In this article we further investigate the construction of graph coherent states, first introduced in [1], in the context of loop quantum gravity. We specifically investigate the possibility of defining a family of graph coherent states adapted to the canonical loop quantum gravity Hamiltonian. After discussing various aspects of the general framework and the choice of operators, we use the Euclidean part of the Hamiltonian operator to propose a generator of the generalized canonical structure, necessary to define the coherent states. We then apply the construction procedure, leading to a new family of graph coherent states partially adapted to the gravity Hamiltonian in loop quantum gravity.
We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop quantum gravity when boundaries are imposed on a quantum spacetime.
We introduce squeezed vacua in loop quantum gravity, a new overcomplete basis of states that contain prescribable correlations between geometric operators. We study the behavior of long-range correlations and discuss the relevance of these states for the reconstruction of a semiclassical spacetime from loop quantum gravity.
We introduce a new technique for dealing with the matrix elements of the Hamiltonian operator in loop quantum gravity, based on the use of intertwiners projected on coherent states of angular momentum. We give explicit expressions for the projections of intertwiners on the spin coherent states in terms of complex numbers describing the unit vectors which label the coherent states. Operators such as the Hamiltonian can then be reformulated as differential operators acting on polynomials of these complex numbers. This makes it possible to describe the action of the Hamiltonian geometrically, in …
We introduce a new loop expansion that provides a resolution of the identity in the Hilbert space of loop quantum gravity on a fixed graph. We work in the bosonic representation obtained by the canonical quantization of the spinorial formalism. The resolution of the identity gives a tool for implementing the projection of states in the full bosonic representation onto the space of solutions to the Gauss and area matching constraints of loop quantum gravity. This procedure is particularly efficient in the semiclassical regime, leading to explicit expressions for the loop expansions of coherent,…
The ambiguity in the calculations of one-loop counterterms by the background field method in nonrenormalizable theories of gravity is discussed. Some examples of such ambiguous calculations are given. The non-equivalence of the first and second order formalism in the quantum gravity is shown.
A simple argument indicates that covariant loop gravity (spinfoam theory) predicts a maximal acceleration, and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.
In this paper we summarize "loop quantum gravity" (LQG) and we show how ideas developed in LQG can solve the black hole singularity problem when applied to a minisuperspace model.
By making use of the background field method, the one-loop quantization for Euclidean Einstein-Weyl quadratic gravity model on the de Sitter universe is investigated. Using generalized zeta function regularization, the on-shell and off-shell one-loop effective actions are explicitly obtained and one-loop renormalizability, as well as the corresponding one-loop renormalization group equations, are discussed. The so called critical gravity is also considered.
We present the complete set of universal one-loop beta functions of cubic gravity in six dimensions. The system admits over 8000 distinct fixed points, of which more than 200 are real. Some of them might be relevant for the quantisation of gravity in the physical case of four dimensions.
I review the definition of n-point functions in loop quantum gravity, discussing what has been done and what are the main open issues. Particular attention is dedicated to gauge aspects and renormalization.
This article reviews the status of several solutions to all the constraints of quantum gravity that have been proposed in terms of loops and extended loops. We discuss pitfalls of several of the results and in particular discuss the issues of covariance and regularization of the constraints in terms of extended loops. We also propose a formalism for ``thickened out loops'' which does not face the covariance problems of extended loops and may allow to regularize expressions in a consistent manner.
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.
Loop quantum gravity, a non-perturbative and manifestly background free, quantum theory of gravity implies that at the kinematical level the spatial geometry is discrete in a specific sense. The spirit of background independence also requires a non-standard quantum representation of matter. While loop quantization of standard model fields has been proposed, detail study of its implications is not yet available. This review aims to survey the various efforts and results.
In this note we reply to the criticism by Corichi concerning our proposal for an equidistant area spectrum in loop quantum gravity. We further comment on the emission properties of black holes and on the statistics of links.
Motivated by the analogy proposed by Witten between Chern-Simons and Conformal Field Theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in Loop Quantum Gravity. The consistency of the result opens a window for the interplay between Conformal Field Theory and the description of black holes in Loop Quantum Gravity.
There are two ways of counting microscopic states of black holes in loop quantum gravity, one counting all allowed spin network labels $j,m$ and the other involving only the labels $m$. Counting states with $|m|=j$, as done in a recent Letter, does not follow either.
The parametrization and gauge dependencies of the one-loop counterterms on the mass-shell in the Einstein gravity are investigated. The physical meaning of the loop calculation results on the mass shell and the parametrization dependence of the renormgroup functions in the nonrenormalizable theories are discussed.
In this note we point out that the one-loop partition function of three-dimensional flat gravity, computed along the lines originally developed for the anti-de Sitter case, reproduces characters of the BMS3 group.
Models of loop quantum gravity based on real connections have a deformed notion of general covariance, which leads to the phenomenon of signature change. This result is confirmed here in a general analysis of all midisuperspace models without local degrees of freedom. As a subclass of models, 2-dimensional theories of dilaton gravity appear, but a larger set of examples is possible based only on the condition of anomaly freedom. While the classical dilaton gravity models are the only such systems without deformed covariance, they do give rise to signature change when holonomy modifications are…
We investigate the influence of the projective invariance on the renormalization properties of the theory. One-loop counterterms are calculated in the most general case of interaction of gravity with scalar field.
We evaluate the 1-loop partition function of conformal gravity in four dimensions around an $AdS_4$ background, using the heat kernel techniques. We give expressions for the relevant thermodynamical quantities and compare our results with the ones from the literature.
This is a historical note. In 1974 I was an undergraduate student of L.D. Faddeev. I was working on quantum gravity [without matter] in one loop approximation. I discovered [simultaneously with G. t'Hooft M. Veltman] that on mass shell ultra-violet divergences cancel. The submission is a translation of the Diploma.
We explicitly construct and characterize all possible independent loop states in 3+1 dimensional loop quantum gravity by regulating it on a 3-d regular lattice in the Hamiltonian formalism. These loop states, characterized by the (dual) angular momentum quantum numbers, describe SU(2) rigid rotators on the links of the lattice. The loop states are constructed using the Schwinger bosons which are harmonic oscillators in the fundamental (spin half) representation of SU(2). Using generalized Wigner Eckart theorem, we compute the matrix elements of the volume operator in the loop basis. Some simpl…
Motivated by the dark energy issue, the one-loop quantization approach for a class of relativistic higher order theories is discussed in some detail. A specific F(R,P,Q) gravity model at the one-loop level in a de Sitter universe is investigated, extending the similar program developed for the case of $F(R)$ gravity. The stability conditions under arbitrary perturbations are derived.
Quantum field theory provides us with the means to calculate scattering amplitudes. In recent years a dramatic new development has lead to great simplification of such calculations. This is based on the discovery of the``amplituhedron'' in the context of scattering of massless gauge bosons in Yang-Mills theory. One of the main challenges facing Loop Quantum Gravity is the lack of a clear description of particle scattering processes and a connection to flat space QFT. Here we show a correspondence between the space of kinematic data of the scattering $ N $ massless particles and $ U(N) $ cohere…
We construct the operator that projects on the physical states in loop quantum gravity. To this aim, we consider a diffeomorphism invariant functional integral over scalar functions. The construction defines a covariant, Feynman-like, spacetime formalism for quantum gravity and relates this theory to the spin foam models. We also discuss how expectation values of physical quantity can be computed.
Affine quantum gravity, which differs notably from either string theory or loop quantum gravity, is briefly reviewed. Emphasis in this article is placed on the use of affine coherent states in this program.
In non-supersymmetric covariant quantum gravity theory, for each system of gravity coupled with single field is one-loop divergent. Since adding other fields or other interactions to each system generates more possible counter-Lagrangian terms, there is room for improvement to restore renormalizability. In this paper, we consider Einstein-Maxwell fields coupled with electrically charged scalar which is the simplest model among the systems of gravity coupled with multiple fields having their own interaction. First, we introduce how to calculate the possible one-loop diagrams in Einstein-SQED sy…
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a perspective on future developments.
We outline how the Wald entropy formula naturally arises in loop quantum gravity based on recently introduced dimension-independent connection variables. The key observation is that in a loop quantization of a generalized gravity theory, the analog of the area operator turns out to measure, morally speaking, the Wald entropy rather than the area. We discuss the explicit example of (higher-dimensional) Lanczos-Lovelock gravity and comment on recent work on finding the correct numerical prefactor of the entropy by comparing it to a semiclassical effective action.
This is a review paper invited by the journal "Classical ad Quantum Gravity" for a "Cluster Issue" on approaches to quantum gravity. I give a synthetic presentation of loop gravity. I spell-out the aims of the theory and compare the results obtained with the initial hopes that motivated the early interest in this research direction. I give my own perspective on the status of the program and attempt of a critical evaluation of its successes and limits.
We investigate the role of the torsion field at the quantum level in the affine-metric theory of gravity. One-loop counterterms are calculated in the theory with terms quadratic in the torsion field.
We argue for black hole entropy in loop quantum gravity (LQG) by taking into account the interpretation that there is no other side of the horizon. This gives new values for the Barbero-Immirzi parameter which are fairly larger than those considered before. We also discuss its consequences.
Counting of microscopic states of black holes is discussed within the framework of loop quantum gravity. There are two different ways, one allowing for all spin states and the other involving only pure horizon states. The number of states with a definite value of the total spin is also found.
An angular momentum operator in loop quantum gravity is defined using spherically symmetric states as a non-rotating reference system. It can be diagonalized simultaneously with the area operator and has the familiar spectrum. The operator indicates how the quantum geometry of non-rotating isolated horizons can be generalized to rotating ones and how the recent computations of black hole entropy can be extended to rotating black holes.
I review the present theoretical attempts to understand the quantum properties of spacetime. In particular, I illustrate the main achievements and the main difficulties in: string theory, loop quantum gravity, discrete quantum gravity (Regge calculus, dynamical triangulations and simplicial models), Euclidean quantum gravity, perturbative quantum gravity, quantum field theory on curved spacetime, noncommutative geometry, null surfaces, topological quantum field theories and spin foam models. I also briefly review several recent advances in understanding black hole entropy and attempt a critica…
We study the matter one-loop quantum corrections to the gravitational sector in a gravity theory coupled with a nonlocal scalar field. We find that non-renormalizable divergences disappear when the propagator of the scalar field approaches to a non-zero constant at high momentum, while the vacuum energy is still divergent. We also comment on non-local modification of fermion, gauge field and graviton.
Using the generalized Schwinger-DeWitt technique, we calculate the divergent part of the one-loop effective action for gravity non-minimally coupled to a multiplet of scalar fields. All the calculations are consistently done in the Jordan frame.
We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.
We study $1/N$ corrections to a Wilson loop in holographic duality. Extending the AdS/CFT correspondence beyond the large $N$ limit is an important but a subtle issue, as it needs quantum gravity corrections in the gravity side. To find a physical property of the quantum corrected geometry of near-horizon black 0-branes previously obtained by Hyakutake, we evaluate a Euclidean string worldsheet hanging down in the geometry, which corresponds to a rectangular Wilson loop in the $SU(N)$ quantum mechanics with 16 supercharges at a finite temperature with finite $N$. We find that the potential ene…
We show that holography arises naturally in the context of spherically symmetric loop quantum gravity. The result is not dependent on detailed assumptions about the dynamics of the theory being considered. It ties strongly the amount of information contained in a region of space to the tight mathematical underpinnings of loop quantum geometry, at least in this particular context.
We review the canonical analysis of the Palatini action without going to the time gauge as in the standard derivation of Loop Quantum Gravity. This allows to keep track of the Lorentz gauge symmetry and leads to a theory of Covariant Loop Quantum Gravity. This new formulation does not suffer from the Immirzi ambiguity, it has a continuous area spectrum and uses spin networks for the Lorentz group. Finally, its dynamics can easily be related to Barrett-Crane like spin foam models.
We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of the quantum Hamiltonian is presented, and then more recent approaches. They are based on toy models which provide new insights into the difficulties and ambiguities faced in Thiemann's construction. The models we use are parametrized field theories, the topological BF model of which a special case is three-dimensional gravity which describes quantum flat space, and Regge lattice gravity.
We elaborate the recently introduced asymptotically exact semiclassical quantum gravity derived from the Wheeler-DeWitt equation by finding a particular coherent state representation of a quantum scalar field in which the back-reaction of the scalar field Hamiltonian exactly gives rise to the classical one. In this coherent state representation classical spacetime emerges naturally from semiclassical quantum gravity.
We analyze detailed properties of BPS coherent states and their connection to gravity. We interpret the group integral coherent state as a path integral over auxiliary variables coupled to the elementary letters of the theory. The eigenvalues of coherent state amplitudes can be viewed as collective coordinates of giant gravitons. Inspired by the above coherent states and by the integrability, we construct a new type of coherent states in the SL(2) sectors and their cousin PSU(1,1|2) sectors, analogous to the aforementioned coherent states. The large spin and small spin limits can be obtained b…
We work out the one-loop contribution to the lepton anomalous magnetic moment coming from Unimodular Gravity. We use Dimensional Regularization and Dimensional Reduction to carry out the computations. In either case, we find that Unimodular Gravity gives rise to the same one-loop correction as that of General Relativity.
We compute some components of the graviton propagator in loop quantum gravity, using the spinfoam formalism, up to some second order terms in the expansion parameter.
As part of a wider study of coherent states in (loop) quantum gravity, we introduce a modification to the standard construction, based on the recently introduced (non-commutative) flux representation. The resulting quantum states have some welcomed features, in particular concerning peakedness properties, when compared to other coherent states in the literature.
As per organizers' request, my talk at the 11th Marcel Grossmann Conference consisted of two parts. In the first, I illustrated recent advances in loop quantum gravity through examples. In the second, I presented an overall assessment of the status of the program by addressing some frequently asked questions. This account is addressed primarily to researchers outside the loop quantum gravity community.
In this paper we show that the instanton representation of Plebanski gravity exhibits a Hilbert space of harmonic oscillator-like coherent states. We put in place the formalism and carry out the construction of the states, and we elucidate on their physical interpretation. Additionally, we provide an invertible map between the Ashtekar variables and this Hilbert space of states, via the instanton representation. Finally, we compare and constrast our formalism and some of our results with the corresponding ones in loop quantum gravity.
Quantum Reduced Loop Gravity is a promising framework for linking Loop Quantum Gravity and the effective semiclassical dynamics of Loop Quantum Cosmology. We review its basic achievements and its main perspectives, outlining how it provides a quantum description of the Universe in terms of a cuboidal graph which constitutes the proper framework for applying loop techniques in a cosmological setting.
In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space structure of loop quantum gravity-type models. Thus, the proposed Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach …
We present a summary for non-specialists of loop quantum gravity as part of the modern legacy of the series of papers by Arnowitt, Deser and Misner circa 1960.
We study particle production of coherently oscillating inflaton in the semiclassical theory of gravity by representing inflaton in coherent and squeezed state formalisms. A comparative study of the inflaton in classical gravity with coherent state inflaton in semiclassical gravity is also presented.
