24 research outputs found
Intertwiner dynamics in the flipped vertex
We continue the semiclassical analysis, started in a previous paper, of the
intertwiner sector of the flipped vertex spinfoam model. We use independently
both a semi-analytical and a purely numerical approach, finding the correct
behavior of wave packet propagation and physical expectation values. In the
end, we show preliminary results about correlation functions.Comment: 12 pages, 7 figure
Asymptotics of LQG fusion coefficients
The fusion coefficients from SO(3) to SO(4) play a key role in the definition
of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we
give a simple analytic formula of the EPRL fusion coefficients. We study the
large spin asymptotics and show that they map SO(3) semiclassical intertwiners
into semiclassical intertwiners. This non-trivial
property opens the possibility for an analysis of the semiclassical behavior of
the model.Comment: 14 pages, minor change
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
The EPRL intertwiners and corrected partition function
Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the
simplicity constraint? What is a complete form of the partition function
written in terms of this parametrization? We prove that the EPRL map is
injective for n-valent vertex in case when it is a map from SO(3) into
SO(3)xSO(3) representations. We find, however, that the EPRL map is not
isometric. In the consequence, in order to be written in a SU(2) amplitude
form, the formula for the partition function has to be rederived. We do it and
obtain a new, complete formula for the partition function. The result goes
beyond the SU(2) spin-foam models framework.Comment: RevTex4, 15 pages, 5 figures; theorem of injectivity of EPRL map
correcte
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
The kernel and the injectivity of the EPRL map
In this paper we prove injectivity of the EPRL map for |\gamma|<1, filling
the gap of our previous paper.Comment: 17 pages, 3 figure
Spinning Loop Black Holes
In this paper we construct four Kerr-like spacetimes starting from the loop
black hole Schwarzschild solutions (LBH) and applying the Newman-Janis
transformation. In previous papers the Schwarzschild LBH was obtained replacing
the Ashtekar connection with holonomies on a particular graph in a
minisuperspace approximation which describes the black hole interior. Starting
from this solution, we use a Newman-Janis transformation and we specialize to
two different and natural complexifications inspired from the complexifications
of the Schwarzschild and Reissner-Nordstrom metrics. We show explicitly that
the space-times obtained in this way are singularity free and thus there are no
naked singularities. We show that the transformation move, if any, the
causality violating regions of the Kerr metric far from r=0. We study the
space-time structure with particular attention to the horizons shape. We
conclude the paper with a discussion on a regular Reissner-Nordstrom black hole
derived from the Schwarzschild LBH and then applying again the Newmann-Janis
transformation.Comment: 18 pages, 18 figure
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
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
We study the large-j asymptotics of the Euclidean EPRL/FK spin foam amplitude
on a 4d simplicial complex with arbitrary number of simplices. We show that for
a critical configuration (j_f, g_{ve}, n_{ef}) in general, there exists a
partition of the simplicial complex into three regions: Non-degenerate region,
Type-A degenerate region and Type-B degenerate region. On both the
non-degenerate and Type-A degenerate regions, the critical configuration
implies a non-degenerate Euclidean geometry, while on the Type-B degenerate
region, the critical configuration implies a vector geometry. Furthermore we
can split the Non-degenerate and Type-A regions into sub-complexes according to
the sign of Euclidean oriented 4-simplex volume. On each sub-complex, the spin
foam amplitude at critical configuration gives a Regge action that contains a
sign factor sgn(V_4(v)) of the oriented 4-simplices volume. Therefore the Regge
action reproduced here can be viewed as a discretized Palatini action with
on-shell connection. The asymptotic formula of the spin foam amplitude is given
by a sum of the amplitudes evaluated at all possible critical configurations,
which are the products of the amplitudes associated to different type of
geometries.Comment: 27 pages, 5 figures, references adde
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