2,971 research outputs found
Holographic description of boundary gravitons in (3+1) dimensions
Gravity is uniquely situated in between classical topological field theories
and standard local field theories. This can be seen in the the quasi-local
nature of gravitational observables, but is nowhere more apparent than in
gravity's holographic formulation. Holography holds promise for simplifying
computations in quantum gravity. While holographic descriptions of
three-dimensional spacetimes and of spacetimes with a negative cosmological
constant are well-developed, a complete boundary description of zero curvature,
four-dimensional spacetime is not currently available. Building on previous
work in three-dimensions, we provide a new route to four-dimensional holography
and its boundary gravitons. Using Regge calculus linearized around a flat
Euclidean background with the topology of a solid hyper-torus, we obtain the
effective action for a dual boundary theory which describes the dynamics of the
boundary gravitons. Remarkably, in the continuum limit and at large radii this
boundary theory is local and closely analogous to the corresponding result in
three-dimensions. The boundary effective action has a degenerate kinetic term
that leads to singularities in the one-loop partition function that are
independent of the discretization. These results establish a rich boundary
dynamics for four-dimensional flat holography.Comment: 43 pages, 3 figures, 1 tabl
A perturbative approach to Dirac observables and their space-time algebra
We introduce a general approximation scheme in order to calculate gauge
invariant observables in the canonical formulation of general relativity. Using
this scheme we will show how the observables and the dynamics of field theories
on a fixed background or equivalently the observables of the linearized theory
can be understood as an approximation to the observables in full general
relativity. Gauge invariant corrections can be calculated up to an arbitrary
high order and we will explicitly calculate the first non--trivial correction.
Furthermore we will make a first investigation into the Poisson algebra between
observables corresponding to fields at different space--time points and
consider the locality properties of the observables.Comment: 23 page
Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order
In our companion paper we identified a complete set of manifestly
gauge-invariant observables for general relativity. This was possible by
coupling the system of gravity and matter to pressureless dust which plays the
role of a dynamically coupled observer. The evolution of those observables is
governed by a physical Hamiltonian and we derived the corresponding equations
of motion. Linear perturbation theory of those equations of motion around a
general exact solution in terms of manifestly gauge invariant perturbations was
then developed. In this paper we specialise our previous results to an FRW
background which is also a solution of our modified equations of motion. We
then compare the resulting equations with those derived in standard
cosmological perturbation theory (SCPT). We exhibit the precise relation
between our manifestly gauge-invariant perturbations and the linearly
gauge-invariant variables in SCPT. We find that our equations of motion can be
cast into SCPT form plus corrections. These corrections are the trace that the
dust leaves on the system in terms of a conserved energy momentum current
density. It turns out that these corrections decay, in fact, in the late
universe they are negligible whatever the value of the conserved current. We
conclude that the addition of dust which serves as a test observer medium,
while implying modifications of Einstein's equations without dust, leads to
acceptable agreement with known results, while having the advantage that one
now talks about manifestly gauge-invariant, that is measurable, quantities,
which can be used even in perturbation theory at higher orders.Comment: 51 pages, no figure
From the discrete to the continuous - towards a cylindrically consistent dynamics
Discrete models usually represent approximations to continuum physics.
Cylindrical consistency provides a framework in which discretizations mirror
exactly the continuum limit. Being a standard tool for the kinematics of loop
quantum gravity we propose a coarse graining procedure that aims at
constructing a cylindrically consistent dynamics in the form of transition
amplitudes and Hamilton's principal functions. The coarse graining procedure,
which is motivated by tensor network renormalization methods, provides a
systematic approximation scheme towards this end. A crucial role in this coarse
graining scheme is played by embedding maps that allow the interpretation of
discrete boundary data as continuum configurations. These embedding maps should
be selected according to the dynamics of the system, as a choice of embedding
maps will determine a truncation of the renormalization flow.Comment: 22 page
Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
In the two previous papers of this series we defined a new combinatorical
approach to quantum gravity, Algebraic Quantum Gravity (AQG). We showed that
AQG reproduces the correct infinitesimal dynamics in the semiclassical limit,
provided one incorrectly substitutes the non -- Abelean group SU(2) by the
Abelean group in the calculations. The mere reason why that
substitution was performed at all is that in the non -- Abelean case the volume
operator, pivotal for the definition of the dynamics, is not diagonisable by
analytical methods. This, in contrast to the Abelean case, so far prohibited
semiclassical computations. In this paper we show why this unjustified
substitution nevertheless reproduces the correct physical result: Namely, we
introduce for the first time semiclassical perturbation theory within AQG (and
LQG) which allows to compute expectation values of interesting operators such
as the master constraint as a power series in with error control. That
is, in particular matrix elements of fractional powers of the volume operator
can be computed with extremely high precision for sufficiently large power of
in the expansion. With this new tool, the non -- Abelean
calculation, although technically more involved, is then exactly analogous to
the Abelean calculation, thus justifying the Abelean analysis in retrospect.
The results of this paper turn AQG into a calculational discipline
Quantum versus Classical Dynamics in a driven barrier: the role of kinematic effects
We study the dynamics of the classical and quantum mechanical scattering of a
wave packet from an oscillating barrier. Our main focus is on the dependence of
the transmission coefficient on the initial energy of the wave packet for a
wide range of oscillation frequencies. The behavior of the quantum transmission
coefficient is affected by tunneling phenomena, resonances and kinematic
effects emanating from the time dependence of the potential. We show that when
kinematic effects dominate (mainly in intermediate frequencies), classical
mechanics provides very good approximation of quantum results. Moreover, in the
frequency region of optimal agreement between classical and quantum
transmission coefficient, the transmission threshold, i.e. the energy above
which the transmission coefficient becomes larger than a specific small
threshold value, is found to exhibit a minimum. We also consider the form of
the transmitted wave packet and we find that for low values of the frequency
the incoming classical and quantum wave packet can be split into a train of
well separated coherent pulses, a phenomenon which can admit purely classical
kinematic interpretation
Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
We develop a gauge invariant canonical perturbation scheme for perturbations
around symmetry reduced sectors in generally covariant theories, such as
general relativity. The central objects of investigation are gauge invariant
observables which encode the dynamics of the system. We apply this scheme to
perturbations around a homogeneous and isotropic sector (cosmology) of general
relativity. The background variables of this homogeneous and isotropic sector
are treated fully dynamically which allows us to approximate the observables to
arbitrary high order in a self--consistent and fully gauge invariant manner.
Methods to compute these observables are given. The question of backreaction
effects of inhomogeneities onto a homogeneous and isotropic background can be
addressed in this framework. We illustrate the latter by considering
homogeneous but anisotropic Bianchi--I cosmologies as perturbations around a
homogeneous and isotropic sector.Comment: 39 pages, 1 figur
Regge calculus from a new angle
In Regge calculus space time is usually approximated by a triangulation with
flat simplices. We present a formulation using simplices with constant
sectional curvature adjusted to the presence of a cosmological constant. As we
will show such a formulation allows to replace the length variables by 3d or 4d
dihedral angles as basic variables. Moreover we will introduce a first order
formulation, which in contrast to using flat simplices, does not require any
constraints. These considerations could be useful for the construction of
quantum gravity models with a cosmological constant.Comment: 8 page
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