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Notable Loop gravity papers this quarter

  1. Oct 23, 2013 #1

    marcus

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    The fourth quarter 2013 has already seen an interesting bunch of Loop gravity research papers. I'll list a few and say why I think they are remarkable. Some make meaningful progress along established lines, while one or more others take an unexpected direction and are clearly exceptional. Highlights in the authors' abstracts are in blue, my comments on why the paper seems especially important are in green.

    http://arxiv.org/abs/1310.5996
    Quantum black holes in Loop Quantum Gravity
    Rodolfo Gambini, Javier Olmedo, Jorge Pullin
    (Submitted on 22 Oct 2013)
    We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and that the singularity inside black holes is resolved. Moreover, we consider an alternative quantization based on a slightly different kinematical Hilbert space. The ambiguity in kinematical spaces stems from how one treats the periodicity of one of the classical variables in these models. The corresponding physical Hilbert spaces solve the diffeomorphism and Hamiltonian constraint but their intrinsic structure is radically different depending on the kinematical Hilbert space one started from. In both cases there are quantum observables that do not have a classical counterpart. However, one can show that at the end of the day, by examining Dirac observables, both quantizations lead to the same physical predictions.
    20 pages

    Progress in showing that the Loop black hole does not develop a singularity. The authors published a result earlier this year in PRL which is now strengthened by showing that when one takes an alternate quantization route it again goes through and gives equivalent physics.

    http://arxiv.org/abs/1310.4795
    Chimera: A hybrid approach to numerical loop quantum cosmology
    Peter Diener, Brajesh Gupt, Parampreet Singh
    (Submitted on 17 Oct 2013)
    The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosing a hybrid spatial grid allowing the use of partial differential equations at large volumes, and with a simple change of geometrical coordinate, we obtain a surprising reduction in the computational cost. This scheme enables us to explore regimes which were so far unachievable for the isotropic model in LQC. Our approach also promises to significantly reduce the computational cost for numerical simulations in anisotropic LQC using high performance computing.
    39 pages, 15 figures

    Computer simulations of have played an important role in Loop cosmology especially since 2006---having been extensively used to check and confirm solvable equation models and verify the Big Bounce under increasingly general assumptions. More efficient code makes further generalization possible.

    http://arxiv.org/abs/1310.3362
    Deformation Operators of Spin Networks and Coarse-Graining
    Etera R. Livine
    (Submitted on 12 Oct 2013)
    In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop gravity, a necessary step is to understand the coarse-graining of these states in order to describe their relevant structure at various scales. Using the spinor network formalism to describe the phase space of loop gravity on a given graph, we focus on a bounded (connected) region of the graph and coarse-grain it to a single vertex using a gauge-fixing procedure. We discuss the ambiguities in the gauge-fixing procedure and their consequences for coarse-graining spin(or) networks. This allows to define the boundary deformations of that region in a gauge-invariant fashion and to identify the area preserving deformations as U(N) transformations similarly to the already well-studied case of a single intertwiner. The novelty is that the closure constraint is now relaxed and the closure defect interpreted as a local measure of the curvature inside the coarse-grained region. It is nevertheless possible to cancel the closure defect by a Lorentz boost. We further identify a Lorentz-invariant observable related to the area and closure defect, which we name "rest area". Its physical meaning remains an open issue.
    24 pages

    The paper explains a new coarsegrain proceedure to collapse a compact region of a spin(or) network with multiple vertices and edges down to a single point. A Fock-style Hilbert space is constructed at the remaining vertex which represents information condensed by the coarsening move. The reverse process of refinement is studied.

    http://arxiv.org/abs/1310.2174
    Radiative corrections to the EPRL-FK spinfoam graviton
    Aldo Riello
    (Submitted on 8 Oct 2013)
    I study the corrections engendered by the insertion of a "melon" graph in the bulk of the first-order spinfoam used for the graviton propagator. I find that these corrections are highly non-trivial and, in particular, that they concern those terms which disappear in the Bojowald-Bianchi-Magliaro-Perini limit of vanishing Barbero-Immirzi parameter at fixed area. This fact is the first realization of the often cited idea that the spinfoam amplitude receives higher order corrections under the refinement of the underlying two-complex.
    13 pages, 4 figures

    Riello's earlier paper this year dealt with spinfoam amplitude divergences which turned out to be at most logarithmic. He continues to make headway in studying details of the covariant Loop gravity path integral under refinement

    http://arxiv.org/abs/1310.1290
    Singularity avoidance in the hybrid quantization of the Gowdy model
    Paula Tarrío, Mikel Fernández Méndez, Guillermo A. Mena Marugán
    (Submitted on 4 Oct 2013)
    One of the most remarkable phenomena in Loop Quantum Cosmology is that, at least for homogeneous cosmological models, the Big Bang is replaced with a Big Bounce that connects our universe with a previous branch without passing through a cosmological singularity. The goal of this work is to study the existence of singularities in Loop Quantum Cosmology including inhomogeneities and check whether the behavior obtained in the purely homogeneous setting continues to be valid. With this aim, we focus our attention on the three-torus Gowdy cosmologies with linearly polarized gravitational waves and use effective dynamics to carry out the analysis. For this model, we prove that all the potential cosmological singularities are avoided, generalizing the results about resolution of singularities to this scenario with inhomogeneities. We also demonstrate that, if a bounce in the (Bianchi background) volume occurs, the inhomogeneities increase the value of this volume at the bounce with respect to its counterpart in the homogeneous case.
    11 pages, 2 figures

    Important to relax the requirement of inhomogeneity and extend the cosmological Big Bounce result to increasingly general cases.
     
  2. jcsd
  3. Oct 27, 2013 #2

    marcus

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    http://arxiv.org/abs/1310.6728
    Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
    Parampreet Singh, Edward Wilson-Ewing
    (Submitted on 24 Oct 2013)
    We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaitre-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaitre-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.
    34 pages

    A technically valuable paper. There are several ways to carry out the quantization in Loop cosmology. They make a comparative study of the main alternatives and arrive at a careful choice.
     
  4. Nov 1, 2013 #3

    marcus

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    http://arxiv.org/abs/1310.8654
    Why are the effective equations of loop quantum cosmology so accurate?
    Carlo Rovelli, Edward Wilson-Ewing
    (Submitted on 31 Oct 2013)
    We point out that the Heisenberg uncertainty relations vanish for non-compact spaces in loop quantum cosmology, thus explaining the surprising accuracy of the effective equations in describing the dynamics of sharply peaked wave packets. This underlines the fact that minisuperspace models ---where it is global variables that are quantized--- do not capture the local quantum fluctuations of the geometry.
    5 pages

    Underscores the need for Loop cosmology models that are not homogeneous and isotropic. Research on inhomogeneous and especially anisotropic models has recently become more common. The paper motivates treating cosmology in the context of the full quantum theory.

    http://arxiv.org/abs/1310.7786
    Group field theory as the 2nd quantization of Loop Quantum Gravity
    Daniele Oriti
    (Submitted on 29 Oct 2013)
    We construct a 2nd quantized reformulation of canonical Loop Quantum Gravity at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the Group Field Theory formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.
    23 pages, 5 figures

    GFT offers a convenient alternative way to look at Loop gravity that has already played a significant part in its development. The paper provides review, summary, pointers to new research directions, and outlook for an increased role.

    http://arxiv.org/abs/1310.6728
    Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
    Parampreet Singh, Edward Wilson-Ewing
    (Submitted on 24 Oct 2013)
    We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaitre-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaitre-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.
    34 pages

    A technically valuable paper. There are several ways to carry out the quantization in Loop cosmology. The authors make a comparative study of the main alternatives and arrive at a reasoned choice.

    http://arxiv.org/abs/1310.5996
    Quantum black holes in Loop Quantum Gravity
    Rodolfo Gambini, Javier Olmedo, Jorge Pullin
    (Submitted on 22 Oct 2013)
    We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and that the singularity inside black holes is resolved. Moreover, we consider an alternative quantization based on a slightly different kinematical Hilbert space. The ambiguity in kinematical spaces stems from how one treats the periodicity of one of the classical variables in these models. The corresponding physical Hilbert spaces solve the diffeomorphism and Hamiltonian constraint but their intrinsic structure is radically different depending on the kinematical Hilbert space one started from. In both cases there are quantum observables that do not have a classical counterpart. However, one can show that at the end of the day, by examining Dirac observables, both quantizations lead to the same physical predictions.
    20 pages

    Progress in showing that the Loop black hole does not develop a singularity. The authors published a result earlier this year in PRL which is now strengthened by showing that when one takes an alternate quantization route it again goes through and gives equivalent physics.

    http://arxiv.org/abs/1310.4795
    Chimera: A hybrid approach to numerical loop quantum cosmology
    Peter Diener, Brajesh Gupt, Parampreet Singh
    (Submitted on 17 Oct 2013)
    The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosing a hybrid spatial grid allowing the use of partial differential equations at large volumes, and with a simple change of geometrical coordinate, we obtain a surprising reduction in the computational cost. This scheme enables us to explore regimes which were so far unachievable for the isotropic model in LQC. Our approach also promises to significantly reduce the computational cost for numerical simulations in anisotropic LQC using high performance computing.
    39 pages, 15 figures

    Computer simulations of have played an important role in Loop cosmology especially since 2006---having been extensively used to check and confirm solvable equation models and verify the Big Bounce under increasingly general assumptions. More efficient code makes possible further generalization to a broader range of cases.

    http://arxiv.org/abs/1310.3362
    Deformation Operators of Spin Networks and Coarse-Graining
    Etera R. Livine
    (Submitted on 12 Oct 2013)
    In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop gravity, a necessary step is to understand the coarse-graining of these states in order to describe their relevant structure at various scales. Using the spinor network formalism to describe the phase space of loop gravity on a given graph, we focus on a bounded (connected) region of the graph and coarse-grain it to a single vertex using a gauge-fixing procedure. We discuss the ambiguities in the gauge-fixing procedure and their consequences for coarse-graining spin(or) networks. This allows to define the boundary deformations of that region in a gauge-invariant fashion and to identify the area preserving deformations as U(N) transformations similarly to the already well-studied case of a single intertwiner. The novelty is that the closure constraint is now relaxed and the closure defect interpreted as a local measure of the curvature inside the coarse-grained region. It is nevertheless possible to cancel the closure defect by a Lorentz boost. We further identify a Lorentz-invariant observable related to the area and closure defect, which we name "rest area". Its physical meaning remains an open issue.
    24 pages

    The paper explains a new coarsegrain procedure to collapse a compact region of a spin(or) network with multiple vertices and edges down to a single point. A Fock-style Hilbert space is constructed at the remaining vertex which represents information condensed by the coarsening move. The reverse process of refinement is studied.

    http://arxiv.org/abs/1310.2174
    Radiative corrections to the EPRL-FK spinfoam graviton
    Aldo Riello
    (Submitted on 8 Oct 2013)
    I study the corrections engendered by the insertion of a "melon" graph in the bulk of the first-order spinfoam used for the graviton propagator. I find that these corrections are highly non-trivial and, in particular, that they concern those terms which disappear in the Bojowald-Bianchi-Magliaro-Perini limit of vanishing Barbero-Immirzi parameter at fixed area. This fact is the first realization of the often cited idea that the spinfoam amplitude receives higher order corrections under the refinement of the underlying two-complex.
    13 pages, 4 figures

    Riello's earlier paper this year dealt with spinfoam amplitude divergences which turned out to be at most logarithmic. He continues to make headway in studying details of the covariant Loop gravity path integral under refinement

    http://arxiv.org/abs/1310.1290
    Singularity avoidance in the hybrid quantization of the Gowdy model
    Paula Tarrío, Mikel Fernández Méndez, Guillermo A. Mena Marugán
    (Submitted on 4 Oct 2013)
    One of the most remarkable phenomena in Loop Quantum Cosmology is that, at least for homogeneous cosmological models, the Big Bang is replaced with a Big Bounce that connects our universe with a previous branch without passing through a cosmological singularity. The goal of this work is to study the existence of singularities in Loop Quantum Cosmology including inhomogeneities and check whether the behavior obtained in the purely homogeneous setting continues to be valid. With this aim, we focus our attention on the three-torus Gowdy cosmologies with linearly polarized gravitational waves and use effective dynamics to carry out the analysis. For this model, we prove that all the potential cosmological singularities are avoided, generalizing the results about resolution of singularities to this scenario with inhomogeneities. We also demonstrate that, if a bounce in the (Bianchi background) volume occurs, the inhomogeneities increase the value of this volume at the bounce with respect to its counterpart in the homogeneous case.
    11 pages, 2 figures

    Important to relax the requirement of inhomogeneity and extend the cosmological Big Bounce result to increasingly general cases.
     
    Last edited: Nov 1, 2013
  5. Nov 5, 2013 #4

    marcus

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    http://arxiv.org/abs/1311.0186
    Twistor relative locality
    Lee Smolin
    (Submitted on 1 Nov 2013)
    We present a version of relative locality based on the geometry of twistor space. This can also be thought of as a new kind of deformation of twistor theory based on the construction of a bundle of twistor spaces over momentum space. Locality in space-time is emergent and is deformed in a precise way when a connection on that bundle is non-flat. This gives a precise and controlled meaning to Penrose's hypothesis that quantum gravity effects will deform twistor space in such a way as to maintain causality and relativistic invariance while weakening the notion that interactions take place at points in spacetime.
    10 pages

    Spacetime is an abstraction and one that Nature might conceivably disagree with. Objectively, we know what happens in our immediate vicinity, which includes exchanging messages with observers elsewhere. Unlikely as it seems, spacetime as a collective abstraction reconciling everybody's local experiences could be vulnerable. Also QG seems to be morphing in the direction of spinor/twistor formulations, see 2013 papers by e.g. Livine, Wieland. I am in doubt about this and want to hear others' opinions.
     
    Last edited: Nov 6, 2013
  6. Nov 15, 2013 #5

    marcus

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    Updated listing. These 4th quarter papers may be on the upcoming poll.

    http://arxiv.org/abs/1311.3279
    Null twisted geometries
    Simone Speziale, Mingyi Zhang
    (Submitted on 13 Nov 2013)
    We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is naturally decomposed into a conformal metric and scale factors, forming locally conjugate pairs. Proper action-angle variables on the gauge-invariant phase space are described by the eigenvectors of the Laplacian of the dual graph. We also identify the variables of the phase space amenable to characterize the extrinsic geometry of the foliation. Finally, we quantise the phase space and its algebra using Dirac's algorithm, obtaining a notion of spin networks for null hypersurfaces. Such spin networks are labelled by SO(2) quantum numbers, and are embedded non-trivially in the unitary, infinite-dimensional irreducible representations of the Lorentz group.
    22 pages, 3 figures

    "... step towards our goal of understanding the dynamics of null surfaces in LQG. .. From the possibility of including dynamical effects in black hole physics, describing the near horizon quantum geometry, to the use in the constraint-free formulation of GR on null hypersurfaces. To that end, many nontrivial steps are needed. First of all, our analysis needs to be complemented with a continuum canonical analysis of the Plebanski action on a null hypersurface [27]. ... one should also investigate what type of spin foams can support the boundary data here studied. We expect this line of research to bring new tools and results to LQG, and to show us how deep the connection with twistors goes."

    Reference [27] is to work said "to appear" by Speziale and Alexandrov


    http://arxiv.org/abs/1311.1798
    Topological lattice field theories from intertwiner dynamics
    Bianca Dittrich, Wojciech Kaminski
    (Submitted on 7 Nov 2013)
    We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and instances of triangulation invariant, that is, topological, models inside this class. These models give examples for symmetry protected topologically ordered 1D quantum phases with quantum group symmetries. Furthermore the models provide realizations for anyon condensation into a new effective vacuum. We explain the relevance of our findings for the problem of identifying the continuum limit of spin foam and spin net models.
    35+9 pages

    Strongly motivated in the paper's introduction (which see.) The brief excerpts here can't do it justice: "...The models, and the investigations of their fixed point structure under coarse graining, are motivated by a research program to understand the phase diagram and continuum limit of spin foam models [1],... There are however several additional tantalizing connections to quantum gravity as well as other areas of physics. One is the theory of anyon condensation [4, 5], for which we provide Hamiltonians. The condensate states appear as ground states of these Hamiltonians and are given by the topological models. ...
    Besides these topics there are other reasons why these models and its fixed points are of interest for quantum gravity:
    • For the construction of spin foam models itself, in particular the intertwiners defining these models. The fixed points of our models define naturally intertwiners for spin foam vertices of arbitrary valency...
    • ...spin net models,..
    • ...geometrical interpretation of the underlying variables…"


    http://arxiv.org/abs/1310.7786
    Group field theory as the 2nd quantization of Loop Quantum Gravity
    Daniele Oriti
    (Submitted on 29 Oct 2013)
    We construct a 2nd quantized reformulation of canonical Loop Quantum Gravity at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the Group Field Theory formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.
    23 pages, 5 figures

    GFT offers a convenient alternative way to look at Loop gravity that has already played a significant part in its development. The paper provides review, summary, pointers to new research directions, and outlook for an increased role.

    http://arxiv.org/abs/1310.6728
    Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
    Parampreet Singh, Edward Wilson-Ewing
    (Submitted on 24 Oct 2013)
    We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaitre-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaitre-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.
    34 pages

    A technically valuable paper. There are several ways to carry out the quantization in Loop cosmology. The authors make a comparative study of the main alternatives and arrive at a reasoned choice.

    http://arxiv.org/abs/1310.5996
    Quantum black holes in Loop Quantum Gravity
    Rodolfo Gambini, Javier Olmedo, Jorge Pullin
    (Submitted on 22 Oct 2013)
    We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and that the singularity inside black holes is resolved. Moreover, we consider an alternative quantization based on a slightly different kinematical Hilbert space. The ambiguity in kinematical spaces stems from how one treats the periodicity of one of the classical variables in these models. The corresponding physical Hilbert spaces solve the diffeomorphism and Hamiltonian constraint but their intrinsic structure is radically different depending on the kinematical Hilbert space one started from. In both cases there are quantum observables that do not have a classical counterpart. However, one can show that at the end of the day, by examining Dirac observables, both quantizations lead to the same physical predictions.
    20 pages

    The Loop black hole does not develop a singularity. The authors published a result earlier this year in PRL which is now strengthened by showing that when one takes an alternate quantization route it again goes through and gives equivalent physics.

    http://arxiv.org/abs/1310.4795
    Chimera: A hybrid approach to numerical loop quantum cosmology
    Peter Diener, Brajesh Gupt, Parampreet Singh
    (Submitted on 17 Oct 2013)
    The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosing a hybrid spatial grid allowing the use of partial differential equations at large volumes, and with a simple change of geometrical coordinate, we obtain a surprising reduction in the computational cost. This scheme enables us to explore regimes which were so far unachievable for the isotropic model in LQC. Our approach also promises to significantly reduce the computational cost for numerical simulations in anisotropic LQC using high performance computing.
    39 pages, 15 figures

    Computer simulations of have played an important role in Loop cosmology especially since 2006---having been extensively used to check and confirm solvable equation models and verify the Big Bounce under increasingly general assumptions. More efficient code makes possible further generalization to a broader range of cases.

    http://arxiv.org/abs/1310.3362
    Deformation Operators of Spin Networks and Coarse-Graining
    Etera R. Livine
    (Submitted on 12 Oct 2013)
    In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop gravity, a necessary step is to understand the coarse-graining of these states in order to describe their relevant structure at various scales. Using the spinor network formalism to describe the phase space of loop gravity on a given graph, we focus on a bounded (connected) region of the graph and coarse-grain it to a single vertex using a gauge-fixing procedure. We discuss the ambiguities in the gauge-fixing procedure and their consequences for coarse-graining spin(or) networks. This allows to define the boundary deformations of that region in a gauge-invariant fashion and to identify the area preserving deformations as U(N) transformations similarly to the already well-studied case of a single intertwiner. The novelty is that the closure constraint is now relaxed and the closure defect interpreted as a local measure of the curvature inside the coarse-grained region. It is nevertheless possible to cancel the closure defect by a Lorentz boost. We further identify a Lorentz-invariant observable related to the area and closure defect, which we name "rest area". Its physical meaning remains an open issue.
    24 pages

    The paper explains a new coarsegrain procedure to collapse a compact region of a spin(or) network with multiple vertices and edges down to a single point. A Fock-style Hilbert space is constructed at the remaining vertex which represents information condensed by the coarsening move. The reverse process of refinement is studied.

    http://arxiv.org/abs/1310.2174
    Radiative corrections to the EPRL-FK spinfoam graviton
    Aldo Riello
    (Submitted on 8 Oct 2013)
    I study the corrections engendered by the insertion of a "melon" graph in the bulk of the first-order spinfoam used for the graviton propagator. I find that these corrections are highly non-trivial and, in particular, that they concern those terms which disappear in the Bojowald-Bianchi-Magliaro-Perini limit of vanishing Barbero-Immirzi parameter at fixed area. This fact is the first realization of the often cited idea that the spinfoam amplitude receives higher order corrections under the refinement of the underlying two-complex.
    13 pages, 4 figures

    Riello's earlier paper this year dealt with spinfoam amplitude divergences which turned out to be at most logarithmic. He continues to make headway in studying details of the covariant Loop gravity path integral under refinement

    http://inspirehep.net/search?ln=en&...search=Search&sf=&so=d&rm=citation&rg=25&sc=0
     
    Last edited: Nov 16, 2013
  7. Nov 22, 2013 #6

    marcus

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    This is a third quarter paper that fell through the cracks. We failed to spot it in September when it came out. Noticed it belatedly thanks to a question Skydivephil asked in Cosmology forum. The paper deviates from mainstream but need not be wrong, in my view. It explores an alternative to inflation that makes use of both the Loop cosmology bounce and the teleparallel variant of GR.

    http://arxiv.org/abs/arXiv:1309.0352
    Cosmological perturbations in teleparallel Loop Quantum Cosmology
    Jaime Haro
    (Submitted on 2 Sep 2013 (v1), last revised 18 Nov 2013 (this version, v3))
    Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator.
    In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of teleparallel F(T) gravity (teleparallel LQC). The main idea of our approach is to mix the simple bounce provided by holonomy corrections in LQC with the non-singular perturbation equations given by F(T) gravity, in order to obtain a matter bounce scenario as a viable alternative to slow-roll inflation.
    In our study, we have obtained an scale invariant power spectrum of cosmological perturbations. However, the ratio of tensor to scalar perturbations is of order 1, which does not agree with the current observations. For this reason, we suggest a model where a transition from the matter domination to a quasi de Sitter phase is produced in order to enhance the scalar power spectrum.
    18 pages.

    The author is at UPC-Barcelona (Universitat Politècnica de Catalunya = Catalonia Polytechnic University).


    http://inspirehep.net/author/profile/J.Haro.1
    http://inspirehep.net/author/profile/J.de.Haro.1
     
  8. Nov 27, 2013 #7

    marcus

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    Another interesting 4th quarter paper came to my attention through yesterday's ILQGS talk (26 Nov) by Johannes Thürigen on DIMENSIONALITY in quantum geometry.
    http://relativity.phys.lsu.edu/ilqgs/thueringen112613.pdf (typo, ingen might sometime be corrected to igen)
    http://relativity.phys.lsu.edu/ilqgs/thueringen112613.wav

    This is based on work at AEI Potsdam with Calcagni and Oriti. JT says there is work in progress and also there's a paper that just appeared this month

    The idea dimensionality seems to get more sophisticated in QG. Maybe it isn't even meaningful at very small scale. If the geometry is quantum mechanical how do you even define it?
    One method we've been hearing about since around 2005 and have discussed here at PF on occasion is spectral dimension where the dimensionality around a given point in space or spacetime is explored by conducting a diffusion process or random walk starting at that point.

    The higher the dimension of the space the less likely the wanderer is to accidentally return to his starting point. It is well-adapted to spaces with vague indeterminate geometry, and it can assume non-integer values. The dimension of the space does not have to be a whole number.

    Looking at JT's seminar slides makes me think they might be getting fairly deep into the idea of dimension--may be finding some new stuff. I want to withhold judgment but watch closely. Here's the November paper:

    http://arxiv.org/abs/1311.3340
    Spectral dimension of quantum geometries
    Gianluca Calcagni, Daniele Oriti, Johannes Thürigen
    (Submitted on 13 Nov 2013)
    The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them.
    38 pages, 18 multiple figures
     
    Last edited: Nov 27, 2013
  9. Nov 28, 2013 #8

    marcus

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    Updated listing. Comments in green.

    http://arxiv.org/abs/1311.6942
    A note on the spinor construction of Spin Foam amplitudes
    Giorgio Immirzi
    (Submitted on 27 Nov 2013)
    I discuss the use of spinors in the construction of spin-foam models, in particular the form of the closure and simplicity constraints for triangles that are space-like, i.e. with (area)2 = 1/2 SIJ SIJ > 0, regardless of whether they belong the tetrahedra with a space-like or time-like normal, emphasizing the role of the light-like 4-vector utσI u ̄t. In the quantization of the model, with the representations of SL(2,C) acting on spaces of functions of light-like vectors, one may use the canonical basis of SU(2) representations, or the pseudobasis limited to the discrete representations of SU(1,1); in alternative it is proposed to use instead a basis of eigenstates of (L3,K3), which might give matrix elements and vertex functions with the same classical limit. A detailed example of a small triangulation is presented, which among other things indicates, on the basis of a classical calculation, that it would be impractical to limit oneself to tetrahedra with time-like normals.
    20 pages, 1 figure.

    Immirzi!

    http://arxiv.org/abs/1311.6841
    Observables in Loop Quantum Gravity with a cosmological constant
    Maïté Dupuis, Florian Girelli
    (Submitted on 26 Nov 2013)
    An open issue in loop quantum gravity (LQG) is the introduction of a non-vanishing cosmological constant Λ. In 3d, Chern-Simons theory provides some guiding lines: Λ appears in the quantum deformation of the gauge group. The Turaev-Viro model, which is an example of spin foam model is also defined in terms of a quantum group. By extension, it is believed that in 4d, a quantum group structure could encode the presence of Λ≠0. In this article, we introduce by hand the quantum group Uq(su(2)) into the LQG framework, that is we deal with Uq(su(2))-spin networks. We explore some of the consequences, focusing in particular on the structure of the observables. Our fundamental tools are tensor operators for Uq(su(2)). We review their properties and give an explicit realization of the spinorial and vectorial ones. We construct the generalization of the U(n) formalism in this deformed case, which is given by the quantum group Uq(u(n)). We are then able to build geometrical observables, such as the length, area or angle operators ... We show that these operators characterize a quantum discrete hyperbolic geometry in the 3d LQG case. Our results confirm that the use of quantum group in LQG can be a tool to introduce a non-zero cosmological constant into the theory.
    29 pages, 2 figures

    Important to work out the consequences for the theory as a whole when the cosmological constant is included this way.

    http://arxiv.org/abs/arXiv:1311.6117
    The Koslowski-Sahlmann representation: Gauge and diffeomorphism invariance
    Miguel Campiglia, Madhavan Varadarajan
    (Submitted on 24 Nov 2013)
    The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non-degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG representation so as to describe states labelled by smooth non-degenerate triad fields. His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods. Motivated by the desire to model asymptotically flat quantum geometry by states with triad labels which are non-degenerate at infinity but not necessarily so in the interior, we initiate a generalisation of Sahlmann's considerations to triads of varying degeneracy. In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us. Our treatment emphasizes the role of symmetries of quantum states in the averaging procedure. Semianalyticity, influential in the proofs of the beautiful uniqueness results for LQG, plays a key role in our considerations. As a by product, we re-derive the group averaging map for standard LQG, highlighting the role of state symmetries and explicitly exhibiting the essential uniqueness of its specification.
    45 pages.

    Earlier paper by MV http://arxiv.org/1306.6126 [Broken] and two in progress by MC and MV, refs 24 and 25 on pages 35 and 36.]

    http://arxiv.org/abs/1311.3340
    Spectral dimension of quantum geometries
    Gianluca Calcagni, Daniele Oriti, Johannes Thürigen
    (Submitted on 13 Nov 2013)
    The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them.
    38 pages, 18 multiple figures

    The spectral dimension around a given point is explored by conducting a diffusion process or random walk starting at that point. Higher dimensionality makes it less likely the wanderer will accidentally return to his starting point. Spectral dimension is well-adapted to spaces with vague indeterminate geometry and can assume non-integer values.

    http://arxiv.org/abs/1311.3279
    Null twisted geometries
    Simone Speziale, Mingyi Zhang
    (Submitted on 13 Nov 2013)
    We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is naturally decomposed into a conformal metric and scale factors, forming locally conjugate pairs. Proper action-angle variables on the gauge-invariant phase space are described by the eigenvectors of the Laplacian of the dual graph. We also identify the variables of the phase space amenable to characterize the extrinsic geometry of the foliation. Finally, we quantise the phase space and its algebra using Dirac's algorithm, obtaining a notion of spin networks for null hypersurfaces. Such spin networks are labelled by SO(2) quantum numbers, and are embedded non-trivially in the unitary, infinite-dimensional irreducible representations of the Lorentz group.
    22 pages, 3 figures

    "... step towards our goal of understanding the dynamics of null surfaces in LQG. .. From the possibility of including dynamical effects in black hole physics, describing the near horizon quantum geometry, to the use in the constraint-free formulation of GR on null hypersurfaces. To that end, many nontrivial steps are needed. First of all, our analysis needs to be complemented with a continuum canonical analysis of the Plebanski action on a null hypersurface [27]. ... one should also investigate what type of spin foams can support the boundary data here studied. We expect this line of research to bring new tools and results to LQG, and to show us how deep the connection with twistors goes."
    Reference [27] is to work said "to appear" by Speziale and Alexandrov


    http://arxiv.org/abs/1311.1798
    Topological lattice field theories from intertwiner dynamics
    Bianca Dittrich, Wojciech Kaminski
    (Submitted on 7 Nov 2013)
    We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and instances of triangulation invariant, that is, topological, models inside this class. These models give examples for symmetry protected topologically ordered 1D quantum phases with quantum group symmetries. Furthermore the models provide realizations for anyon condensation into a new effective vacuum. We explain the relevance of our findings for the problem of identifying the continuum limit of spin foam and spin net models.
    35+9 pages

    Strongly motivated in the paper's introduction (which see.) The brief excerpts here can't do it justice: "...The models, and the investigations of their fixed point structure under coarse graining, are motivated by a research program to understand the phase diagram and continuum limit of spin foam models [1],... There are however several additional tantalizing connections to quantum gravity as well as other areas of physics. One is the theory of anyon condensation [4, 5], for which we provide Hamiltonians. The condensate states appear as ground states of these Hamiltonians and are given by the topological models. ...
    Besides these topics there are other reasons why these models and its fixed points are of interest for quantum gravity:
    • For the construction of spin foam models itself, in particular the intertwiners defining these models. The fixed points of our models define naturally intertwiners for spin foam vertices of arbitrary valency...
    • ...spin net models,..
    • ...geometrical interpretation of the underlying variables…"


    http://arxiv.org/abs/1310.6728
    Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
    Parampreet Singh, Edward Wilson-Ewing
    (Submitted on 24 Oct 2013)
    We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaitre-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaitre-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.
    34 pages

    A technically valuable paper. There are several ways to carry out the quantization in Loop cosmology. The authors make a comparative study of the main alternatives and arrive at a reasoned choice.

    http://arxiv.org/abs/1310.5996
    Quantum black holes in Loop Quantum Gravity
    Rodolfo Gambini, Javier Olmedo, Jorge Pullin
    (Submitted on 22 Oct 2013)
    We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and that the singularity inside black holes is resolved. Moreover, we consider an alternative quantization based on a slightly different kinematical Hilbert space. The ambiguity in kinematical spaces stems from how one treats the periodicity of one of the classical variables in these models. The corresponding physical Hilbert spaces solve the diffeomorphism and Hamiltonian constraint but their intrinsic structure is radically different depending on the kinematical Hilbert space one started from. In both cases there are quantum observables that do not have a classical counterpart. However, one can show that at the end of the day, by examining Dirac observables, both quantizations lead to the same physical predictions.
    20 pages

    The Loop black hole does not develop a singularity. The authors published a result earlier this year in PRL which is now strengthened by showing that when one takes an alternate quantization route it again goes through and gives equivalent physics.

    http://arxiv.org/abs/1310.4795
    Chimera: A hybrid approach to numerical loop quantum cosmology
    Peter Diener, Brajesh Gupt, Parampreet Singh
    (Submitted on 17 Oct 2013)
    The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosing a hybrid spatial grid allowing the use of partial differential equations at large volumes, and with a simple change of geometrical coordinate, we obtain a surprising reduction in the computational cost. This scheme enables us to explore regimes which were so far unachievable for the isotropic model in LQC. Our approach also promises to significantly reduce the computational cost for numerical simulations in anisotropic LQC using high performance computing.
    39 pages, 15 figures

    Computer simulations of have played an important role in Loop cosmology especially since 2006---having been extensively used to check and confirm solvable equation models and verify the Big Bounce under increasingly general assumptions. More efficient code makes possible further generalization to a broader range of cases.

    http://arxiv.org/abs/1310.3362
    Deformation Operators of Spin Networks and Coarse-Graining
    Etera R. Livine
    (Submitted on 12 Oct 2013)
    In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop gravity, a necessary step is to understand the coarse-graining of these states in order to describe their relevant structure at various scales. Using the spinor network formalism to describe the phase space of loop gravity on a given graph, we focus on a bounded (connected) region of the graph and coarse-grain it to a single vertex using a gauge-fixing procedure. We discuss the ambiguities in the gauge-fixing procedure and their consequences for coarse-graining spin(or) networks. This allows to define the boundary deformations of that region in a gauge-invariant fashion and to identify the area preserving deformations as U(N) transformations similarly to the already well-studied case of a single intertwiner. The novelty is that the closure constraint is now relaxed and the closure defect interpreted as a local measure of the curvature inside the coarse-grained region. It is nevertheless possible to cancel the closure defect by a Lorentz boost. We further identify a Lorentz-invariant observable related to the area and closure defect, which we name "rest area". Its physical meaning remains an open issue.
    24 pages

    The paper explains a new coarsegrain procedure to collapse a compact region of a spin(or) network with multiple vertices and edges down to a single point. A Fock-style Hilbert space is constructed at the remaining vertex which represents information condensed by the coarsening move. The reverse process of refinement is studied.

    http://arxiv.org/abs/1310.2174
    Radiative corrections to the EPRL-FK spinfoam graviton
    Aldo Riello
    (Submitted on 8 Oct 2013)
    I study the corrections engendered by the insertion of a "melon" graph in the bulk of the first-order spinfoam used for the graviton propagator. I find that these corrections are highly non-trivial and, in particular, that they concern those terms which disappear in the Bojowald-Bianchi-Magliaro-Perini limit of vanishing Barbero-Immirzi parameter at fixed area. This fact is the first realization of the often cited idea that the spinfoam amplitude receives higher order corrections under the refinement of the underlying two-complex.
    13 pages, 4 figures

    Riello's earlier paper this year dealt with spinfoam amplitude divergences which turned out to be at most logarithmic. He continues to make headway in studying details of the covariant Loop gravity path integral under refinement

    http://arxiv.org/abs/arXiv:1309.0352
    Cosmological perturbations in teleparallel Loop Quantum Cosmology
    Jaime Haro
    (Submitted on 2 Sep 2013)
    Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator.
    In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of teleparallel F(T) gravity (teleparallel LQC). The main idea of our approach is to mix the simple bounce provided by holonomy corrections in LQC with the non-singular perturbation equations given by F(T) gravity, in order to obtain a matter bounce scenario as a viable alternative to slow-roll inflation.
    In our study, we have obtained an scale invariant power spectrum of cosmological perturbations. However, the ratio of tensor to scalar perturbations is of order 1, which does not agree with the current observations. For this reason, we suggest a model where a transition from the matter domination to a quasi de Sitter phase is produced in order to enhance the scalar power spectrum.
    18 pages.

    I missed this 3rd quarter paper when it came out, so I'm including it in the 4th quarter list. It explores an alternative to inflation making use of both the Loop cosmology bounce and the teleparallel variant of GR.

    http://inspirehep.net/search?ln=en&...search=Search&sf=&so=d&rm=citation&rg=25&sc=0
     
    Last edited by a moderator: May 6, 2017
  10. Dec 4, 2013 #9

    marcus

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    Here's a selection of 4th quarter papers taken from this Inspire search:
    http://inspirehep.net/search?ln=en&...&action_search=Search&sf=&so=d&rm=&rg=25&sc=0
    They number thirteen so far. In some cases I've added comment or used highlighting to indicate why I think the paper is especially interesting.

    http://arxiv.org/abs/arXiv:1312.0905
    Quantum group spin nets: refinement limit and relation to spin foams
    Bianca Dittrich, Mercedes Martin-Benito, Sebastian Steinhaus
    (Submitted on 3 Dec 2013)
    So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups SU(2)k and examine their effective continuum dynamics via tensor network renormalization. In the refinement limit of this coarse graining procedure, we find a vast non-trivial fixed point structure beyond the degenerate and the BF phase. In comparison to previous work, we use fixed point intertwiners, inspired by Reisenberger's construction principle [1] and the recent work [2], as the initial parametrization. In this new parametrization fine tuning is not required in order to flow to these new fixed points. Encouragingly, each fixed point has an associated extended phase, which allows for the study of phase transitions in the future. Finally we also present an interpretation of spin nets in terms of melonic spin foams. The coarse graining flow of spin nets can thus be interpreted as describing the effective coupling between two spin foam vertices or space time atoms.
    30+5 pages, many figures

    The reference [2] is to 1311.1798 which appears further down in this list. Foams with a finite label set facilitate numerical investigation and the full treatment can in principle be recovered in the k→∞ limit.
    ==excerpt from page 2==
    To be more precise, we introduce here spin net models with structure group SU(2)k, the quantum deformation (at the root of unity) of the group SU(2). This makes a numerical investigation of the models possible, as in the quantum group only finitely many representations appear. On the technical level this requires the introduction of the Haar projector for the quantum group which we construct in this work. Models based on the quantum deformation of the rotation group describe gravitational systems with a cosmological constant [19]. For the 4D systems one would need SU(2)k × SU(2)k, however also an effective description in terms of SU(2)k alone might be possible [20]. Thus we lift the simplification, considered in [12, 21], of the structure group almost completely. Moreover considering the behaviour of the models for growing level k allows to make conjectures on the limit k → ∞, which gives back the classical group SU(2).
    As in previous work [12, 21] we will employ tensor network techniques [17, 18] to derive a coarse graining flow equation, which is then investigated numerically...
    ==endquote==


    http://arxiv.org/abs/1311.7565
    Time evolution as refining, coarse graining and entangling
    Bianca Dittrich, Sebastian Steinhaus
    (Submitted on 29 Nov 2013)
    We argue that refining, coarse graining and entangling operators can be obtained from time evolution operators. This applies in particular to geometric theories, such as spin foams. We point out that this provides a construction principle for the physical vacuum in quantum gravity theories and more generally allows to construct a (cylindrically) consistent continuum limit of the theory.
    33 pages, 9 figures

    http://arxiv.org/abs/1311.6942
    A note on the spinor construction of Spin Foam amplitudes
    Giorgio Immirzi
    (Submitted on 27 Nov 2013)
    I discuss the use of spinors in the construction of spin-foam models, in particular the form of the closure and simplicity constraints for triangles that are space-like, i.e. with (area)2 = 1/2 SIJ SIJ > 0, regardless of whether they belong the tetrahedra with a space-like or time-like normal, emphasizing the role of the light-like 4-vector utσI u ̄t. In the quantization of the model, with the representations of SL(2,C) acting on spaces of functions of light-like vectors, one may use the canonical basis of SU(2) representations, or the pseudobasis limited to the discrete representations of SU(1,1); in alternative it is proposed to use instead a basis of eigenstates of (L3,K3), which might give matrix elements and vertex functions with the same classical limit. A detailed example of a small triangulation is presented, which among other things indicates, on the basis of a classical calculation, that it would be impractical to limit oneself to tetrahedra with time-like normals.
    20 pages, 1 figure.

    http://arxiv.org/abs/1311.6841
    Observables in Loop Quantum Gravity with a cosmological constant
    Maïté Dupuis, Florian Girelli
    (Submitted on 26 Nov 2013)
    An open issue in loop quantum gravity (LQG) is the introduction of a non-vanishing cosmological constant Λ. In 3d, Chern-Simons theory provides some guiding lines: Λ appears in the quantum deformation of the gauge group. The Turaev-Viro model, which is an example of spin foam model is also defined in terms of a quantum group. By extension, it is believed that in 4d, a quantum group structure could encode the presence of Λ≠0. In this article, we introduce by hand the quantum group Uq(su(2)) into the LQG framework, that is we deal with Uq(su(2))-spin networks. We explore some of the consequences, focusing in particular on the structure of the observables. Our fundamental tools are tensor operators for Uq(su(2)). We review their properties and give an explicit realization of the spinorial and vectorial ones. We construct the generalization of the U(n) formalism in this deformed case, which is given by the quantum group Uq(u(n)). We are then able to build geometrical observables, such as the length, area or angle operators ... We show that these operators characterize a quantum discrete hyperbolic geometry in the 3d LQG case. Our results confirm that the use of quantum group in LQG can be a tool to introduce a non-zero cosmological constant into the theory.
    29 pages, 2 figures

    Important to work out the consequences for the theory as a whole when the cosmological constant is included this way. BTW note parallel with with 1312.0905 by Perimeter authors, listed above.

    http://arxiv.org/abs/arXiv:1311.6117
    The Koslowski-Sahlmann representation: Gauge and diffeomorphism invariance
    Miguel Campiglia, Madhavan Varadarajan
    (Submitted on 24 Nov 2013)
    The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non-degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG representation so as to describe states labelled by smooth non-degenerate triad fields. His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods. Motivated by the desire to model asymptotically flat quantum geometry by states with triad labels which are non-degenerate at infinity but not necessarily so in the interior, we initiate a generalisation of Sahlmann's considerations to triads of varying degeneracy. In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us. Our treatment emphasizes the role of symmetries of quantum states in the averaging procedure. Semianalyticity, influential in the proofs of the beautiful uniqueness results for LQG, plays a key role in our considerations. As a by product, we re-derive the group averaging map for standard LQG, highlighting the role of state symmetries and explicitly exhibiting the essential uniqueness of its specification.
    45 pages.

    Earlier paper by MV http://arxiv.org/1306.6126 [Broken] and two in progress by MC and MV, refs 24 and 25 on pages 35 and 36.]

    http://arxiv.org/abs/1311.3279
    Null twisted geometries
    Simone Speziale, Mingyi Zhang
    (Submitted on 13 Nov 2013)
    We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalism are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is naturally decomposed into a conformal metric and scale factors, forming locally conjugate pairs. Proper action-angle variables on the gauge-invariant phase space are described by the eigenvectors of the Laplacian of the dual graph. We also identify the variables of the phase space amenable to characterize the extrinsic geometry of the foliation. Finally, we quantise the phase space and its algebra using Dirac's algorithm, obtaining a notion of spin networks for null hypersurfaces. Such spin networks are labelled by SO(2) quantum numbers, and are embedded non-trivially in the unitary, infinite-dimensional irreducible representations of the Lorentz group.
    22 pages, 3 figures

    "... step towards our goal of understanding the dynamics of null surfaces in LQG. .. From the possibility of including dynamical effects in black hole physics, describing the near horizon quantum geometry, to the use in the constraint-free formulation of GR on null hypersurfaces. To that end, many nontrivial steps are needed. First of all, our analysis needs to be complemented with a continuum canonical analysis of the Plebanski action on a null hypersurface [27]. ... one should also investigate what type of spin foams can support the boundary data here studied. We expect this line of research to bring new tools and results to LQG, and to show us how deep the connection with twistors goes."
    Reference [27] is to work said "to appear" by Speziale and Alexandrov


    http://arxiv.org/abs/1311.1798
    Topological lattice field theories from intertwiner dynamics
    Bianca Dittrich, Wojciech Kaminski
    (Submitted on 7 Nov 2013)
    We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and instances of triangulation invariant, that is, topological, models inside this class. These models give examples for symmetry protected topologically ordered 1D quantum phases with quantum group symmetries. Furthermore the models provide realizations for anyon condensation into a new effective vacuum. We explain the relevance of our findings for the problem of identifying the continuum limit of spin foam and spin net models.
    35+9 pages

    Strongly motivated in the paper's introduction (which see.) The brief excerpts here can't do it justice: "...The models, and the investigations of their fixed point structure under coarse graining, are motivated by a research program to understand the phase diagram and continuum limit of spin foam models [1],... There are however several additional tantalizing connections to quantum gravity as well as other areas of physics. One is the theory of anyon condensation [4, 5], for which we provide Hamiltonians. The condensate states appear as ground states of these Hamiltonians and are given by the topological models. ...
    Besides these topics there are other reasons why these models and its fixed points are of interest for quantum gravity:
    • For the construction of spin foam models itself, in particular the intertwiners defining these models. The fixed points of our models define naturally intertwiners for spin foam vertices of arbitrary valency...
    • ...spin net models,..
    • ...geometrical interpretation of the underlying variables…"


    http://arxiv.org/abs/1310.6728
    Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
    Parampreet Singh, Edward Wilson-Ewing
    (Submitted on 24 Oct 2013)
    We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaitre-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaitre-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.
    34 pages

    A technically valuable paper. There are several ways to carry out the quantization in Loop cosmology. The authors make a comparative study of the main alternatives and arrive at a reasoned choice.

    http://arxiv.org/abs/1310.5996
    Quantum black holes in Loop Quantum Gravity
    Rodolfo Gambini, Javier Olmedo, Jorge Pullin
    (Submitted on 22 Oct 2013)
    We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and that the singularity inside black holes is resolved. Moreover, we consider an alternative quantization based on a slightly different kinematical Hilbert space. The ambiguity in kinematical spaces stems from how one treats the periodicity of one of the classical variables in these models. The corresponding physical Hilbert spaces solve the diffeomorphism and Hamiltonian constraint but their intrinsic structure is radically different depending on the kinematical Hilbert space one started from. In both cases there are quantum observables that do not have a classical counterpart. However, one can show that at the end of the day, by examining Dirac observables, both quantizations lead to the same physical predictions.
    20 pages

    The Loop black hole does not develop a singularity. The authors published a result earlier this year in PRL which is now strengthened by showing that when one takes an alternate quantization route it again goes through and gives equivalent physics.

    http://arxiv.org/abs/1310.4795
    Chimera: A hybrid approach to numerical loop quantum cosmology
    Peter Diener, Brajesh Gupt, Parampreet Singh
    (Submitted on 17 Oct 2013)
    The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosing a hybrid spatial grid allowing the use of partial differential equations at large volumes, and with a simple change of geometrical coordinate, we obtain a surprising reduction in the computational cost. This scheme enables us to explore regimes which were so far unachievable for the isotropic model in LQC. Our approach also promises to significantly reduce the computational cost for numerical simulations in anisotropic LQC using high performance computing.
    39 pages, 15 figures

    Computer simulations of have played an important role in Loop cosmology especially since 2006---having been extensively used to check and confirm solvable equation models and verify the Big Bounce under increasingly general assumptions. More efficient code makes possible further generalization to a broader range of cases.

    http://arxiv.org/abs/1310.3362
    Deformation Operators of Spin Networks and Coarse-Graining
    Etera R. Livine
    (Submitted on 12 Oct 2013)
    In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop gravity, a necessary step is to understand the coarse-graining of these states in order to describe their relevant structure at various scales. Using the spinor network formalism to describe the phase space of loop gravity on a given graph, we focus on a bounded (connected) region of the graph and coarse-grain it to a single vertex using a gauge-fixing procedure. We discuss the ambiguities in the gauge-fixing procedure and their consequences for coarse-graining spin(or) networks. This allows to define the boundary deformations of that region in a gauge-invariant fashion and to identify the area preserving deformations as U(N) transformations similarly to the already well-studied case of a single intertwiner. The novelty is that the closure constraint is now relaxed and the closure defect interpreted as a local measure of the curvature inside the coarse-grained region. It is nevertheless possible to cancel the closure defect by a Lorentz boost. We further identify a Lorentz-invariant observable related to the area and closure defect, which we name "rest area". Its physical meaning remains an open issue.
    24 pages

    The paper explains a new coarsegrain procedure to collapse a compact region of a spin(or) network with multiple vertices and edges down to a single point. A Fock-style Hilbert space is constructed at the remaining vertex which represents information condensed by the coarsening move. The reverse process of refinement is studied.

    http://arxiv.org/abs/1310.2174
    Radiative corrections to the EPRL-FK spinfoam graviton
    Aldo Riello
    (Submitted on 8 Oct 2013)
    I study the corrections engendered by the insertion of a "melon" graph in the bulk of the first-order spinfoam used for the graviton propagator. I find that these corrections are highly non-trivial and, in particular, that they concern those terms which disappear in the Bojowald-Bianchi-Magliaro-Perini limit of vanishing Barbero-Immirzi parameter at fixed area. This fact is the first realization of the often cited idea that the spinfoam amplitude receives higher order corrections under the refinement of the underlying two-complex.
    13 pages, 4 figures

    Riello's earlier paper this year dealt with spinfoam amplitude divergences which turned out to be at most logarithmic. He continues to make headway in studying details of the covariant Loop gravity path integral under refinement

    http://arxiv.org/abs/arXiv:1309.0352
    Cosmological perturbations in teleparallel Loop Quantum Cosmology
    Jaime Haro
    (Submitted on 2 Sep 2013)
    Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator.
    In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of teleparallel F(T) gravity (teleparallel LQC). The main idea of our approach is to mix the simple bounce provided by holonomy corrections in LQC with the non-singular perturbation equations given by F(T) gravity, in order to obtain a matter bounce scenario as a viable alternative to slow-roll inflation.
    In our study, we have obtained an scale invariant power spectrum of cosmological perturbations. However, the ratio of tensor to scalar perturbations is of order 1, which does not agree with the current observations. For this reason, we suggest a model where a transition from the matter domination to a quasi de Sitter phase is produced in order to enhance the scalar power spectrum.
    18 pages.

    I missed this 3rd quarter paper when it came out, so I'm including it in the 4th quarter list. It explores an alternative to inflation making use of both the Loop cosmology bounce and the teleparallel variant of GR.

    http://inspirehep.net/search?ln=en&...&action_search=Search&sf=&so=d&rm=&rg=25&sc=0
     
    Last edited by a moderator: May 6, 2017
  11. Dec 9, 2013 #10

    marcus

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    This Brunetti Fredenhagen Rejzner paper risks being lost track of because it doesn't belong to any of the usual categories. It seems to say that QG is an easy problem if you realize that below a certain scale (above a certain energy density) geometry doesn't make operational sense. You can't measure lengths, areas, angles. So we just want an "effective" theory after all. So it appears to contradict the need for a radical departure in QG. The much heralded "non-renormalizableness" of gravity is shrugged off (for what they argue are good reasons) and one just plows ahead with the usual perturbative treatment. Somehow they manage to include diffeomorphism invariance ("general covariance") and background independence to their own satisfaction. It's a "new/old" approach to QG.
     
    Last edited: Dec 9, 2013
  12. Dec 12, 2013 #11

    marcus

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    Here's a selection of 4th quarter QG papers, numbering seventeen in all. In some cases I've added comment or used highlighting to indicate why I think the paper is especially interesting.

    http://arxiv.org/abs/1312.3595
    Hawking radiation from a spherical loop quantum gravity black hole
    Rodolfo Gambini, Jorge Pullin
    (Submitted on 12 Dec 2013)
    We introduce quantum field theory on quantum space-times techniques to characterize the quantum vacua as a first step towards studying black hole evaporation in spherical symmetry in loop quantum gravity and compute the Hawking radiation. We use as quantum space time the recently introduced exact solution of the quantum Einstein equations in vacuum with spherical symmetry and consider a spherically symmetric test scalar field propagating on it. The use of loop quantum gravity techniques in the background space-time naturally regularizes the matter content, solving one of the main obstacles to back reaction calculations in more traditional treatments. The discreteness of area leads to modifications of the quantum vacua, eliminating the trans-Planckian modes close to the horizon, which in turn eliminates all singularities from physical quantities, like the expectation value of the stress energy tensor. Apart from this, the Boulware, Hartle--Hawking and Unruh vacua differ little from the treatment on a classical space-time. The asymptotic modes near scri are reproduced very well. We show that the Hawking radiation can be computed, leading to an expression similar to the conventional one but with a high frequency cutoff. Since many of the conclusions concern asymptotic behavior, where the spherical mode of the field behaves in a similar way as higher multipole modes do, the results can be readily generalized to non spherically symmetric fields.
    13 pages

    "We have studied the quantization of a scalar field on a quantum space time that approximates well the geometry of a Schwarzschild black hole. The treatment reproduces the results of quantum field theory on a classical space-time well, with some interesting differences. The presence of a discrete structure for the space-time eliminates the divergences…" Based on paper #1310.5996 below.

    ]http://arxiv.org/abs/1312.3253
    General Relativity from a Thermodynamic Perspective
    T. Padmanabhan
    (Submitted on 11 Dec 2013)
    Several recent results suggest that gravity is an emergent phenomenon with its field equations having the same status as, say, the equations of fluid dynamics. I describe several additional results, supporting this paradigm and connecting the gravitational dynamics in a bulk region of space with a thermodynamic description in the boundary of that region:
    (1) The Noether charge contained in a bulk region, associated with a specific time evolution vector field, has a direct thermodynamic interpretation as the gravitational heat content of the boundary surface.
    (2) This result, in turn, shows that all static spacetimes maintain holographic equipartition; in these spacetimes, the number of degrees of freedom in the boundary is equal to the number of degrees of freedom in the bulk.
    (3) In a general, evolving spacetime, the rate of change of gravitational momentum is related to the difference between the number of bulk and boundary degrees of freedom. It is this departure from the holographic equipartition which drives the time evolution of the spacetime.
    (4) When the equations of motion hold, the (naturally defined) total energy of the gravity plus matter within a bulk region, will be equal to the boundary heat content.
    (5) After motivating the need for an alternate description of gravity (if we have to solve the cosmological constant problem), I describe a thermodynamic variational principle based on null surfaces to achieve this goal. The concept of gravitational heat density of the null surfaces arises naturally from the Noether charge associated with the null congruence. The null surface variational principle, in fact, extremises the total heat content of the matter plus gravity system. Several variations on this theme and implications are described.
    53 pages
    See also Freidel paper below.

    http://arxiv.org/abs/1312.3220
    Multisymplectic effective General Boundary Field Theory
    Mona Arjang, José A. Zapata
    (Submitted on 11 Dec 2013)
    The transfer matrix in lattice field theory connects the covariant and the initial data frameworks; in spin foam models, it can be written as a composition of elementary cellular amplitudes/propagators. We present a framework for discrete spacetime classical field theory in which solutions to the field equations over elementary spacetime cells may be amalgamated if they satisfy simple gluing conditions matching the composition rules of cellular amplitudes in spin foam models. Furthermore, the formalism is endowed with a multisymplectic structure responsible for local conservation laws.
    Some models within our framework are effective theories modeling a system at a given scale. Our framework allows us to study coarse graining and the continuum limit.
    47 pages

    http://arxiv.org/abs/1312.1538
    Gravitational Energy, Local Holography and Non-equilibrium Thermodynamics
    Laurent Freidel
    (Submitted on 5 Dec 2013)
    We study the properties of gravitational system in finite regions bounded by gravitational screens. We present the detail construction of the total energy of such regions and of the energy and momentum balance equations due to the flow of matter and gravitational radiation through the screen. We establish that the gravitational screen possesses analogs of surface tension, internal energy and viscous stress tensor, while the conservations are analogs of non-equilibrium balance equations for a viscous system. This gives a precise correspondence between gravity in finite regions and non-equilibrium thermodynamics.
    41 pages, 3 figures
    See above.

    http://arxiv.org/abs/arXiv:1312.0905
    Quantum group spin nets: refinement limit and relation to spin foams
    Bianca Dittrich, Mercedes Martin-Benito, Sebastian Steinhaus
    (Submitted on 3 Dec 2013)
    So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups SU(2)k and examine their effective continuum dynamics via tensor network renormalization. In the refinement limit of this coarse graining procedure, we find a vast non-trivial fixed point structure beyond the degenerate and the BF phase. In comparison to previous work, we use fixed point intertwiners, inspired by Reisenberger's construction principle [1] and the recent work [2], as the initial parametrization. In this new parametrization fine tuning is not required in order to flow to these new fixed points. Encouragingly, each fixed point has an associated extended phase, which allows for the study of phase transitions in the future. Finally we also present an interpretation of spin nets in terms of melonic spin foams. The coarse graining flow of spin nets can thus be interpreted as describing the effective coupling between two spin foam vertices or space time atoms.
    30+5 pages, many figures

    The reference [2] is to 1311.1798 which appears further down in this list. Foams with a finite label set (e.g. derived from SU(2)k) facilitate numerical investigation and the full treatment can in principle be recovered in the k→∞ limit.

    http://arxiv.org/abs/1311.7565
    Time evolution as refining, coarse graining and entangling
    Bianca Dittrich, Sebastian Steinhaus
    (Submitted on 29 Nov 2013)
    We argue that refining, coarse graining and entangling operators can be obtained from time evolution operators. This applies in particular to geometric theories, such as spin foams. We point out that this provides a construction principle for the physical vacuum in quantum gravity theories and more generally allows to construct a (cylindrically) consistent continuum limit of the theory.
    33 pages, 9 figures

    http://arxiv.org/abs/1311.6942
    A note on the spinor construction of Spin Foam amplitudes
    Giorgio Immirzi
    (Submitted on 27 Nov 2013)
    I discuss the use of spinors in the construction of spin-foam models, in particular the form of the closure and simplicity constraints for triangles that are space-like, i.e. with (area)2 = 1/2 SIJ SIJ > 0, regardless of whether they belong the tetrahedra with a space-like or time-like normal, emphasizing the role of the light-like 4-vector utσI u ̄t. In the quantization of the model, with the representations of SL(2,C) acting on spaces of functions of light-like vectors, one may use the canonical basis of SU(2) representations, or the pseudobasis limited to the discrete representations of SU(1,1); in alternative it is proposed to use instead a basis of eigenstates of (L3,K3), which might give matrix elements and vertex functions with the same classical limit. A detailed example of a small triangulation is presented, which among other things indicates, on the basis of a classical calculation, that it would be impractical to limit oneself to tetrahedra with time-like normals.
    20 pages, 1 figure.

    http://arxiv.org/abs/arXiv:1311.6117
    The Koslowski-Sahlmann representation: Gauge and diffeomorphism invariance
    Miguel Campiglia, Madhavan Varadarajan
    (Submitted on 24 Nov 2013)
    The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non-degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG representation so as to describe states labelled by smooth non-degenerate triad fields. His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods. Motivated by the desire to model asymptotically flat quantum geometry by states with triad labels which are non-degenerate at infinity but not necessarily so in the interior, we initiate a generalisation of Sahlmann's considerations to triads of varying degeneracy. In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us. Our treatment emphasizes the role of symmetries of quantum states in the averaging procedure. Semianalyticity, influential in the proofs of the beautiful uniqueness results for LQG, plays a key role in our considerations. As a by product, we re-derive the group averaging map for standard LQG, highlighting the role of state symmetries and explicitly exhibiting the essential uniqueness of its specification.
    45 pages.

    Earlier paper by MV http://arxiv.org/1306.6126 [Broken] and two in progress by MC and MV, refs 24 and 25 on pages 35 and 36.]

    http://arxiv.org/abs/1311.3279
    Null twisted geometries
    Simone Speziale, Mingyi Zhang
    (Submitted on 13 Nov 2013)
    We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalism are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is naturally decomposed into a conformal metric and scale factors, forming locally conjugate pairs. Proper action-angle variables on the gauge-invariant phase space are described by the eigenvectors of the Laplacian of the dual graph. We also identify the variables of the phase space amenable to characterize the extrinsic geometry of the foliation. Finally, we quantise the phase space and its algebra using Dirac's algorithm, obtaining a notion of spin networks for null hypersurfaces. Such spin networks are labelled by SO(2) quantum numbers, and are embedded non-trivially in the unitary, infinite-dimensional irreducible representations of the Lorentz group.
    22 pages, 3 figures

    "... step towards our goal of understanding the dynamics of null surfaces in LQG. .. from the possibility of including dynamical effects in black hole physics, describing the near horizon quantum geometry, to the use in the constraint-free formulation of GR on null hyper surfaces... We expect this line of research to bring new tools and results to LQG, and to show us how deep the connection with twistors goes."
    Reference [27] is to work by Speziale and Alexandrov to appear.


    http://arxiv.org/abs/1311.1798
    Topological lattice field theories from intertwiner dynamics
    Bianca Dittrich, Wojciech Kaminski
    (Submitted on 7 Nov 2013)
    We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and instances of triangulation invariant, that is, topological, models inside this class. These models give examples for symmetry protected topologically ordered 1D quantum phases with quantum group symmetries. Furthermore the models provide realizations for anyon condensation into a new effective vacuum. We explain the relevance of our findings for the problem of identifying the continuum limit of spin foam and spin net models.
    35+9 pages

    "...The models, and the investigations of their fixed point structure under coarse graining, are motivated by a research program to understand the phase diagram and continuum limit of spin foam models [1],..
    ... the theory of anyon condensation [4, 5], for which we provide Hamiltonians. The condensate states appear as ground states of these Hamiltonians…
    … the construction of spin foam models itself, in particular the intertwiners defining these models. The fixed points of our models define naturally intertwiners for spin foam vertices of arbitrary valency…"


    http://arxiv.org/abs/1310.6728
    Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
    Parampreet Singh, Edward Wilson-Ewing
    (Submitted on 24 Oct 2013)
    We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaitre-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaitre-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.
    34 pages

    A technically valuable paper. There are several ways to carry out the quantization in Loop cosmology. The authors make a comparative study of the main alternatives and arrive at a reasoned choice.

    http://arxiv.org/abs/1310.5996
    Quantum black holes in Loop Quantum Gravity
    Rodolfo Gambini, Javier Olmedo, Jorge Pullin
    (Submitted on 22 Oct 2013)
    We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and that the singularity inside black holes is resolved. Moreover, we consider an alternative quantization based on a slightly different kinematical Hilbert space. The ambiguity in kinematical spaces stems from how one treats the periodicity of one of the classical variables in these models. The corresponding physical Hilbert spaces solve the diffeomorphism and Hamiltonian constraint but their intrinsic structure is radically different depending on the kinematical Hilbert space one started from. In both cases there are quantum observables that do not have a classical counterpart. However, one can show that at the end of the day, by examining Dirac observables, both quantizations lead to the same physical predictions.
    20 pages

    The Loop black hole does not develop a singularity. The authors published a result earlier this year in PRL which is now strengthened by showing that when one takes an alternate quantization route it again goes through and gives equivalent physics.

    http://arxiv.org/abs/1310.4795
    Chimera: A hybrid approach to numerical loop quantum cosmology
    Peter Diener, Brajesh Gupt, Parampreet Singh
    (Submitted on 17 Oct 2013)
    The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosing a hybrid spatial grid allowing the use of partial differential equations at large volumes, and with a simple change of geometrical coordinate, we obtain a surprising reduction in the computational cost. This scheme enables us to explore regimes which were so far unachievable for the isotropic model in LQC. Our approach also promises to significantly reduce the computational cost for numerical simulations in anisotropic LQC using high performance computing.
    39 pages, 15 figures

    Computer simulations of have played an important role in Loop cosmology especially since 2006---having been extensively used to check and confirm solvable equation models and verify the Big Bounce under increasingly general assumptions. More efficient code makes possible further generalization to a broader range of cases.

    http://arxiv.org/abs/1310.3362
    Deformation Operators of Spin Networks and Coarse-Graining
    Etera R. Livine
    (Submitted on 12 Oct 2013)
    In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop gravity, a necessary step is to understand the coarse-graining of these states in order to describe their relevant structure at various scales. Using the spinor network formalism to describe the phase space of loop gravity on a given graph, we focus on a bounded (connected) region of the graph and coarse-grain it to a single vertex using a gauge-fixing procedure. We discuss the ambiguities in the gauge-fixing procedure and their consequences for coarse-graining spin(or) networks. This allows to define the boundary deformations of that region in a gauge-invariant fashion and to identify the area preserving deformations as U(N) transformations similarly to the already well-studied case of a single intertwiner. The novelty is that the closure constraint is now relaxed and the closure defect interpreted as a local measure of the curvature inside the coarse-grained region. It is nevertheless possible to cancel the closure defect by a Lorentz boost. We further identify a Lorentz-invariant observable related to the area and closure defect, which we name "rest area". Its physical meaning remains an open issue.
    24 pages

    The paper explains a new coarsegrain procedure to collapse a compact region of a spin(or) network with multiple vertices and edges down to a single point. A Fock-style Hilbert space is constructed at the remaining vertex which represents information condensed by the coarsening move. The reverse process of refinement is studied.

    http://arxiv.org/abs/1310.2174
    Radiative corrections to the EPRL-FK spinfoam graviton
    Aldo Riello
    (Submitted on 8 Oct 2013)
    I study the corrections engendered by the insertion of a "melon" graph in the bulk of the first-order spinfoam used for the graviton propagator. I find that these corrections are highly non-trivial and, in particular, that they concern those terms which disappear in the Bojowald-Bianchi-Magliaro-Perini limit of vanishing Barbero-Immirzi parameter at fixed area. This fact is the first realization of the often cited idea that the spinfoam amplitude receives higher order corrections under the refinement of the underlying two-complex.
    13 pages, 4 figures

    Riello's earlier paper this year dealt with spinfoam amplitude divergences which turned out to be at most logarithmic. He continues to make headway in studying details of the covariant Loop gravity path integral under refinement

    http://arxiv.org/abs/arXiv:1309.0352
    Cosmological perturbations in teleparallel Loop Quantum Cosmology
    Jaime Haro
    (Submitted on 2 Sep 2013)
    Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator.
    In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of teleparallel F(T) gravity (teleparallel LQC). The main idea of our approach is to mix the simple bounce provided by holonomy corrections in LQC with the non-singular perturbation equations given by F(T) gravity, in order to obtain a matter bounce scenario as a viable alternative to slow-roll inflation.
    In our study, we have obtained an scale invariant power spectrum of cosmological perturbations. However, the ratio of tensor to scalar perturbations is of order 1, which does not agree with the current observations. For this reason, we suggest a model where a transition from the matter domination to a quasi de Sitter phase is produced in order to enhance the scalar power spectrum.
    18 pages.

    I missed this 3rd quarter paper when it came out, so I'm including it in the 4th quarter list. It explores an alternative to inflation making use of both the Loop cosmology bounce and the teleparallel variant of GR.

    http://arxiv.org/abs/1306.1058
    Quantum gravity from the point of view of locally covariant quantum field theory
    Romeo Brunetti, Klaus Fredenhagen, Katarzyna Rejzner
    (Submitted on 5 Jun 2013)
    We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin-Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales.
    51 pages, in this version: proof of the background independence corrected

    A noteworthy 2nd quarter paper I missed earlier and so include with the 4th quarter titles. Arnold Neumaier called this to our attention: a signal advance in a "new/old" approach to QG. https://www.physicsforums.com/showthread.php?p=4596143#post4596143
     
    Last edited by a moderator: May 6, 2017
  13. Dec 16, 2013 #12

    marcus

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    Dearly Missed

    Another one that just came out:

    http://arxiv.org/abs/1312.3657
    Structural aspects of loop quantum gravity and loop quantum cosmology from an algebraic perspective
    Alexander Stottmeister, Thomas Thiemann
    (Submitted on 12 Dec 2013)
    We comment on structural properties of the algebras ALQG/LQC underlying loop quantum gravity and loop quantum cosmology, especially the representation theory, relating the appearance of the (dynamically induced) superselection structure (θ-sectors) in loop quantum cosmology to recently proposed representations with non-degenerate background geometries in loop quantum gravity with Abelian structure group. To this end, we review and employ the concept of extending a given (observable) algebra with possibly non-trivial centre to a (charged) field algebra with (global) gauge group.We also interpret the results in terms of the geometry of the structure group G. Furthermore, we analyze the Koslowski-Sahlmann representations with non-degenerate background in the case of a non-Abelian structure group. We find that these representations can be interpreted from two different, though related, points view: Either, the standard algebras of loop quantum gravity need to be extended by a (possibly) central term, or the elementary flux vector fields need to acquire a shift related to the (classical) background to make these representations well-defined. Both perspectives are linked by the fact that the background shift is not an automorphism of the algebras, but rather an affine transformation. Finally, we show how similar algebraic mechanisms, which are used to explain the breaking of chiral symmetry and the occurrence of θ-vacua in quantum field theory, extend to loop quantum gravity. Thus, opening a path for the discussion of these questions in loop quantum gravity.
    45 pages

    Have to think about this. It got my attention that they chose to study the Koslowski-Sahlmann representation, which was also the subject of Madhavan Varadarajan's paper listed above.
    http://arxiv.org/abs/arXiv:1311.6117
    The Koslowski-Sahlmann representation: Gauge and diffeomorphism invariance
    Miguel Campiglia, Madhavan Varadarajan
    (Submitted on 24 Nov 2013)
    The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non-degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG representation so as to describe states labelled by smooth non-degenerate triad fields. His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods...
     
    Last edited: Dec 16, 2013
  14. Dec 30, 2013 #13

    marcus

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    Rough draft of 4th quarter poll listing. I've included two papers from earlier, which were overlooked when they first appeared.

    http://arxiv.org/abs/1312.7273
    On How Neutrino Protects the Axion
    Gia Dvali, Sarah Folkerts, Andre Franca
    (Submitted on 27 Dec 2013)
    9 pages

    http://arxiv.org/abs/1312.3657
    Structural aspects of loop quantum gravity and loop quantum cosmology from an algebraic perspective
    Alexander Stottmeister, Thomas Thiemann
    (Submitted on 12 Dec 2013)
    45 pages

    http://arxiv.org/abs/1312.3595
    Hawking radiation from a spherical loop quantum gravity black hole
    Rodolfo Gambini, Jorge Pullin
    (Submitted on 12 Dec 2013)
    13 pages

    http://arxiv.org/abs/1312.3253
    General Relativity from a Thermodynamic Perspective
    Thanu Padmanabhan
    (Submitted on 11 Dec 2013)
    53 pages

    http://arxiv.org/abs/1312.1538
    Gravitational Energy, Local Holography and Non-equilibrium Thermodynamics
    Laurent Freidel
    (Submitted on 5 Dec 2013)
    41 pages, 3 figures

    http://arxiv.org/abs/arXiv:1312.0905
    Quantum group spin nets: refinement limit and relation to spin foams
    Bianca Dittrich, Mercedes Martin-Benito, Sebastian Steinhaus
    (Submitted on 3 Dec 2013)
    30+5 pages, many figures

    http://arxiv.org/abs/1311.7565
    Time evolution as refining, coarse graining and entangling
    Bianca Dittrich, Sebastian Steinhaus
    (Submitted on 29 Nov 2013)
    33 pages, 9 figures

    http://arxiv.org/abs/arXiv:1311.6117
    The Koslowski-Sahlmann representation: Gauge and diffeomorphism invariance
    Miguel Campiglia, Madhavan Varadarajan
    (Submitted on 24 Nov 2013)
    45 pages.

    http://arxiv.org/abs/1311.5325
    Note on the super inflation in loop quantum cosmology
    Kui Xiao, Xiao-Kai He, Jian-Yang Zhu
    (Submitted on 21 Nov 2013)
    9 pages, 4 figures. Physics Letters B

    http://arxiv.org/abs/1311.3279
    Null twisted geometries
    Simone Speziale, Mingyi Zhang
    (Submitted on 13 Nov 2013)
    22 pages, 3 figures

    http://arxiv.org/abs/1311.2898
    Matter matters in asymptotically safe quantum gravity
    Pietro Donà, Astrid Eichhorn, Roberto Percacci
    (Submitted on 12 Nov 2013)
    22 pages, 18 figures, 4 tables

    http://arxiv.org/abs/1311.0186
    Twistor relative locality
    Lee Smolin
    (Submitted on 1 Nov 2013)
    10 pages

    http://arxiv.org/abs/1311.0054
    Relative information at the foundation of physics
    Carlo Rovelli
    (Submitted on 31 Oct 2013)
    3 pages. Second prize in the 2013 FQXi contest "It From Bit or Bit From It?"

    http://arxiv.org/abs/1310.7786
    Group field theory as the 2nd quantization of Loop Quantum Gravity
    Daniele Oriti
    (Submitted on 29 Oct 2013)
    23 pages, 5 figures

    http://arxiv.org/abs/1310.6728
    Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
    Parampreet Singh, Edward Wilson-Ewing
    (Submitted on 24 Oct 2013)
    34 pages

    http://arxiv.org/abs/1310.5167
    A Gravitational Origin of the Arrows of Time
    Julian Barbour, Tim Koslowski, Flavio Mercati
    (Submitted on 18 Oct 2013)
    44+14 pages, 8 figures, 1 table

    http://arxiv.org/abs/1310.3362
    Deformation Operators of Spin Networks and Coarse-Graining
    Etera R. Livine
    (Submitted on 12 Oct 2013)
    24 pages

    http://arxiv.org/abs/1310.2174
    Radiative corrections to the EPRL-FK spinfoam graviton
    Aldo Riello
    (Submitted on 8 Oct 2013)
    I study the corrections engendered by the insertion of a "melon" graph in the bulk of the first-order spinfoam used for the graviton propagator. I find that these corrections are highly non-trivial and, in particular, that they concern those terms which disappear in the Bojowald-Bianchi-Magliaro-Perini limit of vanishing Barbero-Immirzi parameter at fixed area. This fact is the first realization of the often cited idea that the spinfoam amplitude receives higher order corrections under the refinement of the underlying two-complex.
    13 pages, 4 figures

    http://arxiv.org/abs/arXiv:1309.0352
    Cosmological perturbations in teleparallel Loop Quantum Cosmology
    Jaime Haro
    (Submitted on 2 Sep 2013)
    Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator.
    In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of teleparallel F(T) gravity (teleparallel LQC). The main idea of our approach is to mix the simple bounce provided by holonomy corrections in LQC with the non-singular perturbation equations given by F(T) gravity, in order to obtain a matter bounce scenario as a viable alternative to slow-roll inflation.
    In our study, we have obtained an scale invariant power spectrum of cosmological perturbations. However, the ratio of tensor to scalar perturbations is of order 1, which does not agree with the current observations. For this reason, we suggest a model where a transition from the matter domination to a quasi de Sitter phase is produced in order to enhance the scalar power spectrum.
    18 pages. Journal of Cosmology and Astroparticle Physics

    http://arxiv.org/abs/1306.1058
    Quantum gravity from the point of view of locally covariant quantum field theory
    Romeo Brunetti, Klaus Fredenhagen, Katarzyna Rejzner
    (Submitted on 5 Jun 2013)
    51 pages
     
    Last edited: Dec 30, 2013
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