, we expect only four
detections. Gaia is critically sensitive to the properties of giant
circumbinary planets and will therefore make the detailed study of their
population possible. Gaia's precision is such that the distribution in mutual
inclination between the binary and planetary orbital planes will be obtained.
It also possesses the capacity to establish the frequency of planets across the
H-R diagram, both as a function of mass and of stellar evolutionary state from
pre-main sequence to stellar remnants. Gaia's discoveries can reveal whether a
second epoch of planetary formation occurs after the red-giant phase.Comment: 12 pages, 11 figures. Submitted to MNRAS. Revised version after
referee repor
Gaia's potential for the discovery of circumbinary planets
The abundance and properties of planets orbiting binary stars - circumbinary planets - are largely unknown because they are difficult to detect with currently available techniques. Results from the Kepler satellite and other studies indicate a minimum occurrence rate of circumbinary giant planets of ∼10 per cent, yet only a handful are presently known. Here, we study the potential of ESA's Gaia mission to discover and characterize extrasolar planets orbiting nearby binary stars by detecting the binary's periodic astrometric motion caused by the orbiting planet. We expect that Gaia will discover hundreds of giant planets around binaries with FGK-dwarf primaries within 200pc of the Sun, if we assume that the giant planet mass distribution and abundance are similar around binaries and single stars. If on the other hand all circumbinary gas giants have masses lower than two Jupiter masses, we expect only four detections. Gaia is critically sensitive to the properties of giant circumbinary planets and will therefore make the detailed study of their population possible. Gaia's precision is such that the distribution in mutual inclination between the binary and planetary orbital planes will be obtained. It also possesses the capacity to establish the frequency of planets across the Hertzsprung-Russell diagram, both as a function of mass and of stellar evolutionary state from pre-main sequence to stellar remnants. Gaia's discoveries can reveal whether a second epoch of planetary formation occurs after the red giant phas
On (Cosmological) Singularity Avoidance in Loop Quantum Gravity
Loop Quantum Cosmology (LQC), mainly due to Bojowald, is not the cosmological
sector of Loop Quantum Gravity (LQG). Rather, LQC consists of a truncation of
the phase space of classical General Relativity to spatially homogeneous
situations which is then quantized by the methods of LQG. Thus, LQC is a
quantum mechanical toy model (finite number of degrees of freedom) for LQG(a
genuine QFT with an infinite number of degrees of freedom) which provides
important consistency checks. However, it is a non trivial question whether the
predictions of LQC are robust after switching on the inhomogeneous fluctuations
present in full LQG. Two of the most spectacular findings of LQC are that 1.
the inverse scale factor is bounded from above on zero volume eigenstates which
hints at the avoidance of the local curvature singularity and 2. that the
Quantum Einstein Equations are non -- singular which hints at the avoidance of
the global initial singularity. We display the result of a calculation for LQG
which proves that the (analogon of the) inverse scale factor, while densely
defined, is {\it not} bounded from above on zero volume eigenstates. Thus, in
full LQG, if curvature singularity avoidance is realized, then not in this
simple way. In fact, it turns out that the boundedness of the inverse scale
factor is neither necessary nor sufficient for curvature singularity avoidance
and that non -- singular evolution equations are neither necessary nor
sufficient for initial singularity avoidance because none of these criteria are
formulated in terms of observable quantities.After outlining what would be
required, we present the results of a calculation for LQG which could be a
first indication that our criteria at least for curvature singularity avoidance
are satisfied in LQG.Comment: 34 pages, 16 figure
Coherent States for Black Holes
We determine coherent states peaked at classical space-time of the
Schwarzschild black hole in the frame-work of canonical quantisation of general
relativity. The information about the horizon is naturally encoded in the phase
space variables, and the perturbative quantum fluctuations around the classical
geometry depend on the distance from the horizon. For small black holes, space
near the vicinity of the singularity appears discrete with the singular point
excluded from the spectrum.Comment: 48 pages, 18+1 figures, some modifications, references adde
The Early Universe in Loop Quantum Cosmology
Loop quantum cosmology applies techniques derived for a background
independent quantization of general relativity to cosmological situations and
draws conclusions for the very early universe. Direct implications for the
singularity problem as well as phenomenology in the context of inflation or
bouncing universes result, which will be reviewed here. The discussion focuses
on recent new results for structure formation and generalizations of the
methods.Comment: 10 pages, 3 figures, plenary talk at VI Mexican School on Gravitation
and Mathematical Physics, Nov 21-27, 200
On low energy quantum gravity induced effects on the propagation of light
Present models describing the interaction of quantum Maxwell and
gravitational fields predict a breakdown of Lorentz invariance and a non
standard dispersion relation in the semiclassical approximation. Comparison
with observational data however, does not support their predictions. In this
work we introduce a different set of ab initio assumptions in the canonical
approach, namely that the homogeneous Maxwell equations are valid in the
semiclassical approximation, and find that the resulting field equations are
Lorentz invariant in the semiclassical limit. We also include a
phenomenological analysis of possible effects on the propagation of light, and
their dependence on energy, in a cosmological context.Comment: 12 page
The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space
We combine I. background independent Loop Quantum Gravity (LQG) quantization
techniques, II. the mathematically rigorous framework of Algebraic Quantum
Field Theory (AQFT) and III. the theory of integrable systems resulting in the
invariant Pohlmeyer Charges in order to set up the general representation
theory (superselection theory) for the closed bosonic quantum string on flat
target space. While we do not solve the, expectedly, rich representation theory
completely, we present a, to the best of our knowledge new, non -- trivial
solution to the representation problem. This solution exists 1. for any target
space dimension, 2. for Minkowski signature of the target space, 3. without
tachyons, 4. manifestly ghost -- free (no negative norm states), 5. without
fixing a worldsheet or target space gauge, 6. without (Virasoro) anomalies
(zero central charge), 7. while preserving manifest target space Poincar\'e
invariance and 8. without picking up UV divergences. The existence of this
stable solution is exciting because it raises the hope that among all the
solutions to the representation problem (including fermionic degrees of
freedom) we find stable, phenomenologically acceptable ones in lower
dimensional target spaces, possibly without supersymmetry, that are much
simpler than the solutions that arise via compactification of the standard Fock
representation of the string. Moreover, these new representations could solve
some of the major puzzles of string theory such as the cosmological constant
problem. The solution presented in this paper exploits the flatness of the
target space in several important ways. In a companion paper we treat the more
complicated case of curved target spaces.Comment: 46 p., LaTex2e, no figure
Polymer quantization of the free scalar field and its classical limit
Building on prior work, a generally covariant reformulation of free scalar
field theory on the flat Lorentzian cylinder is quantized using Loop Quantum
Gravity (LQG) type `polymer' representations. This quantization of the {\em
continuum} classical theory yields a quantum theory which lives on a discrete
spacetime lattice. We explicitly construct a state in the polymer Hilbert space
which reproduces the standard Fock vacuum- two point functions for long
wavelength modes of the scalar field. Our construction indicates that the
continuum classical theory emerges under coarse graining. All our
considerations are free of the "triangulation" ambiguities which plague
attempts to define quantum dynamics in LQG. Our work constitutes the first
complete LQG type quantization of a generally covariant field theory together
with a semi-classical analysis of the true degrees of freedom and thus provides
a perfect infinite dimensional toy model to study open issues in LQG,
particularly those pertaining to the definition of quantum dynamics.Comment: 58 page
The Semiclassical Limit of Loop Quantum Cosmology
The continuum and semiclassical limits of isotropic, spatially flat loop
quantum cosmology are discussed, with an emphasis on the role played by the
Barbero-Immirzi parameter \gamma in controlling space-time discreteness. In
this way, standard quantum cosmology is shown to be the simultaneous limit
\gamma \to 0, j \to \infty of loop quantum cosmology. Here, j is a label of the
volume eigenvalues, and the simultaneous limit is technically the same as the
classical limit \hbar \to 0, l \to \infty of angular momentum in quantum
mechanics. Possible lessons for semiclassical states at the dynamical level in
the full theory of quantum geometry are mentioned.Comment: 10 page
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