Thursday parallel sessions (9 July) Loops 2015(adsbygoogle = window.adsbygoogle || []).push({});

Parallel Session: Foundations of Covariant LQG (Spin Foams)

Thursday, 14:30 - 16:00, Room: Seminar Room 5

Chair: Benjamin Bahr

The area-law sector of loop quantum gravity

14:30 - 15:00, Eugenio Bianchi (Penn State, USA)

In this talk I present a concrete realization of the conjecture that semiclassical states in quantum gravity satisfy an area law. In loop quantum gravity the entanglement entropy of a random spin-network state scales linearly with the volume of a region of space. I describe a class of spin-network states that are fully characterized by the expectation value and the 2-point correlation function of geometric observables. Such states are semiclassical, have non-vanishing graviton-graviton correlations, and satisfy the area law. The framework extends previous results about the black hole horizon entropy to all regions of space.

Area-law and its consequences for LQG

15:00 - 15:30, Antonino Marciano (Fudan University, China)

We will first comment on the importance of quantum entanglement entropy in characterizing semiclassical properties of quantum theories. We will then introduce techniques mutuated from quantum many-body theory in order to calculate entanglement in LQG, taking into account gauge invariance. In preparation for Mingyi Zhang seminar, we will present a one-link state that satisfies the area-law, and is a viable building block for constructing new semi-classical states in LQG. We will finally comment on the eigenvalues distribution for these newly found states.

Derivation of the area law in LQG

15:30 - 16:00, Mingyi ZHANG (Fudan University, China)

I will present a preliminary result on computing the entanglement entropy in the context of loop quantum gravity. The gauge invariance is concerned, and the area law can be obtained in the semi-classical limit and low energy limit of spin foam model. This talk follows Prof. Antonino Marciano's talk.

Parallel Session: Foundations of Canonical LQG

Thursday, 14:30 - 16:00, Room: Lecture Hall

Chair: Norbert Bodendorfer

Coherent States and Intertwiners

14:30 - 15:00, John Schliemann (University of Regensburg, Germany)

Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values of products of arbitrary operators within both oscillator coherent states and SU(2) coherent states. In particular, we generally prove that the energy fluctuations of an arbitrary Hamiltonian are in leading order entirely due to the time dependence of the classical variables. We apply our general results to the calculation of expectation values within coherent intertwiners in spin networks. For expectation values of rotationally invariant operators (and these are the only ones contributing) one finds here a subleading correction to the classical limit given in terms of universal (i.e. operator-independent) expansion coefficients which contain only geometric information about the network node and show an interesting formal analogy to classical inertia tensors of rigid bodies.

A stability criterion for coherent states

15:00 - 15:30, Antonia Zipfel (University of Warsaw, Poland)

Coherent states play an important role in the semiclassical analysis of a given quantum theory. In order to also study the semiclassical features of the dynamics it is necessary to construct a system of states that does not loose its semiclassical properties during the evolution. I will introduce and discuss a stability criterion for complexifier coherent states, which are used in LQG. It turns out that already for quantum mechanical system the introduced criterion is quite restrictive. However, there is a way to circumvent these restrictions by introducing action-angle coordinates. These mechanisms are potentially also applicable in symmetry reduced models such as LQC.

Typicality and local thermalisation in spin networks

15:30 - 16:00, Goffredo Chirco (CPT - AMU, France)

We investigate the notion of quantum typicality in spin networks, by applying the general approach proposed by Popescu, Short and Winter in 2006, in the context of LQG. In particular, we focus on a basic spin network building block consisting in a N-valent SU(2) intertwiner with fixed total spin, the equivalent of a space of convex polyhedra with N face and fixed total boundary area at the classical level. On the fixed-area subspace of the intertwiner, we study the reduced state associated to a small region of the boundary surface.

By exploiting the "concentration of measure phenomenon", we show how the distribution for such a state is highly peaked around the "thermal state" for almost all pure states of the global intertwiner. We obtain a Gibbs state written in terms of the area preserving generator of the U(N) group, the area having the role played by the energy in the standard canonical picture. Local thermalisation arises as the result of the degree of correlations between local state and environment.

We study the temperature of the local surface patch state and we confront the specific structure of correlations of our result with the previous derivations of a single link thermal state present in the literature.

Parallel Session: Isolated Horizons and Quantum Black Holes

Thursday, 14:30 - 16:00, Room: Seminar Room 4

Chair: Jonathan Engle

BF Theory Explanation of Isolated Horizon Entropy in Loop Quantum Gravity

14:30 - 15:00, Yongge Ma (Beijing Normal University, China)

We consider an isolated horizon as the inner boundary of a four-dimensional asymptotically flat spacetime region. Due to the isolated horizon condition, it turns out that in certain gauge the boundary degrees of freedom can be described by a SO(1,1) BF theory with sources. This

provides a new alternative approach to the usual one using Chern-Simons theory to study the black hole entropy. To count the microscopical degrees of freedom with the boundary BF theory, the entropy of the isolated horizon can also be calculated in the framework of loop quantum gravity. This approach is applicable in arbitrary dimensions of spacetime.

Neutron Star Masses : A Black Hole Entropic Perspective

15:00 - 15:30, Parthasarathi Majumdar (Ramakrishna Mission Vivekananda Univ, India)

This talk is motivated by the need to understand the observed absence of neutron stars heavier than 2 solar masses. Extant approaches to this involve an adaptation of Chandrasekhar’s ideas of a limiting mass for white dwarf stars, based on hydrostatic equilibrium, to situations where general relativity can no longer be ignored. We survey the complications that this might introduce to the already difficult problem of determining the equation of state of this superdense system as an essential part of hydrostatic equilibrium. We then describe an alternative perspective, still under construction, to this problem, based on certain results from the analysis of (quantum) black hole entropy and thermal stability. These results, derived from a non perturbative, background-independent formulation of canonical quantum gravity (Loop Quantum Gravity), will be discussed in some detail. Some attempts to incorporate entanglement entropy ideas into the construction are also to be discussed. The aim here is a formulation of the issue of neutron star instability in terms of the stability and growth of a nascent quantum horizon deep inside a collapsing neutron star. If this perspective works, this might be a first indirect evidence of quantum gravity playing an important role in the gravitational collapse of neutron stars.

Dilatonic black holes in LQG

15:30 - 16:00, Saeed Rastgoo (Universidad Autonoma Metropolitana, Mexico)

We review some of the more recent results about the dilatonic black holes in LQG. These include the singularity resolution in the CGHS model, derivation of a true local Hamiltonian in this generic class, to be used in reduced phase space methods, and the problem of access to the saddle point approximation in these systems, and how and if, one can overcome this issue using polymerization.

We will also briefly comment on some of the works in progress.

Parallel Session: Group Field Theory and Tensor Models

Thursday, 14:30 - 16:00, Room: Seminar Room 3

Chair: John Barrett

FRG approach for tensorial group field theory

14:30 - 15:00, Joseph Bengeloun (Max-Planck Institute, AEI, Germany)

The functional renormalization group approach for tensorial group field theory models will be introduced. Focusing on concrete examples, the peculiarities of the FRG method when applied to tensorial models will be then emphasized.

FRG methods for a tensorial group field theory on R

15:00 - 15:30, Riccardo Martini (Alma Mater Studiorum, University of Bologna, Italy)

I will present an application of Functional Renormalization Group methods to a rank 3 Tensorial Group Field Theory model endowed with phi^4 interaction and defined over three copies of R. This is the first renormalization analysis for TGFT's on non-compact groups. The model has non-Gaussian fixed points which suggest the existence of phase transitions in the IR regime.

Conservation laws in Group Field Theory

15:30 - 16:00, Alexander Kegeles (Albert Einstein Institute, Germany)

Group Field Theories are quantum field theories which perturbative description is strongly connected to spin foam models in Loop Quantum Gravity. On the other hand it was recently shown that already classical equations of motion of Group Field Theory can encode cosmological data. From this perspective a natural question arise: what are the fundamental implications to spin foams and/or cosmology of the general frame work of Group Field Theory. In this talk I am addressing the consequences of symmetries in Group Field Theory and show that for such theories the usual conservation equations have to be modified, which can lead to interesting results in applications to spin foams and cosmology.

Parallel Session: Foundations of Covariant LQG (Spin Foams)

Thursday, 16:30 - 18:00, Room: Seminar Room 5

Chair: Benjamin Bahr

On the observable algebra of local covariant effective field theories

16:30 - 17:00, Jose A. Zapata (Centro de Ciencias Matematicas UNAM, Mexico)

In previous work we developed a geometrical formalism for local covariant effective field theories: we developed a discrete version of the first jet bundle and a multisymplectic geometry in it. Here we describe aspects of the algebraic counterpart of the formalism. The approach follows the spirit of general boundary field theory.

Regge Quantum Gravity

17:00 - 17:30, Aleksandar Mikovic (Lusofona University, Portugal)

If we assume that the short-distance structure of the spacetime is a picewise linear manifold corresponding to a triangulation of a smooth manifold, then we can obtain a finite state-sum model which is a generalization of the Regge path integral for GR. By using the effective action approach we show how to compute the quantum corrections and how the diffeomorphism invariance appears. We also show how the model can solve the problem of the cosmological constant.

Spincube model of QG and connection to CDT

17:30 - 18:00, Marko Vojinovic (GFM Lisbon, Portugal)

Spincube model is a categorical generalization of spinfoam models, based on the Poincare 2-group. Its main advantage is the automatic and explicit presence of the tetrads as basic degrees of freedom, which simplifies the model and allows for seamless coupling of all matter fields. An additional unexpected property is that, if the simplicity constraint is enforced strongly, the model contains the Causal Dynamical Triangulations state-sum as its special case. This relationship between SC model and CDT is a novel result, and will be explained in detail, along with other interesting properties of the SC approach to QG.

Parallel Session: Foundations of Canonical LQG

Thursday, 16:30 - 18:00, Room: Lecture Hall

Chair: Norbert Bodendorfer

Correlations and entanglement in loop quantum gravity

16:30 - 16:55, Alexandre Feller (ENS LYON, France)

In a background independent context, correlations are essential to understand the emergence of geometry, locality and a metric to describe gravity. Typical kinematical states have trivial correlations but physical states are expected to have non trival ones, reproducing for instance the graviton propagator.

Another landmark of quantum gravity is black hole entropy and one of its interpretation as entanglement entropy.

What I wish to present here is a first investigation of those topics in loop quantum gravity with a quantum information and condensed matter perspective by constructing Ising and toric code types states and analysing their properties and structure, in particular which constraints they solve for the first and the area law for entanglement entropy for the second. Such a point of view has the potential to shed some lights on the coarse graining of spin networks and the dynamic of loop gravity.

Entangled spin network states

16:55 - 17:20, Lucas Hackl (IGC, Pennsylvania State University, USA)

We present a class of entangled spin network states that are labeled by symplectic matrices and are generated via unitary transformations of the Ashtekar-Lewandowski vacuum. We show that the entanglement entropy between a subgraph and its complement can be calculated analytically as a function of the symplectic matrix labeling the state. In particular, we identify states whose entanglement entropy satisfies an area law. Projecting these states onto the kinematical Hilbert space provides a new candidate for highly entangled semi-classical states.

[based on work with Eugenio Bianchi & Nelson Yokomizo]

Tagged and Loopy Spin Networks

17:20 - 17:40, Christoph Charles (ENS Lyon, France)

In the context of the coarse-graining of loop quantum gravity, we introduce tagged and loopy spin networks, which generalize the standard spin network states to account explicitly for non-trivial curvature and torsion. We illustrate their use in some simple dynamical toy-models.

Statistical geometry: classical and quantum picture

17:40 - 18:00, Seramika Ariwahjoedi (CPT Marseille, France)

We study the statistical aspect of a system of quanta of space in both classical discrete and canonical loop quantum gravity picture, by proposing a coarse-graining and averaging procedure. This procedure could provide a link between theory described by finite degrees of freedom with a theory described by infinite degrees of freedom (its 'continuum limit'), both in the classical discrete and quantum picture.

Parallel Session: Quantum Gravity Phenomenology

Thursday, 16:30 - 18:00, Room: Seminar Room 3

Chair: Aurelien Barrau

Time, vacuum energy, and the cosmological constant

16:30 - 17:00, Viqar Husain (University of New Brunswick, Canada)

I review the assumptions (and their limitations) underlying the standard formulation of the cosmological constant problem. I then describe a link between the cosmological constant problem and the problem of time in quantum gravity. This arises by examining the relationship between the cosmological constant and vacuum energy in non-perturbative formulations of quantum gravity.

Dimensional reduction and scale-invariant primordial fluctuations

17:00 - 17:30, Giulia Gubitosi (Imperial College, UK)

I discuss the properties of vacuum fluctuations in general theories with modified dispersion relations which represent dimensional running at high energies, showing that in all theories which run to 2 dimensions in the ultraviolet the vacuum fluctuations, in this regime, are scale-invariant. This is true in flat space but also for “inside the horizon” modes in an expanding universe. I discuss the conditions upon the gravity theory for this scale-invariance to be preserved as the modes are frozen-in outside the horizon.

Planck scale modified dispersion relations in FRW spacetime

17:30 - 18:00, Giacomo Rosati (University of Wroclaw, Poland)

In recent years Planck scale modifications of the dispersion relation have been attracting increasing interest also from the viewpoint of possible applications in astrophysics and cosmology, where spacetime curvature cannot be neglected. Nonetheless the interplay between Planck scale effects and spacetime curvature is still poorly understood, particularly in cases where curvature is not constant. These challanges have been so far postponed by relying on an ansatz, first introduced by Jacob and Piran. We here propose a general strategy of analysis of the effects of modifications of dispersion relation in FRW spacetimes, applicable both to classical cases where the relativistic equivalence of frames is spoiled (preferred frame scenarios) and to the alternative possibility of theories that are fully relativistic but with relativistic laws deformed so that the modified dispersion relation is observer independent.

Parallel Session: Homogeneous and Hybrid Loop Quantum Cosmology (LQC)

Thursday, 16:30 - 18:00, Room: Seminar Room 4

Chair: Mercedes Martin-Benito

Loop quantization of the linearly polarized Gowdy T3 model with local rotational symmetry

16:30 - 17:00, Daniel Martín de Blas (Universidad Nacional Andrés Bello, Chile)

In this talk we will present a full quantization of the vacuum linearly polarized Gowdy three torus model with local rotational symmetry using the techniques of loop quantum gravity. First, we consider a redefinition of the constraints such that the new scalar constraint Poisson-commutes with itself. Then we apply of the canonical quantization program of loop quantum gravity. We identify the exact solutions of the constraints and the physical observables, and we construct the physical Hilbert space. It is remarkable that quantum spacetimes are free of singularities. Besides, new quantum observables (not present at the classical level) appear codifying partially the discretization of the geometry.

Approximate solutions of the hybrid quantum Gowdy model with FRW dynamics

17:00 - 17:30, Beatriz Elizaga de Navascués (Instituto de Estructura de la Materia - CSIC, Spain)

We construct approximate solutions of the hybrid quantum Gowdy cosmology with three-torus topology, linear polarization, and local rotational symmetry, in the presence of a massless scalar field. More specifically, we determine some families of states for which the complicated inhomogeneous and anisotropic Hamiltonian constraint operator of the Gowdy model is approximated by a much simpler one. Our quantum states follow the dynamics governed by this simpler constraint, while being at the same time also approximate solutions of the full Gowdy model. This is so thanks to the quantum correlations that the considered states present between the isotropic and anisotropic sectors of the model. Remarkably, this simpler constraint can be regarded as that of a flat Friedmann-Robertson-Walker universe filled with different kinds of perfect fluids and geometrically corrected by homogeneous and isotropic curvature-like terms. Therefore, our quantum states, which are intrinsically inhomogeneous, admit approximate homogeneous and isotropic effective descriptions similar to those considered in modified theories of gravity.

Extension of LQC to arbitrary spacetime dimensions

17:30 - 18:00, Xiangdong Zhang (FAU Erlangen, Germany)

Loop quantum cosmology(LQC) is the symmetric model of loop quantum gravity. In this talk, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogenous cosmological model in n+1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n+1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n+1 dimensional model and the 3+1 dimensional one.

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