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Session 8
Loop Quantum Gravity
Chair:
Jerzy Lewandowski (University of Warsaw, Poland)
Titles and Abstracts
Emanuele Alesci (University of Erlangen-Nürnberg, Germany)
Title: LQG Cosmology from the full LQG
Abstract: We present a new perspective on early cosmology based on Loop Quantum
Gravity. We use projected spinnetworks, coherent states and spinfoam tecniques, to
implement a quantum reduction of the full Kinematical Hilbert space of LQG, suitable
to descrive inhomogeneous cosmological models. Some preliminar results on the
solutions of the Scalar constraint of the reduced theory are also presented.
Benjamin Bahr (University of Cambridge, UK)
Title: Spin Foam Models: Towards diffeomorphism-invariant path integral measures
Abstract: The aim of this talk is to describe how Spin Foam Models can be used to
construct normalized Borel measure spaces that carry the action of a group of
diffeomorphisms of a manifold Diff(M). These measure spaces can have the
interpretation of a path integral for physical theories of connections, and in interesting
cases the constructed measure is invariant under Diff(M). We outline the construction,
give some easy examples, and comment on how the conditions for cylindrical
consistency of measures corresponds to Wilsonian renormalization group flow
equations. This construction could provide a framework for background-independent
renormalization, which is in particular of interest for constructing a theory of quantum
gravity.
Norbert Bodendorfer (University of Erlangen-Nuremberg, Germany)
Title: Towards loop quantum supergravity
Abstract: An introduction aimed at non-experts in loop quantum gravity will be given
into the recently developed generalization of loop quantum gravity to higher
dimensional supergravity. Possible applications will be discussed.
You Ding (Beijing Jiaotong University, China)
Title: The time-oriented boundary states and the Lorentzian-spinfoam correlation
functions
Abstract: A time-oriented semiclassical boundary state is introduced to calculate the
correlation function in the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam model.
The resulting semiclassical correlation function is shown to match with the one in
Regge calculus in a proper limit.
Bianca Dittrich (Perimeter Institute for Theoretical Physics, Canada)
Title: Coarse graining spin foam models: a tensor network approach
Abstract: Spin foams are microscopic models for quantum gravity and space time.
We discuss coarse graining methods to extract large scale physics from these model
and derive consistency conditions that these models should satisfy to be viable models
of gravity.
Jonathan Engle (Florida Atlantic University, USA)
Title: Plebanski sectors, orientation, and spin-foams
Abstract: Spin-foams are a path integral quantization of gravity which, since several
years now, remarkably has been shown to be compatible with canonical loop quantum
gravity. Spin-foams start from the Plebanski formulation, in which gravity is
recovered from a topological field theory, BF theory, by the imposition of constraints,
called simplicity constraints. These constraints, however, select not just one
gravitational sector, but two copies of the gravitational sector, as well as a degenerate
sector. Furthermore, within each copy of the gravitational sector, two possible
space-time orientations appear. In this talk, in addition to giving a brief introduction to
spin-foams, we clarify the meaning of the different Plebanski sectors and orientations,
show how one can remove the additional sectors, and discuss arguments in favor of
doing so.
Marc Geiller (APC-University Paris 7, France)
Title: A three-dimensional Holst-Plebanski spin foam (toy) model
Abstract: We introduce an action for three-dimensional gravity that mimics key
features of the four-dimensional Holst-Plebanski theory. In particular, the action
admits an extension with Barbero-Immirzi parameter, and its canonical structure
contains second class constraints. At the classical level, we discuss two variants of the
canonical analysis, and study the properties of the three-dimensional
Ashtekar-Barbero connection. Then we perform the spin foam quantization of the
theory, and emphasize the role of the secondary second class constraints. Finally, we
draw conclusions about the construction of four-dimensional spin foam models and
more generally about the agreement between the canonical and covariant
quantizations
Hal Haggard (Centre de Physique Theorique de Luminy, France)
Title: Pentahedral Volume, Chaos, and Quantum Gravity
Abstract: The space of convex polyhedra can be given a dynamical structure.
Exploiting this dynamics we have performed a Bohr-Sommerfeld quantization of the
volume of a tetrahedral grain of space, which is in excellent agreement with loop
gravity. Here we present investigations of the volume of a 5-faced convex polyhedron.
We give for the first time a constructive method for finding these polyhedra given
their face areas and normals to the faces and find an explicit formula for the volume.
This results in new information about cylindrical consistency in loop gravity and a
couple of surprises about polyhedra. In particular, we are interested in discovering
whether the evolution generated by this volume is chaotic or integrable as this will
impact the interpretation of the spin network basis in loop gravity.
Frank Hellmann (Albert Einstein Institute, Germany)
Title: Wave Front Set analysis of EPRL type Spin Foam models
Abstract: I show how to use tools from microlocal analysis in order to understand the
asymptotic dynamics of spin foam models. Using these tools it is shown that the PRL
model suffers a flatness problem, and how to modify the model in order to resolve this
issue.
Wojciech Kaminski (Albert Einstein Institute, Germany)
Title: Coherent states and 6j symbols' asymptotics
Abstract: Coherent states proved to be useful both in defining spin foam models of
Quantum Gravity as well as in deriving their asymptotic limits. The method of
coherent states combined with stationary point analysis gives nice geometric
interpretation of contributions to asymptotic expansion and dominating phase of each
term. It is, however, very inefficient in providing full expansion due to problems with
computation of the Hessian determinant. Even in the case of 6j symbols where
Ponzano-Regge formula is well known, it was not obtained this way so far. By the
slight modification of the method we circumvented the problem. We are able to prove
conjectured alternating cos/sin form of the full asymptotic expansion, as well as
derive different form of the next to leading order term. The latest can be obtained by a
symmetric recursion relation similar to proposed by Bonzom-Livine but applicable to
6j symbol itself not its square. Our method works both in 3D euclidean and lorentzian
case.
Marcin Kisielowski (University of Warsaw, Poland)
Title: Spin Foams contributing in first order of vertex expansion to the Dipole
Cosmology transition amplitude
Abstract: In this talk we will present a general method for finding all foams with
given boundary and given number of internal vertices. We will apply the method to
the Dipole Cosmology model and find all spin foams contributing to the transition
amplitude in first order of vertex expansion.
Yongge Ma (Beijing Normal University, China)
Title: Connection Dynamics of Scalar-Tensor Theories and Their Loop Quantization
Abstract: The successful background-independent quantization of loop quantum
gravity (LQG) relies on the key observation that classical general relativity (GR) can
be cast into the connection-dynamical formalism with the structure group of $SU(2)$.
Due to this particular formalism, LQG was generally considered as a quantization
scheme that applies only to GR. Our work shows that the nonperturbative
quantization procedure of LQG can be extended to a rather general class of
4-dimensional metric theories of gravity, which have received increased attention
recently due to motivations coming form cosmology and astrophysics. I will introduce
how to reformulate the 4-dimensional scalar-tensor theories of gravity, including
$f(R)$ theories, into connection-dynamical formalism with real $SU(2)$ connections
as configuration variables. The Hamiltonian formalism marks off two sectors of the
theories by the coupling parameter $\omega(\phi)$. In the sector of
$\omega(\phi)=-\frac{3}{2}$, the feasible theories are restricted and a new primary
constraint generating conformal transformations of spacetime is obtained, while in the
other sector of $\omega(\phi)\neq-\frac{3}{2}$, the canonical structure and constraint
algebra of the theories are similar to those of general relativity coupled with a scalar
field. Both sectors can be cast into connection dynamics by canonical transformations.
Through the connection dynamical formalisms, I will further outline the
nonpertubative canonical quantization of the scalar-tensor theories by extending the
loop quantization scheme of GR.
Wolfgang Wieland (Universite de la Mediterranee (Marseille), France)
Title: The twistorial structure of spinfoam transistion amplitudes
Abstract: The EPRL spinfoam model is a proposal to define transition amplitudes for
loop quantum gravity. Although its semiclassical properties are well understood little
is known how the model can actually be derived from first principles. In this talk I
will sketch a proof built upon the twistorial framework of loop quantum gravity. I will
introduce a gauge-fixed integration measure on twistor space, study the quantum
states on the boundary, solve the reality conditions, rewrite the classical action in
terms of twistors, in order to then define a path integral. The integral can be
performed explicitly, and reproduces the EPRL vertex amplitude. It fixes the face
amplitude too, the correct form of which has always been a matter of debate. The
formalism also allows to study the curvature tensor and to decompose it into its
irreducible components, including the Weyl spinor and the torsion parts.
Mingyi Zhang (Aix-Marseille Universite, France)
Title: Asymptotic Behavior of Spinfoam Amplitude
Abstract: We give the detail analysis of the asymptotic behavior of EPRL spin foam
model. The asymptotics of spin foam amplitude is totally controlled by its critical
configurations. Using critical configurations we can reconstruct the classical geometry.
We show that spin foam goes back to Palatini-Regge gravity when we take large spin
limit.