12 research outputs found
Physical boundary state for the quantum tetrahedron
We consider stability under evolution as a criterion to select a physical
boundary state for the spinfoam formalism. As an example, we apply it to the
simplest spinfoam defined by a single quantum tetrahedron and solve the
associated eigenvalue problem at leading order in the large spin limit. We show
that this fixes uniquely the free parameters entering the boundary state.
Remarkably, the state obtained this way gives a correlation between edges which
runs at leading order with the inverse distance between the edges, in agreement
with the linearized continuum theory. Finally, we give an argument why this
correlator represents the propagation of a pure gauge, consistently with the
absence of physical degrees of freedom in 3d general relativity.Comment: 20 pages, 6 figure
Numerical indications on the semiclassical limit of the flipped vertex
We introduce a technique for testing the semiclassical limit of a quantum
gravity vertex amplitude. The technique is based on the propagation of a
semiclassical wave packet. We apply this technique to the newly introduced
"flipped" vertex in loop quantum gravity, in order to test the intertwiner
dependence of the vertex. Under some drastic simplifications, we find very
preliminary, but surprisingly good numerical evidence for the correct classical
limit.Comment: 4 pages, 8 figure
Second-order amplitudes in loop quantum gravity
We explore some second-order amplitudes in loop quantum gravity. In
particular, we compute some second-order contributions to diagonal components
of the graviton propagator in the large distance limit, using the old version
of the Barrett-Crane vertex amplitude. We illustrate the geometry associated to
these terms. We find some peculiar phenomena in the large distance behavior of
these amplitudes, related with the geometry of the generalized triangulations
dual to the Feynman graphs of the corresponding group field theory. In
particular, we point out a possible further difficulty with the old
Barrett-Crane vertex: it appears to lead to flatness instead of Ricci-flatness,
at least in some situations. The observation raises the question whether this
difficulty remains with the new version of the vertex.Comment: 22 pages, 18 figure
Spinfoams in the holomorphic representation
We study a holomorphic representation for spinfoams. The representation is
obtained via the Ashtekar-Lewandowski-Marolf-Mour\~ao-Thiemann coherent state
transform. We derive the expression of the 4d spinfoam vertex for Euclidean and
for Lorentzian gravity in the holomorphic representation. The advantage of this
representation rests on the fact that the variables used have a clear
interpretation in terms of a classical intrinsic and extrinsic geometry of
space. We show how the peakedness on the extrinsic geometry selects a single
exponential of the Regge action in the semiclassical large-scale asymptotics of
the spinfoam vertex.Comment: 10 pages, 1 figure, published versio
LQG propagator: III. The new vertex
In the first article of this series, we pointed out a difficulty in the
attempt to derive the low-energy behavior of the graviton two-point function,
from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex
amplitude. Here we show that this difficulty disappears when using the
corrected vertex amplitude recently introduced in the literature. In
particular, we show that the asymptotic analysis of the new vertex amplitude
recently performed by Barrett, Fairbairn and others, implies that the vertex
has precisely the asymptotic structure that, in the second article of this
series, was indicated as the key necessary condition for overcoming the
difficulty.Comment: 9 page
Euclidean three-point function in loop and perturbative gravity
We compute the leading order of the three-point function in loop quantum
gravity, using the vertex expansion of the Euclidean version of the new spin
foam dynamics, in the region of gamma<1. We find results consistent with Regge
calculus in the limit gamma->0 and j->infinity. We also compute the tree-level
three-point function of perturbative quantum general relativity in position
space, and discuss the possibility of directly comparing the two results.Comment: 16 page
Many-nodes/many-links spinfoam: the homogeneous and isotropic case
I compute the Lorentzian EPRL/FK/KKL spinfoam vertex amplitude for regular
graphs, with an arbitrary number of links and nodes, and coherent states peaked
on a homogeneous and isotropic geometry. This form of the amplitude can be
applied for example to a dipole with an arbitrary number of links or to the
4-simplex given by the compete graph on 5 nodes. All the resulting amplitudes
have the same support, independently of the graph used, in the large j (large
volume) limit. This implies that they all yield the Friedmann equation: I show
this in the presence of the cosmological constant. This result indicates that
in the semiclassical limit quantum corrections in spinfoam cosmology do not
come from just refining the graph, but rather from relaxing the large j limit.Comment: 8 pages, 4 figure
Loop quantum gravity: the first twenty five years
This is a review paper invited by the journal "Classical ad Quantum Gravity"
for a "Cluster Issue" on approaches to quantum gravity. I give a synthetic
presentation of loop gravity. I spell-out the aims of the theory and compare
the results obtained with the initial hopes that motivated the early interest
in this research direction. I give my own perspective on the status of the
program and attempt of a critical evaluation of its successes and limits.Comment: 24 pages, 3 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
Laplacians on discrete and quantum geometries
We extend discrete calculus for arbitrary (-form) fields on embedded
lattices to abstract discrete geometries based on combinatorial complexes. We
then provide a general definition of discrete Laplacian using both the primal
cellular complex and its combinatorial dual. The precise implementation of
geometric volume factors is not unique and, comparing the definition with a
circumcentric and a barycentric dual, we argue that the latter is, in general,
more appropriate because it induces a Laplacian with more desirable properties.
We give the expression of the discrete Laplacian in several different sets of
geometric variables, suitable for computations in different quantum gravity
formalisms. Furthermore, we investigate the possibility of transforming from
position to momentum space for scalar fields, thus setting the stage for the
calculation of heat kernel and spectral dimension in discrete quantum
geometries.Comment: 43 pages, 2 multiple figures. v2: discussion improved, references
added, minor typos correcte