We compute metric correlations in loop quantum gravity with the dynamics
defined by the new spin foam models. The analysis is done at the lowest order
in a vertex expansion and at the leading order in a large spin expansion. The
result is compared to the graviton propagator of perturbative quantum gravity.Comment: 28 page
In this paper we discuss a proposal of coherent states for Loop Quantum
Gravity. These states are labeled by a point in the phase space of General
Relativity as captured by a spin-network graph. They are defined as the gauge
invariant projection of a product over links of Hall's heat-kernels for the
cotangent bundle of SU(2). The labels of the state are written in terms of two
unit-vectors, a spin and an angle for each link of the graph. The heat-kernel
time is chosen to be a function of the spin. These labels are the ones used in
the Spin Foam setting and admit a clear geometric interpretation. Moreover, the
set of labels per link can be written as an element of SL(2,C). Therefore,
these states coincide with Thiemann's coherent states with the area operator as
complexifier. We study the properties of semiclassicality of these states and
show that, for large spins, they reproduce a superposition over spins of
spin-networks with nodes labeled by Livine-Speziale coherent intertwiners.
Moreover, the weight associated to spins on links turns out to be given by a
Gaussian times a phase as originally proposed by Rovelli.Comment: 15 page
We consider the elementary radiative-correction terms in loop quantum
gravity. These are a two-vertex "elementary bubble" and a five-vertex "ball";
they correspond to the one-loop self-energy and the one-loop vertex correction
of ordinary quantum field theory. We compute their naive degree of (infrared)
divergence.Comment: 11 pages, 3 figure
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
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