Eugenio Bianchi, Elena Magliaro, Claudio Perini
We compute metric correlations in loop quantum gravity with the dynamics defined by the new spin foam models. The analysis is done at the lowest order in a vertex expansion and at the leading order in a large spin expansion. The result is compared to the graviton propagator of perturbative quantum gravity.
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In a seminal paper, Kaminski, Kisielowski an Lewandowski for the first time extended the definition of spin foam models to arbitrary boundary graphs. This is a prerequisite in order to make contact to the canonical formulation of Loop Quantum Gravity (LQG) whose Hilbert space contains all these graphs. This makes it finally possible to investigate the question whether any of the presently considered spin foam models yields a rigging map for any of the presently defined Hamiltonian constraint operators. In the analysis of this would-be spin foam rigging map we are able to identify an elementary…
The U(N) framework and the spinor representation for loop quantum gravity are two new points of view that can help us deal with the most fundamental problems of the theory. Here, we review the detailed construction of the U(N) framework explaining how one can endow the Hilbert space of N-leg intertwiners with a Fock structure. We then give a description of the classical phase space corresponding to this system in terms of the spinors, and we will study its quantization using holomorphic techniques. We take special care in constructing the usual holonomy operators of LQG in terms of spinors, an…
It is often emphasized that spin-foam models could realize a projection on the physical Hilbert space of canonical Loop Quantum Gravity (LQG). As a first test we analyze the one-vertex expansion of a simple Euclidean spin-foam. We find that for fixed Barbero-Immirzi parameter γ=1 the one vertex-amplitude in the KKL prescription annihilates the Euclidean Hamiltonian constraint of LQG. Since for γ=1 the Lorentzian part of the Hamiltonian constraint does not contribute this gives rise to new solutions of the Euclidean theory. Furthermore, we find that the new states only depend on the diagonal ma…
In a previous article we have show that there are difficulties in obtaining the correct graviton propagator from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude that depends nontrivially on the intertwiners can yield the correct propagator. We give an explicit example of asymptotic behavior of a vertex amplitude that gives the correct full graviton propagator in the large distance limit.
The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity (LQG) is a promising proposal for addressing this difficult task. Despite the steady progress of the field, dynamics remains to a large extend an open issue in LQG. Here we present the main ideas behind a series of proposals for addressing the issue of dynamics. We refer to these constructions as the {\em spin foam representation} of LQG. This set of ideas can be viewed as a systematic attempt at …
We review the construction of the tensorial structure of the graviton propagator in the context of loop quantum gravity and spinfoam formalism. The main result of this analysis is that applying the same strategy used to compute the diagonal terms, the Barrett-Crane vertex is unable to yield the correct propagator in the long distance limit. The problem is in the intertwiner-independence of the Barrett-Crane vertex. We also review the asymptotic behavior of an alternative vertex that is able to give the correct propagator.
"The Spin Foams for People Without the 3d/4d Imagination" could be an alternative title of our work. We derive spin foams from operator spin network diagrams} we introduce. Our diagrams are the spin network analogy of the Feynman diagrams. Their framework is compatible with the framework of Loop Quantum Gravity. For every operator spin network diagram we construct a corresponding operator spin foam. Admitting all the spin networks of LQG and all possible diagrams leads to a clearly defined large class of operator spin foams. In this way our framework provides a proposal for a class of 2-cell c…
In the first article of this series, we pointed out a difficulty in the attempt to derive the low-energy behavior of the graviton two-point function, from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that this difficulty disappears when using the corrected vertex amplitude recently introduced in the literature. In particular, we show that the asymptotic analysis of the new vertex amplitude recently performed by Barrett, Fairbairn and others, implies that the vertex has precisely the asymptotic structure that, in the second article of this series…
We numerically estimate the divergence of several two-vertex diagrams that contribute to the radiative corrections for the Lorentzian EPRL spin foam propagator. We compute the amplitudes as functions of a homogeneous cutoff over the bulk quantum numbers, fixed boundary data, and different Immirzi parameters, and find that for a class of two-vertex diagrams, those with fewer than six internal faces are convergent. The calculations are done with the numerical framework sl2cfoam-next.
Some components of the graviton two-point function have been recently computed in the context of loop quantum gravity, using the spinfoam Barrett-Crane vertex. We complete the calculation of the remaining components. We find that, under our assumptions, the Barrett-Crane vertex does not yield the correct long distance limit. We argue that the problem is general and can be traced to the intertwiner-independence of the Barrett-Crane vertex, and therefore to the well-known mismatch between the Barrett-Crane formalism and the standard canonical spin networks. In a companion paper we illustrate the…
We consider the EPRL spin foam amplitude for arbitrary embedded two-complexes. Choosing a definition of the face- and edge amplitudes which lead to spin foam amplitudes invariant under trivial subdivisions, we investigate invariance properties of the amplitude under consistent deformations, which are deformations of the embedded two-complex where faces are allowed to pass through each other in a controlled way. Using this surprising invariance, we are able to show that in the physical Hilbert space as defined by the sum over all spin foams contains no knotting classes of graphs anymore.
We discuss the notion of causality in Quantum Gravity in the context of sum-over-histories approaches, in the absence therefore of any background time parameter. In the spin foam formulation of Quantum Gravity, we identify the appropriate causal structure in the orientation of the spin foam 2-complex and the data that characterize it; we construct a generalised version of spin foam models introducing an extra variable with the interpretation of proper time and show that different ranges of integration for this proper time give two separate classes of spin foam models: one corresponds to the sp…
In recent years, the calculation of the first non-vanishing order of the metric 2-point function or graviton propagator in a semiclassical limit has evolved as a standard test for the credibility of a proposed spin foam model. The existing results of spinfoam graviton propagator rely heavily on the so-called double scaling limit where spins $j$ are large and the Barbero-Immirzi parameter $γ$ is small such that the area $A\propto jγ$ is approximately constant. However, it seems that this double scaling limit is bound to break down in models including a cosmological constant. We explore this in …
The spinfoam framework is a proposal for a regularized path integral for quantum gravity. Spinfoams define quantum space-time structures describing the evolution in time of the spin network states for quantum geometry derived from Loop Quantum Gravity (LQG). The construction of this covariant approach is based on the formulation of General Relativity as a topological theory plus the so-called simplicity constraints which introduce local degrees of freedom. The simplicity constraints are essential in turning the non-physical topological theory into 4d gravity. In this PhD manuscript, an origina…
The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into $SU(2)_L\times SU(2)_R$ semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.
We link the notion causality with the orientation of the 2-complex on which spin foam models are based. We show that all current spin foam models are orientation-independent, pointing out the mathematical structure behind this independence. Using the technology of evolution kernels for quantum fields/particles on Lie groups/homogeneous spaces, we construct a generalised version of spin foam models, introducing an extra proper time variable and prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum g…
A Primer of Group Theory for Loop Quantum Gravity and Spin-foams
本文为循环量子引力和spin-foams研究者提供简洁的数学工具介绍，整理公式集，并翻译不同文献间的惯例。
We study the classical limit of the ELPR/FK spin foam models by analyzing the large-distance asymptotics of the corresponding graviton propagators. This is done by examining the large-spin asymptotics of the Hartle-Hawking wavefunction which is peaked around a classical flat spatial geometry. By using the stationary phase method we determine the wavefunction asymptotics. The obtained asymptotics does not give the desired large-distance asymptotics for the corresponding graviton propagator. However, we show that the ELPR/FK vertex amplitude can be redefined such that the corresponding Hartle-Ha…
We compute Teitelboim's causal propagator in the context of canonical loop quantum gravity. For the Lorentzian signature, we find that the resultant power series can be expressed as a sum over branched, colored two-surfaces with an intrinsic causal structure. This leads us to define a general structure which we call a ``causal spin foam''. We also demonstrate that the causal evolution models for spin networks fall in the general class of causal spin foams.
Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity (LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries satisfying Einstein equation can emerge from discrete SFMs under an appropriate low energy limit, which corresponds to a semiclassical continuum limit of SFMs. In particular, we show that the low energy excitations of SFMs on a flat background give all smooth solutions of linearized Einstein equations (spin-2 gravitons). This indicates that at the linearized …
The Spin Foam Model for the SO(4,C) BF theory is discussed. The Barrett-Crane intertwiner for the SO(4,C) general relativity is systematically derived. The SO(4,C) Barret-Crane interwiner is unique. The propagators of the SO(4,C) Barrett-Crane model are discussed. The asymptotic limit of the SO(4,C) general relativity is discussed. The asymptotic limit is controlled by the SO(4,C) Regge calculus.
This article presents an "in-a-nutshell" yet self-contained introductory review on loop quantum gravity (LQG) -- a background-independent, nonperturbative approach to a consistent quantum theory of gravity. Instead of rigorous and systematic derivations, it aims to provide a general picture of LQG, placing emphasis on the fundamental ideas and their significance. The canonical formulation of LQG, as the central topic of the article, is presented in a logically orderly fashion with moderate details, while the spin foam theory, black hole thermodynamics, and loop quantum cosmology are covered br…
We study the problem of semiclassical limit of Loop Quantum Gravity theory defined by the new spin foam models. This is done by analyzing the large-spin asymptotics of the Hartle-Hawking wavefunction. By using the stationary phase method we determine the wavefunction asymptotics, which then determines the large-distance asymptotics of the corresponding graviton propagator. We show that the graviton propagator behaves as the inverse distance to the fourth power. Our result is a direct consequence of the large-spin asymptotics of the spin foam model vertex amplitude, and it is valid for all new …
The volume operator plays a pivotal role for the quantum dynamics of Loop Quantum Gravity (LQG), both in the full theory and in truncated models adapted to cosmological situations coined Loop Quantum Cosmology (LQC). It is therefore crucial to check whether its semiclassical limit coincides with the classical volume operator plus quantum corrections. In the present article we investigate this question by generalizing and employing previously defined coherent states for LQG which derive from a cylindrically consistently defined complexifier operator which is the quantization of a known classica…
We show that if the flat-spacetime wavefunction in the spin network basis of Loop Quantum Gravity has a large-spin asymptotics given by Rovelli's ansatz then the corresponding graviton propagator has the correct large-distance asymptotics nonperturbatively and independently of the spin foam model used to describe the evolution operator. We also argue that even in the Rovelli approach the wavefunction should satisfy the Hamiltonian constraint and we give an explanation for the spin parameter appearing in Rovelli's ansatz.
Quantum Dynamics of Lorentzian Spacetime Foam
一个简单的时空虫洞，它经典地从零喉半径演化到最大值并重新收缩，可以被认为是惠勒首先提出的微观“时空泡沫”中的一种可能的波动模式。这种虫洞的一个特别简单的版本的动力学可以减少到一个单一的量，它的喉部半径;这个虫洞因此提供了一个“迷你超空间模型”的结构在洛伦兹签名泡沫。从爱因斯坦场方程和喉道处物质的状态方程出发，得到了虫洞喉道的经典运动方程。然后，从对应于该运动方程的作用出发，对空穴的量子行为进行分析。简单地通过计算空穴时空的标量曲率得到的作用量产生了一个具有相对论性自由粒子特征的模型。特别是哈密顿量是非本地的，并且对于虫洞，甚至不能作为封闭形式的微分算子给出。尽管如此，虫洞波函数的薛定谔方程的一般解，即，波函数传播子可以表示为路径积分。由于太复杂而无法精确执行，因此可以通过WKB近似来评估。结果表明，经典稳定的虫洞是量子力学不稳定的：一个Feynman-Kac分解的WKB传播子产生的束缚态的光谱。虽然一个初始局部化的虫洞波函数可能会振荡许多经典的膨胀/收缩周期，它最终必须泄漏到大半径值。这种模式对增长不稳定的可能性，加上
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 $Λ\neq0$. In this article, we introduce by hand the quantum group $\mathcal{U}_{q}(\mathfrak{su}(2))$ into the LQG framework, that is we deal with $\mathcal{U}_{q}(\mathfra…
The semiclassical propagator for coherent state on twisted geometry
引入扭曲几何变量参数化LQG相空间并验证其泊松代数性质，据此建立相干态路径积分新表述，通过二阶展开解析计算得到量子传播子的半经典近似。
A certain operator $\T=\int_{\SL}\dd g\, Y^{\dagger}gY$ can be found in various Lorentzian EPRL calculations. The properties of this operator has been studied here in large $j$ limit. The leading order of $\T$ is proportional to the identity operator. Knowing the operator $\T$ one can renormalize spin-foam's edge self-energy by computing the amplitude of sum of a series of edges with increasing number of vertices and bubbles. This amplitude is calculated and is shown to be convergent. Moreover some technical tools useful in Lorentzian Spin-Foam calculation has been developed.
The aim of this dissertation is to review `Loop Quantum Gravity', explaining the main structure of the theory and indicating its main open issues. We will develop the two main lines of research for the theory: the canonical quantization (first two chapters) and spin foams (third). The final chapter will be devoted to studying some of the problems of the theory and what things remain to be developed. In chapter 3 we will also include an example of a simple calculation done in the frame of LQG: Schwarzschild black hole entropy.
We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the EPRL model leads to the appearance of the Ashtekar-Barbero connection, thus bringing this model even closer to LQG. Second, we however argue that the quantization procedure used to derive the new models is inconsistent since it relies on the symplectic structure of the unconstraint BF theory.
In this paper we perform the calculation of the spectral dimension of spacetime in 4d quantum gravity using the Barrett-Crane (BC) spinfoam model. We realize this considering a very simple decomposition of the 4d spacetime already used in the graviton propagator calculation and we introduce a boundary state which selects a classical geometry on the boundary. We obtain that the spectral dimension of the spacetime runs from $\approx 2$ to 4, across a $\approx 1.5$ phase, when the energy of a probe scalar field decreases from high $E \lesssim E_P/25$ to low energy. The spectral dimension at the P…
The proper spin-foam vertex amplitude is obtained from the EPRL vertex by projecting out all but a single gravitational sector, in order to achieve correct semi-classical behavior. In this paper we calculate the gravitational two-point function predicted by the proper spin-foam vertex to lowest order in the vertex expansion. We find the same answer as in the EPRL case in the `continuum spectrum' limit, so that the theory is consistent with the predictions of linearized gravity in the regime of small curvature. The method for calculating the two-point function is similar to that used in prior w…
In this paper we have calculated the spectral dimension of loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We have obtained that the spectral dimension of the spatial section runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar field decrees from high to low energy. We have calculated the spectral dimension of the space-time also using results from spin-foam models, obtaining a 2-dimensional effective manifold at hight energy. Our result is consistent with other two approach to non perturbative quantum gravity: caus…
In this paper we tackle the issue of causality in quantum gravity, in the context of 3d spin foam models. We identify the correct procedure for implementing the causality/orientation dependence restriction that reduces the path integral for BF theory to that of quantum gravity in first order form. We construct explicitly the resulting causal spin foam model. We then add matter degrees of freedom to it and construct a causal spin foam model for 3d quantum gravity coupled to matter fields. Finally, we show that the corresponding spin foam amplitudes admit a natural approximation as the Feynman a…
We analyse the classical and quantum geometry of the Barrett-Crane spin foam model for four dimensional quantum gravity, explaining why it has to be considering as a covariant realization of the projector operator onto physical quantum gravity states. We discuss how causality requirements can be consistently implemented in this framework, and construct causal transiton amplitudes between quantum gravity states, i.e. realising in the spin foam context the Feynman propagator between states. The resulting causal spin foam model can be seen as a path integral quantization of Lorentzian first order…
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 model…
We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be resummed. This leads to the conclusion that the dynamics of quantum particles coupled to quantum 3d gravity can be expressed in terms of an effective new non commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models …
The most important part of the new spin-foam loop quantum gravity formulation is the map $Y$: $H^{SU(2)} \rightarrow H^{SL(2,C)}$. It was only recently shown that the Y-Map is convergent in spite of the fact that the classical Peter-Weyl theorem is not applicable to it, as Lorentz group is not compact. In this paper we provide an alternative map $\tilde{Y}$. The $\tilde{Y}$ map has an advantage of preserving the Lorentz covariance, which gets broken in the case of Y-Map. The image of a new map $\tilde{Y}$ contains the weighted infinite sum of $SL(2,C)$ matrix coefficients. The sum is convergen…
Recent attempts to recover the graviton propagator from spin foam models involve the use of a boundary quantum state peaked on a classical geometry. The question arises whether beyond the case of a single simplex this suffices for peaking the interior geometry in a semiclassical configuration. In this paper we explore this issue in the context of quantum Regge calculus with a general triangulation. Via a stationary phase approximation, we show that the boundary state succeeds in peaking the interior in the appropriate configuration, and that boundary correlations can be computed order by order…
We analyze the large-spin asymptotics of a class of spin-network wavefunctions of Euclidean Loop Quantum Gravity, which corresponds to a flat spacetime. A wavefunction from this class can be represented as a sum over the spins of an amplitude for a spin network whose graph is a composition of the the wavefunction spin network graph with the dual one-complex graph and the tetrahedron graphs for a triangulation of the spatial 3-manifold. This spin-network amplitude can be represented as a product of 6j symbols, which is then used to find the large-spin asymptotics of the wavefunction. By using t…
The Barrett-Crane model for the SO(4,C) general relativity is systematically derived. This procedure makes rigorous the calculation of the Barrett-Crane intertwiners from the Barrett-Crane constraints of both real and complex Riemannian general relativity. The reality of the scalar products of the complex bivectors associated with the triangles of a flat four simplex is equivalent to the reality of the associated flat geometry. Spin foam models in 4D for the real and complex orthogonal gauge groups are discussed in a unified manner from the point of view of the bivector scalar product reality …
We calculate the most divergent contribution to the non-degenerate sector of the self-energy (or "melonic") graph in the context of the Lorentzian EPRL-FK Spin Foam model of Quantum Gravity. We find that such a contribution is logarithmically divergent in the cut-off over the SU(2)-representation spins when one chooses the face amplitude guaranteeing the face-splitting invariance of the foam.We also find that the dependence on the boundary data is different from that of the bare propagator. This fact has its origin in the non-commutativity of the EPRL-FK Y-map with the projector onto SL(2,C)-i…
We construct a class of spin foam models describing matter coupled to gravity, such that the gravitational sector is described by the unitary irreducible representations of the appropriate symmetry group, while the matter sector is described by the finite-dimensional irreducible representations of that group. The corresponding spin foam amplitudes in the four-dimensional gravity case are expressed in terms of the spin network amplitudes for pentagrams with additional external and internal matter edges. We also give a quantum field theory formulation of the model, where the matter degrees of fr…
Precanonical quantization is based on a generalization of the Hamiltonian formalism to field theory, the so-called De Donder-Weyl (DW) theory, which does not require a spacetime splitting and treats the space-time variables on an equal footing. Quantum dynamics is described by a precanonical wave function on the finite dimensional space of field coordinates and space-time coordinates, which satisfies a partial derivative precanonical Schrödinger equation. The standard QFT in the functional Schrödinger representation can be derived from the precanonical quantization in a limiting case. An analy…
Recently, a new path integral formulation of Loop Quantum Gravity (LQG) has been derived in arXiv:1910.03763 from the reduced phase space formulation of the canonical LQG. This paper focuses on the semiclassical analysis of this path integral formulation. We show that dominant contributions of the path integral come from solutions of semiclassical equations of motion (EOMs), which reduces to Hamilton's equations of holonomies and fluxes ${h}(e),{p}^a(e)$ in the reduced phase space $\mathcal{P}_γ$ of the cubic lattice $γ$: $\dot{h}(e)=\{{h}(e),\, \mathbf{H}\}$, $\dot{p}^a(e)=\{{p}^a(e),\, \math…
The one-loop effective action from the coherent state path integral of loop quantum gravity
本研究结合路径积分方法与环量子引力（LQG）相干态路径积分公式计算单圈有效作用量，对比QFT传统方案并扩展至边界态依赖，检验紫外有限性、探索红外性质，获平直时空下解析/数值结果且无发散，推导运动方程并验证半经典一致性。
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The mechanical models we consider are deparametrized and thus the group averaging technique is used to deal with the corresponding constraints. The transition amplitudes are written in a vertex expansion form used in the spin foam models, where here a vertex is actually a jump in position. Polymer propagators previously obtained by spectral methods for a nonrelativisti…
We investigate a way of imposing simplicity constraints in a holomorphic Spin Foam model that we recently introduced. Rather than imposing the constraints on the boundary spin network, as is usually done, one can impose the constraints directly on the Spin Foam propagator. We find that the two approaches have the same leading asymptotic behaviour, with differences appearing at higher order. This allows us to obtain a model that greatly simplifies calculations, but still has Regge Calculus as its semi-classical limit.
In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian states. We obtained that the spectral dimension of the spatial section runs from 1.5 to 3, and under particular assumptions from 2 to 3 across a 1.5 phase when the energy of a probe scalar field decreases from high to low energy in a fictitious time T. We calculated also the spectral dimension of space-time using the scaling of the area spectrum operator calc…
We investigate the group field theory formulation of the EPRL/FK spin foam models. These models aim at a dynamical, i.e. non-topological formulation of 4D quantum gravity. We introduce a saddle point method for general group field theory amplitudes and compare it with existing results, in particular for a second order correction to the EPRL/FK propagator.
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 mo…
The Hamiltonian constraint remains the major unsolved problem in Loop Quantum Gravity (LQG). Seven years ago a mathematically consistent candidate Hamiltonian constraint has been proposed but there are still several unsettled questions which concern the algebra of commutators among smeared Hamiltonian constraints which must be faced in order to make progress. In this paper we propose a solution to this set of problems based on the so-called {\bf Master Constraint} which combines the smeared Hamiltonian constraints for all smearing functions into a single constraint. If certain mathematical con…
ER = EPR in Loop Quantum Gravity: the Immirzi Parameter and the Continuum Limit
本文将 ER=EPR 的有限区域分析嵌入圈量子引力，建立纠缠与量子几何的精确字典，从中推导出 Immirzi 参数并使黑洞熵系数普适化，同时构造了抑制发散并给出连续极限的自旋泡沫重整化流。
To obtain a well defined path integral one often employs discretizations. In the case of gravity and reparametrization invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mec…
In the context of spin foam models for quantum gravity, group field theories are a useful tool allowing on the one hand a non-perturbative formulation of the partition function and on the other hand admitting an interpretation as generalized matrix models. Focusing on 2d group field theories, we review their explicit relation to matrix models and show their link to a class of non-commutative field theories invariant under a quantum deformed 3d Poincare symmetry. This provides a simple relation between matrix models and non-commutative geometry. Moreover, we review the derivation of effective 2…
Area-metric gravity revisited
本文研究了面积度量引力作用量空间，发现一个双参数子类具有额外平移对称性，可在积分掉非长度自由度后得到无鬼引力子传播子，并分析了洛伦兹号差下的稳定性。
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