920 research outputs found
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
Shape in an Atom of Space: Exploring quantum geometry phenomenology
A phenomenology for the deep spatial geometry of loop quantum gravity is
introduced. In the context of a simple model, an atom of space, it is shown how
purely combinatorial structures can affect observations. The angle operator is
used to develop a model of angular corrections to local, continuum flat-space
3-geometries. The physical effects involve neither breaking of local Lorentz
invariance nor Planck scale suppression, but rather reply on only the
combinatorics of SU(2) recoupling. Bhabha scattering is discussed as an example
of how the effects might be observationally accessible.Comment: 14 pages, 7 figures; v2 references adde
Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
A covariant spin-foam formulation of quantum gravity has been recently
developed, characterized by a kinematics which appears to match well the one of
canonical loop quantum gravity. In this paper we reconsider the implementation
of the constraints that defines the model. We define in a simple way the
boundary Hilbert space of the theory, introducing a slight modification of the
embedding of the SU(2) representations into the SL(2,C) ones. We then show
directly that all constraints vanish on this space in a weak sense. The
vanishing is exact (and not just in the large quantum number limit.) We also
generalize the definition of the volume operator in the spinfoam model to the
Lorentzian signature, and show that it matches the one of loop quantum gravity,
as does in the Euclidean case.Comment: 11 page
Complex Ashtekar variables and reality conditions for Holst's action
From the Holst action in terms of complex valued Ashtekar variables
additional reality conditions mimicking the linear simplicity constraints of
spin foam gravity are found. In quantum theory with the results of You and
Rovelli we are able to implement these constraints weakly, that is in the sense
of Gupta and Bleuler. The resulting kinematical Hilbert space matches the
original one of loop quantum gravity, that is for real valued Ashtekar
connection. Our result perfectly fit with recent developments of Rovelli and
Speziale concerning Lorentz covariance within spin-form gravity.Comment: 24 pages, 2 picture
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
The present paper studies the large-j asymptotics of the Lorentzian EPRL
spinfoam amplitude on a 4d simplicial complex with an arbitrary number of
simplices. The asymptotics of the spinfoam amplitude is determined by the
critical configurations. Here we show that, given a critical configuration in
general, there exists a partition of the simplicial complex into three type of
regions R_{Nondeg}, R_{Deg-A}, R_{Deg-B}, where the three regions are
simplicial sub-complexes with boundaries. The critical configuration implies
different types of geometries in different types of regions, i.e. (1) the
critical configuration restricted into R_{Nondeg} is degenerate of type-A in our definition of degeneracy, but implies
a nondegenerate discrete Euclidean geometry on R_{Deg-A}, (3) the critical
configuration restricted into R_{Deg-B} is degenerate of type-B, and implies a
vector geometry on R_{Deg-B}. With the critical configuration, we further make
a subdivision of the regions R_{Nondeg} and R_{Deg-A} into sub-complexes (with
boundary) according to their Lorentzian/Euclidean oriented 4-simplex volume
V_4(v), such that sgn(V_4(v)) is a constant sign on each sub-complex. Then in
the each sub-complex, the spinfoam amplitude at the critical configuration
gives the Regge action in Lorentzian or Euclidean signature respectively on
R_{Nondeg} or R_{Deg-A}. The Regge action reproduced here contains a sign
factor sgn(V_4(v)) of the oriented 4-simplex volume. Therefore the Regge action
reproduced here can be viewed a discretized Palatini action with on-shell
connection. Finally the asymptotic formula of the spinfoam 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: 54 pages, 2 figures, reference adde
A new look at loop quantum gravity
I describe a possible perspective on the current state of loop quantum
gravity, at the light of the developments of the last years. I point out that a
theory is now available, having a well-defined background-independent
kinematics and a dynamics allowing transition amplitudes to be computed
explicitly in different regimes. I underline the fact that the dynamics can be
given in terms of a simple vertex function, largely determined by locality,
diffeomorphism invariance and local Lorentz invariance. I emphasize the
importance of approximations. I list open problems.Comment: 15 pages, 5 figure
Simple model for quantum general relativity from loop quantum gravity
New progress in loop gravity has lead to a simple model of `general-covariant
quantum field theory'. I sum up the definition of the model in self-contained
form, in terms accessible to those outside the subfield. I emphasize its
formulation as a generalized topological quantum field theory with an infinite
number of degrees of freedom, and its relation to lattice theory. I list the
indications supporting the conjecture that the model is related to general
relativity and UV finite.Comment: 8 pages, 3 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
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 Plebanski sectors of the EPRL vertex
Modern spin-foam models of four dimensional gravity are based on a discrete
version of the Plebanski formulation. Beyond what is already in the
literature, we clarify the meaning of different Plebanski sectors in this
classical discrete model. We show that the linearized simplicity constraints
used in the EPRL and FK models are not sufficient to impose a restriction to a
single Plebanski sector, but rather, three Plebanski sectors are mixed. We
propose this as the reason for certain extra `undesired' terms in the
asymptotics of the EPRL vertex analyzed by Barrett et al. This explanation for
the extra terms is new and different from that sometimes offered in the
spin-foam literature thus far.Comment: 17 page
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