Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

First part of fourth quarter 2014 MIP poll

  1. Projective Loop Quantum Gravity I. State Space

    50.0%
  2. Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model

    25.0%
  3. Geometry and the Quantum: Basics

    75.0%
  4. Silent initial conditions for cosmological perturbations with a change of space-time signature

    25.0%
  5. No firewalls in quantum gravity: the role of discreteness in resolving the information loss paradox

    0 vote(s)
    0.0%
  6. A quantum reduction to spherical symmetry in loop quantum gravity

    0 vote(s)
    0.0%
  7. Further evidence for asymptotic safety of quantum gravity

    25.0%
  8. Loop Quantum Cosmology from Loop Quantum Gravity

    25.0%
  9. Consistency of matter models with asymptotically safe quantum gravity

    25.0%
  10. Loop quantum gravity and observations

    50.0%
Multiple votes are allowed.
  1. Nov 15, 2014 #1

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    The quarter is half over. I've assembled a list of ten potentially important papers which have appeared so far this quarter. Please help us evaluate them by indicating the ones you think will prove most significant for future Loop-and-allied QG research. The poll is multiple choice, so it's possible to vote for several papers. Abstracts follow in the next post.
    There is not one of these I believe I could reasonably exclude, regardless of what papers appear in the second half. There will be a second list of ten at the end of December, for the second half of the poll,

    http://arxiv.org/abs/1411.3592
    Projective Loop Quantum Gravity I. State Space
    Suzanne Lanéry, Thomas Thiemann

    http://arxiv.org/abs/1411.3180
    Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
    Dario Benedetti, Joseph Ben Geloun, Daniele Oriti

    http://arxiv.org/abs/1411.0977
    Geometry and the Quantum: Basics
    Ali H. Chamseddine, Alain Connes, Viatcheslav Mukhanov

    http://arxiv.org/abs/1411.0272
    Silent initial conditions for cosmological perturbations with a change of space-time signature
    Jakub Mielczarek, Linda Linsefors, Aurelien Barrau

    http://arxiv.org/abs/1410.7062
    No firewalls in quantum gravity: the role of discreteness of quantum geometry in resolving the information loss paradox
    Alejandro Perez

    http://arxiv.org/abs/1410.5609
    A quantum reduction to spherical symmetry in loop quantum gravity
    Norbert Bodendorfer, Jerzy Lewandowski, Jedrzej Świeżewski

    http://arxiv.org/abs/1410.4815
    Further evidence for asymptotic safety of quantum gravity
    Kevin Falls, Daniel F. Litim, Konstantinos Nikolakopoulos, Christoph Rahmede

    http://arxiv.org/abs/1410.4788
    Loop Quantum Cosmology from Loop Quantum Gravity
    Emanuele Alesci, Francesco Cianfrani

    http://arxiv.org/abs/1410.4411
    Consistency of matter models with asymptotically safe quantum gravity
    P. Donà, Astrid Eichhorn, Roberto Percacci

    http://arxiv.org/abs/1410.1714
    Loop quantum gravity and observations
    A. Barrau, J. Grain
     
    Last edited: Nov 15, 2014
  2. jcsd
  3. Nov 15, 2014 #2

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    Here are the abstracts for the ten paper on the poll.

    http://arxiv.org/abs/1411.3592
    Projective Loop Quantum Gravity I. State Space
    Suzanne Lanéry, Thomas Thiemann
    (Submitted on 11 Nov 2014)
    Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In [Okolów 2013, arXiv:1304.6330] the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels.
    If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.
    81 pages, many figures
    google search tag [projective LQG]
    pirsa video presentation http://pirsa.org/14120011/
    googlekey for the video [pirsa lanery projective]

    http://arxiv.org/abs/1411.3180
    Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
    Dario Benedetti, Joseph Ben Geloun, Daniele Oriti
    (Submitted on 12 Nov 2014)
    We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The system of FRG equations turns out to be non-autonomous in the RG flow parameter. This feature is explained by the existence of a hidden scale, the radius of the group manifold. We investigate in detail the opposite regimes of large cut-off (UV) and small cut-off (IR) of the FRG equations, where the system becomes autonomous, and we find, in both case, Gaussian and non-Gaussian fixed points. We derive and interpret the critical exponents and flow diagrams associated with these fixed points, and discuss how the UV and IR regimes are matched at finite N. Finally, we discuss the evidence for a phase transition from a symmetric phase to a broken or condensed phase, from an RG perspective, finding that this seems to exist only in the approximate regime of very large radius of the group manifold, as to be expected for systems on compact manifolds.
    28 pages, 14 figures

    http://arxiv.org/abs/1411.0977
    Geometry and the Quantum: Basics
    Ali H. Chamseddine, Alain Connes, Viatcheslav Mukhanov
    (Submitted on 4 Nov 2014)
    Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M2(H) and M4(C) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume >4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics. Physical applications of this quantization scheme will follow in a separate publication.
    33 pages, 2 figures

    http://arxiv.org/abs/1411.0272
    Silent initial conditions for cosmological perturbations with a change of space-time signature
    Jakub Mielczarek, Linda Linsefors, Aurelien Barrau
    (Submitted on 2 Nov 2014)
    Recent calculations in loop quantum cosmology suggest that a transition from a Lorentzian to an Euclidean space-time might take place in the very early Universe. The transition point leads to a state of silence, characterized by a vanishing speed of light. This behavior can be interpreted as a decoupling of different space points, similar to the one characterizing the BKL phase.
    In this study, we address the issue of imposing initial conditions for the cosmological perturbations at the transition point between the Lorentzian and Euclidean phases. Motivated by the decoupling of space points, initial conditions characterized by a lack of correlations are investigated. We show that the "white noise" initial conditions are supported by the analysis of the vacuum state in the Euclidean regime adjacent to the state of silence.
    Furthermore, the possibility of imposing the silent initial conditions at the trans-Planckian surface, characterized by a vanishing speed for the propagation of modes with wavelengths of the order of the Planck length, is studied. Such initial conditions might result from a loop-deformations of the Poincaré algebra. The conversion of the silent initial power spectrum to a scale-invariant one is also examined.
    12 pages, 8 figures.

    http://arxiv.org/abs/1410.7062
    No firewalls in quantum gravity: the role of discreteness of quantum geometry in resolving the information loss paradox
    Alejandro Perez
    (Submitted on 26 Oct 2014)
    In an approach to quantum gravity where space-time arises from coarse graining of fundamentally discrete structures, black hole formation and subsequent evaporation can be described by a unitary evolution without the problems encountered by the standard remnant scenario or the schemes where information is assumed to come out with the radiation while evaporation (firewalls and complementarity). The final state is purified by correlations with the fundamental pre-geometric structures (in the sense of Wheeler) which are available in such approaches, and, like defects in the underlying space-time weave, can carry zero energy.
    12 pages, 7 figures.

    http://arxiv.org/abs/1410.5609
    A quantum reduction to spherical symmetry in loop quantum gravity
    Norbert Bodendorfer, Jerzy Lewandowski, Jedrzej Świeżewski
    (Submitted on 21 Oct 2014)
    Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3+1-dimensional loop quantum gravity. The construction of observables corresponds to using the radial gauge for the spatial metric and allows to identify rotations around a central observer as unitary transformations in the quantum theory. Group averaging over these rotations yields our first proposal for spherical symmetry. Hamiltonians of the full theory with angle-independent lapse preserve this spherically symmetric subsector of the full Hilbert space. A second proposal consists in implementing the vanishing of a certain vector field in spherical symmetry as a constraint on the full Hilbert space, leading to a close analogue of diffeomorphisms invariant states. While this second set of spherically symmetric states does not allow for using the full Hamiltonian, it is naturally suited to implement the spherically symmetric midisuperspace Hamiltonian, as an operator in the full theory, on it. Due to the canonical structure of the reduced variables, the holonomy-flux algebra behaves effectively as a one parameter family of 2+1-dimensional algebras along the radial coordinate, leading to a diagonal non-vanishing volume operator on 3-valent vertices. The quantum dynamics thus becomes tractable, including scenarios like spherically symmetric dust collapse.
    5 pages

    http://arxiv.org/abs/1410.4815
    Further evidence for asymptotic safety of quantum gravity
    Kevin Falls, Daniel F. Litim, Konstantinos Nikolakopoulos, Christoph Rahmede
    (Submitted on 17 Oct 2014)
    The asymptotic safety conjecture is examined for quantum gravity in four dimensions. Using the renormalisation group, we find evidence for an interacting UV fixed point for polynomial actions up to the 34th power in the Ricci scalar. The extrapolation to infinite polynomial order is given, and the self-consistency of the fixed point is established using a bootstrap test. All details of our analysis are provided. We also clarify further aspects such as stability, convergence, the role of boundary conditions, and a partial degeneracy of eigenvalues. Within this setting we find strong support for the conjecture.
    43 pages, 17 figures

    http://arxiv.org/abs/1410.4788
    Loop Quantum Cosmology from Loop Quantum Gravity
    Emanuele Alesci, Francesco Cianfrani
    (Submitted on 17 Oct 2014)
    We show how Loop Quantum Cosmology can be derived as an effective semiclassical description of Loop Quantum Gravity. Using the tools of QRLG, a gauge fixed version of LQG, we take the coherent states of the fundamental microscopic theory suitable to describe a Bianchi I Universe and we find a mapping between the expectation value of the Hamiltonian and the dynamics of LQC. Our results are in agreement with a lattice refinement framework for LQC, thus the so called ``old'' and ``improved-dynamics'' regularization schemes can be reproduced. These amount to different choices of relations between local variables and the smeared ones entering the definition of the coherent states. The leading order of the fundamental theory corresponds to LQC, but we also find different inverse volume corrections, that depend on a purely quantum observable, namely the number of nodes of the states.
    5 pages

    http://arxiv.org/abs/1410.4411
    Consistency of matter models with asymptotically safe quantum gravity
    P. Donà, Astrid Eichhorn, Roberto Percacci
    (Submitted on 16 Oct 2014)
    We discuss the compatibility of quantum gravity with dynamical matter degrees of freedom. Specifically, we present bounds we obtained in [1] on the allowed number and type of matter fields within asymptotically safe quantum gravity. As a novel result, we show bounds on the allowed number of spin-3/2 (Rarita-Schwinger) fields, e.g., the gravitino. These bounds, obtained within truncated Renormalization Group flows, indicate the compatibility of asymptotic safety with the matter fields of the standard model. Further, they suggest that extensions of the matter content of the standard model are severely restricted in asymptotic safety. This means that searches for new particles at colliders could provide experimental tests for this particular approach to quantum gravity.
    8 pages, 1 figure, 1 table. Proceedings of Theory Canada 9; new results on the gravitino,

    http://arxiv.org/abs/1410.1714
    Loop quantum gravity and observations
    A. Barrau, J. Grain
    (Submitted on 7 Oct 2014)
    Quantum gravity has long been thought to be completely decoupled from experiments or observations. Although it is true that smoking guns are still missing, there are now serious hopes that quantum gravity phenomena might be tested. We review here some possible ways to observe loop quantum gravity effects either in the framework of cosmology or in astroparticle physics.
    25 pages, 8 figures. To be published in the World Scientific series "100 Years of General Relativity" as a chapter in the Loop Quantum Gravity volume, edited by A. Ashtekar and J. Pullin.
    google search key [barrau LQG observations]
     
    Last edited: Dec 15, 2014
  4. Nov 20, 2014 #3

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    David, thanks for joining me in the early half of the poll! I'll have the other half of the list ready by the end of December. I agree with you strongly about LQG and observations. Deriving observational predictions and figuring out how to test the various versions of the theory are some of the most important work being done. Also on the subject of Alain Connes spectral geometry that seems able to combine the particles of the standard model with his version of quantum gravity. You may have noticed, since you are interested in NCG, that Connes has written a nice non-technical account of the new paper and posted it at the NCG blog. I'll get the link in a moment:
    http://noncommutativegeometry.blogspot.nl/2014/11/particles-in-quantum-gravity.html
    The title is "Particles in Quantum Gravity", which is a good layman header for the paper he is talking about, "Geometry and the Quantum", on our 4th quarter poll.

    I'll start gathering papers for the second half of this quarter's poll. With luck there will be ten really good ones. Here's one by Philipp Hoehn that came out today which seems to dovetail both with the line of research pursued by Bianca Dittrich and also that by Cortes Smolin and by Wolfgang Wieland. The idea of a geometric process based on Pachner moves:
    http://arxiv.org/abs/1411.5672
    Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves
    Philipp A. Hoehn
    (Submitted on 20 Nov 2014)
    We afford a systematic and comprehensive account of the canonical dynamics of 4D Regge Calculus perturbatively expanded to linear order around a flat background. To this end, we consider the Pachner moves which generate the most basic and general simplicial evolution scheme. The linearized regime features a vertex displacement (`diffeomorphism') symmetry for which we derive an abelian constraint algebra. This permits to identify gauge invariant `lattice gravitons' as propagating curvature degrees of freedom. The Pachner moves admit a simple method to explicitly count the gauge and `graviton' degrees of freedom on an evolving triangulated hypersurface and we clarify the distinct role of each move in the dynamics. It is shown that the 1-4 move generates four `lapse and shift' variables and four conjugate vertex displacement generators; the 2-3 move generates a `graviton'; the 3-2 move removes one `graviton' and produces the only non-trivial equation of motion; and the 4-1 move removes four `lapse and shift' variables and trivializes the four conjugate symmetry generators. It is further shown that the Pachner moves preserve the vertex displacement generators. These results may provide new impetus for exploring `graviton dynamics' in discrete quantum gravity models.
    26+12 pages, 2 appendices, many figures. This article is fairly self-contained

    David, you may be able to advise about the next. I've seen people do fractional dimension expansions in perturbation theory, but I don't understand it all that well and I can't recall ever seeing it done in Quantum Gravity. Look at what Carrozza says about what he is doing, in the first paragraph of the introduction. I quote it here, following the abstract. Judging by what he says this could be an important development, completing the definition of the dynamics of LQG.

    http://arxiv.org/abs/1411.5385
    Group Field Theory in dimension four minus epsilon
    Sylvain Carrozza
    (Submitted on 19 Nov 2014)
    Building on an analogy with ordinary scalar field theories, an epsilon expansion for rank-3 tensorial group field theories with gauge invariance condition is introduced. This allows to continuously interpolate between the dimension four group SU(2) X U(1) and the dimension three SU(2). In the first situation, there is a unique marginal 4-valent coupling constant, but in contrast to ordinary scalar field theory this model is asymptotically free. In the SU(2) case, the presence of two marginally relevant 6-valent coupling constants and one 4-valent super-renormalizable interaction spoils this interesting property. However, the existence of a non-trivial fixed point is established in dimension four minus epsilon, hence suggesting that the SU(2) theory might be asymptotically safe. To pave the way to future non-perturbative calculations, the present perturbative results are discussed in the framework of the effective average action.
    14 pages, 6 figures
    ==quote introduction==
    Group Field Theory (GFT) [1–4] is a general formalism aiming at completing the definition of the dynamics of Loop Quantum Gravity (LQG) [5–9], either from a covariant perspective as was historically proposed and since then has been the main line of investigation [10, 11], or directly from the canonical picture as was more recently suggested [12, 13]. An alternative but related approach to the same question relies on lattice gauge theory methods [14–17]. In both Wilson’s renormalization group is central, first to consistently define the theory, and at a later stage to explore its phase structure. In the long run, we hope to understand the effective, low energy limit of LQG, and be in a position to check whether Einstein’s gravity is reproduced or not.
    ==endquote==

    In a way BOTH these papers which just appeared have to do with completing the dynamics of discrete quantum geometry. The first one, by Philipp Höhn, offers what I think is a very exciting idea to implement gravitons (or at least propagating quanta of curvature) through PACHNER moves. Interactions of tetrahedra. To me it seems similar in spirit to the recent works by Cortes Smolin, and by Wieland, which were on the 3rd quarter poll,
     
    Last edited: Nov 20, 2014
  5. Dec 12, 2014 #4

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    More candidates for the second installment of the 4th quarter MIP poll. Important papers clearly,
    1. a carefully considered reformulation of canonical LQG, which brings it closer to Spinfoam "sum over histories" dynamics and facilitates coarse-graining. Possible consequences for the continuum limit.
    2. how to introduce initial conditions into quantum cosmology. Important when it comes to confronting the cosmic model with all kinds of observations.
    3. very important! combining bounce cosmology with the standard LambdaCDM model, more realistic (less "toy") universe contents, also opening to a concordat between LQC bounce and the McGill group's "matter bounce".

    http://arxiv.org/abs/1412.3752
    Flux formulation of loop quantum gravity: Classical framework
    Bianca Dittrich, Marc Geiller
    (Submitted on 11 Dec 2014)
    We recently introduced a new representation for loop quantum gravity, which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper we lay out the classical framework underlying this new formulation. The central objects in our construction are the so-called integrated fluxes, which are defined as the integral of the electric field variable over surfaces of codimension one, and related in turn to Wilson surface operators. These integrated flux observables will play an important role in the coarse graining of states in loop quantum gravity, and can be used to encode in this context the notion of curvature-induced torsion. We furthermore define a continuum phase space as the modified projective limit of a family of discrete phase spaces based on triangulations. This continuum phase space yields a continuum (holonomy-flux) algebra of observables. We show that the corresponding Poisson algebra is closed by computing the Poisson brackets between the integrated fluxes, which have the novel property of being allowed to intersect each other.
    60 pages, 13 figures
    google search key [flux formulation LQG]

    http://arxiv.org/abs/1412.3524
    Preferred instantaneous vacuum for linear scalar fields in cosmological space-times
    Ivan Agullo, William Nelson, Abhay Ashtekar
    (Submitted on 11 Dec 2014)
    We discuss the problem of defining a preferred vacuum state at a given time for a quantized scalar field in Friedmann, Lemaître, Robertson Walker (FLRW) space-time. Among the infinitely many homogeneous, isotropic vacua available in the theory, we show that there exists at most one for which every Fourier mode makes vanishing contribution to the adiabatically renormalized energy-momentum tensor at any given instant. For massive fields such a state exists in the most commonly used backgrounds in cosmology, and provides a natural candidate for the ground state at that instant of time. The extension to the massless and the conformally coupled case are also discussed.
    14 pages.
    ==excerpt from conclusions==
    ...The definition of preferred vacua for quantized fields in cosmological space-times is an interesting problem, not only for its conceptual importance but also for its relevance in the computation of primordial cosmic perturbations in the early universe. In those computations one needs to specify the quantum state for perturbations at some “initial” time η0. ...
    ...
    ...
    By contrast, the instantaneous vacuum introduced in this paper is free of these limitations. In the most widely used FLRW models, it provides a natural avenue to select a preferred vacuum at any given instant of time. ... it is the state with the least possible back-reaction at η = η0. In this sense, it can be thought of as the analog of the standard vacuum in Minkowski space-time, albeit only at a given instant of time. The background time dependence is reflected in the fact that in (even the Heisenberg picture) the state so selected changes from one instant to another. The preferred instantaneous vacuum has been applied satisfactorily in the study of cosmological perturbation in loop quantum cosmology, where initial conditions are specified at or near the bounce time [18, 26]. We expect it will be also useful in other scenarios to select “initial conditions” for cosmological perturbations.
    ==endquote==

    http://arxiv.org/abs/1412.2914
    A ΛCDM bounce scenario
    Yi-Fu Cai, Edward Wilson-Ewing
    (Submitted on 9 Dec 2014)
    We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. As is well known from standard cosmological perturbation theory, under the assumption of initial quantum vacuum fluctuations the Fourier modes of the comoving curvature perturbation that exit the (sound) Hubble radius in such a contracting universe at a time of matter-domination will be nearly scale-invariant. Furthermore, the modes that exit the (sound) Hubble radius when the effective equation of state is slightly negative due to the cosmological constant will have a slight red tilt, in agreement with observations. We assume that loop quantum cosmology captures the correct high-curvature dynamics of the space-time, and this ensures that the big-bang singularity is resolved and is replaced by a bounce. We calculate the evolution of the perturbations through the bounce and find that they remain nearly scale-invariant. We also show that the amplitude of the scalar perturbations in this cosmology depends on a combination of the sound speed of cold dark matter, the Hubble rate in the contracting branch at the time of equality of the energy densities of cold dark matter and radiation, and the curvature scale that the loop quantum cosmology bounce occurs at. Finally, for a small sound speed of cold dark matter, this scenario predicts a small tensor-to-scalar ratio.
    14 pages, 8 figures
    google search key [LambdaCDM bounce]
     
    Last edited: Dec 12, 2014
  6. Dec 13, 2014 #5
  7. Dec 13, 2014 #6
  8. Dec 13, 2014 #7
  9. Dec 13, 2014 #8
    Just added info . I've been a follower on the sidelines of 2d QG. I'm just curious on how does it relate to the MCMC.

    BTW, I been using the QMC in my field of work. Global illumination computation for faster ray trace approx. (It has nothing to do with cosmology).
     
  10. Dec 14, 2014 #9

    atyy

    User Avatar
    Science Advisor

    Sounds cool. Can I get some pointers to read up on the subject?
     
  11. Dec 14, 2014 #10
  12. Dec 15, 2014 #11

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    Atyy, David H., and Julcab, thanks for getting the poll started! There was confusion about the poll format size limit. I think now it is 20, so the first quarter 2015 poll can be the customary size with 20 candidates. But this time the poll is split 10+10. I think the first paper on the list, the one by Lanery and Thiemann, has special importance. Atyy I'm glad you agree! My impression comes partly just from thinking it over: the Ashtekar Lewandowski formulation with holonomy&flux variables was good, and opened the way for the UNIQUENESS theorem of FLOST (Fleischhack, Lewandowski, Okolow, Sahlmann, Thiemann), but some of the same people have been looking for ways to improve on it. Actually Lanery and Thiemann took their cue from a 2007 paper by Okolow that used the projective family of density matrices idea.

    Another thing that impressed me (that this present development is well thought-out) was watching the Suzanne Lanery talk on Pirsa. She motivates the new formulation extremely well. Also it helped that there were intensely interested people (Bianca Dittrich and Laurent Freidel) in the audience who asked a lot of questions.
    http://pirsa.org/14120011/
    Extending the state space of LQG
    Suzanne Lanery
    Instead of formulating the state space of a quantum field theory over a single big Hilbert space, it has been proposed by Jerzy Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. I will discuss the physical motivations for this approach and explain how it can be implemented in the context of LQG. While the resulting state space forms a natural extension of the Ashtekar-Lewandowski Hilbert space, it treats position and momentum variables on equal footing. This paves the way for the construction of semi-classical states beyond fixed graph level, and eventually for the derivation of LQC from full LQG.
    10/12/2014 - 3:30
    ======================================
    Because there is a lot going on in Loop and related areas, particularly as affects the basic formulation of Loop gravity, Spinfoam, and Loop cosmology, I am trying to put the new developments into perspective and keep them in context of each other. It's hard to remember all the arXiv numbers, so I've assembled search tags ("googlekeys") for some of the more important 2014 papers I've been referring to lately. When you google the words in brackets you typically get the article (sometimes pirsa or ILQGS talk) as the first hit.
    [flux formulation LQG] [projective LQG arxiv] [pirsa lanery]
    The first googlekey gets you an article by Bianca Dittrich and that I think is somehow related to the Lanery Thiemann work, but haven't quite figured out what the connection is. The other two are discussed some in this thread and in the "LQG Act Two" thread.

    The next three have to do with cosmology.
    [barrau LQG observations] [LambdaCDM bounce] [inflation selfreproduction]
    Because Loop QG predicts a bounce from prior contracting phase at the start of expansion, it has observable consequences and so observations of stuff from early universe are important. Aurelien Barrau is a leader in this and the key gets a Barrau et al paper. The next key gets a paper by Cai and Wilson-Ewing that works in the standard cosmic model LambdaCDM to get an unprecedentedly realistic bounce. The third key is a great paper by Slava Mukhanov which shows that multiverseness isn't necessary from an inflation standpoint. You can have inflation without it going hog wild and generating a multiverse (by "selfreproduction")

    There are two papers I think are important from an ONTOLOGICAL standpoint because they show how we can the passage of time and the growing universe into the mathematical model. This is a departure from the "block universe" idea.
    [wieland new action] [cortes causal spinfoam]

    Finally there are two papers that interest me very much and present ideas with what seem to me a high degree of originality. The Haggard and Riello ILQGS talk introduces a new kind of simplicial complex (triangles, tetrahedra, pentachorons) where the bulk interior of simplexes is not flat but actually has a constant curvature thus embodying the cosmological constant a spacetime curvature constant provides a very slight tendency for distances to increase. This seems a natural and perfect way to put the Lambda curvature constant into the theory, as what it is. The Barrau et al "Silent initial conditions" paper brings into the Loop cosmology bounce the intriguing idea that extreme density causes a breakdown of interaction between neighboring points---so that the bounce would involve a phase change. In a classical context the idea goes back to three Russian physicists (around 1970) with initials B., K., and L.
    [barrau silent initial conditions] [haggard SL(2,C) spinfoam]
     
    Last edited: Dec 17, 2014
  13. Dec 16, 2014 #12
  14. Dec 16, 2014 #13

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    Hi Twistor, thanks for the suggestions. The fifth one on your list (1411.3180, by Benedetti, Geloun, Oriti) is already on part I of the poll! I hope you will express your interest in it by voting for it. :w Also the poll allows voting for several papers, so if you see any others you like, go for it! Functional renormalization is the basis of the Asymptotic Safety approach of people like Percacci and Reuter, it's interesting to see it carried over into a completely different approach to QG, namely Group Field Theory.

    Your fourth one (1411.5385, Sylvain Carrozza) is one I already listed for consideration on the second half of the poll, look back to post #3 of this thread. It is another GFT one.
     
  15. Dec 27, 2014 #14

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    Getting ready to complete the 4th quarter MIP poll. Search keys that currently work on google are included, as are three papers brought forward from the initial part of the poll:

    http://arxiv.org/abs/1412.8247
    Pachner moves in a 4d Riemannian holomorphic Spin Foam model
    Andrzej Banburski, Lin-Qing Chen, Laurent Freidel, Jeff Hnybida
    (Submitted on 29 Dec 2014)
    In this work we study a Spin Foam model for 4d Riemannian gravity, and propose a new way of imposing the simplicity constraints that uses the recently developed holomorphic representation. Using the power of the holomorphic integration techniques, and with the introduction of two new tools: the homogeneity map and the loop identity, for the first time we give the analytic expressions for the behaviour of the Spin Foam amplitudes under 4-dimensional Pachner moves. It turns out that this behaviour is controlled by an insertion of nonlocal mixing operators. In the case of the 5-1 move, the expression governing the change of the amplitude can be interpreted as a vertex renormalisation equation. We find a natural truncation scheme that allows us to get an invariance up to an overall factor for the 4-2 and 5-1 moves, but not for the 3-3 move. The study of the divergences shows that there is a range of parameter space for which the 4-2 move is finite while the 5-1 move diverges. This opens up the possibility to recover diffeomorphism invariance in the continuum limit of Spin Foam models for 4D Quantum Gravity.
    48 pages, 30 figures

    http://arxiv.org/abs/1412.7546
    SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
    Hal M. Haggard, Muxin Han, Wojciech Kamiński, Aldo Riello
    (Submitted on 23 Dec 2014)
    We study the expectation value of a nonplanar Wilson graph operator in SL(2,C) Chern-Simons theory on S3. In particular we analyze its asymptotic behaviour in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains at the leading order an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern-Simons action. This can be understood as arising from the relation between Chern-Simons theory on the boundary of a region, and a theory defined by an F2 action in the bulk. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. In other words, this work suggests a relation between 4-dimensional loop quantum gravity with a cosmological constant and SL(2,C) Chern-Simons theory in 3-dimensions with knotted graph defects.
    54+11 pages, 9 figures
    search key [SL(2,C) Chern-Simons LQG]

    http://arxiv.org/abs/1412.7435
    Horizon entropy with loop quantum gravity methods
    Daniele Pranzetti, Hanno Sahlmann
    (Submitted on 23 Dec 2014)
    We show that the spherically symmetric isolated horizon can be described in terms of an SU(2) connection and a su(2) valued one form, obeying certain constraints. The horizon symplectic structure is precisely the one of 3d gravity in a first order formulation. We quantize the horizon degrees of freedom in the framework of loop quantum gravity, with methods recently developed for 3d gravity with non-vanishing cosmological constant. Bulk excitations ending on the horizon act very similar to particles in 3d gravity. The Bekenstein-Hawking law is recovered in the limit of imaginary Barbero-Immirzi parameter. Alternative methods of quantization are also discussed.
    17 pages, 2 figures
    search key [horizon entropy loop methods]

    http://arxiv.org/abs/1412.6015
    On the Effective Metric of a Planck Star
    Tommaso De Lorenzo, Costantino Pacilio, Carlo Rovelli, Simone Speziale
    (Submitted on 18 Dec 2014)
    Spacetime metrics describing `non-singular' black holes are commonly studied in the literature as effective modification to the Schwarzschild solution that mimic quantum gravity effects removing the central singularity. Here we point out that to be physically plausible, such metrics should also incorporate the 1-loop quantum corrections to the Newton potential and a non-trivial time delay between an observer at infinity and an observer in the regular center. We present a modification of the well-known Hayward metric that features these two properties. We discuss bounds on the maximal time delay imposed by conditions on the curvature, and the consequences for the weak energy condition, in general violated by the large transversal pressures introduced by the time delay.
    10 pages, many figures
    search key [metric planck star]

    http://arxiv.org/abs/1412.5851
    Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy
    Olivier Asin, Jibril Ben Achour, Marc Geiller, Karim Noui, Alejandro Perez
    (Submitted on 18 Dec 2014)
    We study the thermodynamical properties of black holes when described as gases of indistinguishable punctures with a chemical potential. In this picture, which arises from loop quantum gravity, the black hole microstates are defined by finite families of half-integers spins coloring the punctures, and the near-horizon energy measured by quasi-local stationary observers defines the various thermodynamical ensembles. The punctures carry excitations of quantum geometry in the form of quanta of area, and the total horizon area aH is given by the sum of these microscopic contributions. We assume here that the system satisfies the Bose-Einstein statistics, and that each microstate is degenerate with a holographic degeneracy given by exp(λaH/ℓPl2) and λ>0.
    We analyze in detail the thermodynamical properties resulting from these inputs, and in particular compute the grand canonical entropy. We explain why the requirements that the temperature be fixed to the Unruh temperature and that the chemical potential vanishes do not specify completely the semi-classical regime of large horizon area, and classify in turn what the various regimes can be. When the degeneracy saturates the holographic bound (λ=1/4), there exists a semi-classical regime in which the subleading corrections to the entropy are logarithmic. Furthermore, this regime corresponds to a Bose-Einstein condensation, in the sense that it is dominated by punctures carrying the minimal (or ground state) spin value 1/2.
    22 pages
    search key [black hole gas punctures]

    http://arxiv.org/abs/1412.3752
    Flux formulation of loop quantum gravity: Classical framework
    Bianca Dittrich, Marc Geiller
    (Submitted on 11 Dec 2014)
    We recently introduced a new representation for loop quantum gravity, which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper we lay out the classical framework underlying this new formulation. The central objects in our construction are the so-called integrated fluxes, which are defined as the integral of the electric field variable over surfaces of codimension one, and related in turn to Wilson surface operators. These integrated flux observables will play an important role in the coarse graining of states in loop quantum gravity, and can be used to encode in this context the notion of curvature-induced torsion. We furthermore define a continuum phase space as the modified projective limit of a family of discrete phase spaces based on triangulations. This continuum phase space yields a continuum (holonomy-flux) algebra of observables. We show that the corresponding Poisson algebra is closed by computing the Poisson brackets between the integrated fluxes, which have the novel property of being allowed to intersect each other.
    60 pages, 13 figures
    search key [flux formulation LQG]

    http://arxiv.org/abs/1412.2914
    A ΛCDM bounce scenario
    Yi-Fu Cai, Edward Wilson-Ewing
    (Submitted on 9 Dec 2014)
    We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. As is well known from standard cosmological perturbation theory, under the assumption of initial quantum vacuum fluctuations the Fourier modes of the comoving curvature perturbation that exit the (sound) Hubble radius in such a contracting universe at a time of matter-domination will be nearly scale-invariant. Furthermore, the modes that exit the (sound) Hubble radius when the effective equation of state is slightly negative due to the cosmological constant will have a slight red tilt, in agreement with observations. We assume that loop quantum cosmology captures the correct high-curvature dynamics of the space-time, and this ensures that the big-bang singularity is resolved and is replaced by a bounce. We calculate the evolution of the perturbations through the bounce and find that they remain nearly scale-invariant. We also show that the amplitude of the scalar perturbations in this cosmology depends on a combination of the sound speed of cold dark matter, the Hubble rate in the contracting branch at the time of equality of the energy densities of cold dark matter and radiation, and the curvature scale that the loop quantum cosmology bounce occurs at. Finally, for a small sound speed of cold dark matter, this scenario predicts a small tensor-to-scalar ratio.
    14 pages, 8 figures
    search key [LambdaCDM bounce]

    http://arxiv.org/abs/1411.5672
    Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves
    Philipp A. Hoehn
    (Submitted on 20 Nov 2014)
    We afford a systematic and comprehensive account of the canonical dynamics of 4D Regge Calculus perturbatively expanded to linear order around a flat background. To this end, we consider the Pachner moves which generate the most basic and general simplicial evolution scheme. The linearized regime features a vertex displacement (`diffeomorphism') symmetry for which we derive an abelian constraint algebra. This permits to identify gauge invariant `lattice gravitons' as propagating curvature degrees of freedom. The Pachner moves admit a simple method to explicitly count the gauge and `graviton' degrees of freedom on an evolving triangulated hypersurface and we clarify the distinct role of each move in the dynamics. It is shown that the 1-4 move generates four `lapse and shift' variables and four conjugate vertex displacement generators; the 2-3 move generates a `graviton'; the 3-2 move removes one `graviton' and produces the only non-trivial equation of motion; and the 4-1 move removes four `lapse and shift' variables and trivializes the four conjugate symmetry generators. It is further shown that the Pachner moves preserve the vertex displacement generators. These results may provide new impetus for exploring `graviton dynamics' in discrete quantum gravity models.
    26+12 pages, 2 appendices, many figures. This article is fairly self-contained.
    search key [graviton Pachner moves]

    http://arxiv.org/abs/1411.3589
    Projective Limits of State Spaces I. Classical Formalism
    Suzanne Lanéry, Thomas Thiemann
    (Submitted on 11 Nov 2014)
    In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski and Andrzej Okolów, which describes the states of a quantum (field) theory as projective families of density matrices. The present first paper aims at clarifying the classical structures that underlies this formalism, namely projective limits of symplectic manifolds. In particular, this allows us to discuss accurately the issues hindering an easy implementation of the dynamics in this context, and to formulate a strategy for overcoming them.
    51 pages, many figures
    search key [projective limit state classical]

    http://arxiv.org/abs/1411.3590
    Projective Limits of State Spaces II. Quantum Formalism
    Suzanne Lanéry, Thomas Thiemann
    (Submitted on 11 Nov 2014)
    In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski and Andrzej Okolów, which describes the states of a quantum theory as projective families of density matrices. After discussing the formalism at the classical level in a first paper, the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okolów [arXiv:1304.6330], that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces.
    56 pages, 2 figures
    search key [projective limit state quantum]

    http://arxiv.org/abs/1411.3591
    Projective Limits of State Spaces III. Toy-Models
    Suzanne Lanéry, Thomas Thiemann
    (Submitted on 11 Nov 2014)
    In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski and Andrzej Okolów, which describes the states of a quantum theory as projective families of density matrices. A strategy to implement the dynamics in this formalism was presented in our first paper, which we now test in two simple toy-models. The first one is a very basic linear model, meant as an illustration of the general procedure, and we will only discuss it at the classical level. In the second one, we reformulate the Schrödinger equation, treated as a classical field theory, within this projective framework, and proceed to its (non-relativistic) second quantization. We are then able to reproduce the physical content of the usual Fock quantization.
    40 pages
    search key [projective limit state model]
    ==============brought forward================
    http://arxiv.org/abs/1411.3592
    Projective Loop Quantum Gravity I. State Space
    Suzanne Lanéry, Thomas Thiemann
    (Submitted on 11 Nov 2014)
    Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In [Okolów 2013, arXiv:1304.6330] the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels.
    If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.
    81 pages, many figures

    http://arxiv.org/abs/1411.0977
    Geometry and the Quantum: Basics
    Ali H. Chamseddine, Alain Connes, Viatcheslav Mukhanov
    (Submitted on 4 Nov 2014)
    Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M2(H) and M4(C) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume >4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics. Physical applications of this quantization scheme will follow in a separate publication.
    33 pages, 2 figures

    http://arxiv.org/abs/1410.1714
    Loop quantum gravity and observations
    A. Barrau, J. Grain
    (Submitted on 7 Oct 2014)
    Quantum gravity has long been thought to be completely decoupled from experiments or observations. Although it is true that smoking guns are still missing, there are now serious hopes that quantum gravity phenomena might be tested. We review here some possible ways to observe loop quantum gravity effects either in the framework of cosmology or in astroparticle physics.
    25 pages, 8 figures. To be published in the World Scientific series "100 Years of General Relativity" as a chapter in the Loop Quantum Gravity volume, edited by A. Ashtekar and J. Pullin.
     
    Last edited: Dec 29, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook