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 S
3. 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 F
2 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 a
H 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(λa
H/ℓ
Pl2) 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 M
2(H) and M
4(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.
