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Carlo Rovelli - One of the best experts on this subject based on the ideXlab platform.
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geometry of loop Quantum Gravity on a graph
Physical Review D, 2010Co-Authors: Carlo Rovelli, Simone SpezialeAbstract: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.
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Loop Quantum Gravity
Living Reviews in Relativity, 2008Co-Authors: Carlo RovelliAbstract:The problem of describing the Quantum behavior of Gravity, and thus understanding Quantum spacetime , is still open. Loop Quantum Gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop Quantum Gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of Quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard Quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler’s “spacetime foam” intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n -point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent Quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of Quantum Gravity, and a guide to the relevant literature.
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loop Quantum Gravity
Albert Einstein Century International Conference, 2006Co-Authors: Carlo RovelliAbstract:Bernard d’Espagnat. We welcome today Carlo Rovelli, who has kindly accepted to speak to us about his book Quantum Gravity. Carlo has already participated several times in our discussions; consequently we are familiar with his very novel ideas on Quantum mechanics. We are delighted to have the opportunity to hear him speak about his ideas, not unrelated to the former, on cosmology. So without further ado, I give him the floor.
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graviton propagator in loop Quantum Gravity
arXiv: General Relativity and Quantum Cosmology, 2006Co-Authors: Eugenio Bianchi, Carlo Rovelli, Leonardo Modesto, Simone SpezialeAbstract: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.
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particle scattering in loop Quantum Gravity
Physical Review Letters, 2005Co-Authors: Leonardo Modesto, Carlo RovelliAbstract:We devise a technique for defining and computing n-point functions in the context of a background-independent gravitational Quantum field theory. We construct a tentative implementation of this technique in a perturbatively finite model defined using spin foam techniques in the context of loop Quantum Gravity.
Daniele Oriti - One of the best experts on this subject based on the ideXlab platform.
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group field theory and loop Quantum Gravity
Loop Quantum Gravity: The First 30 Years, 2014Co-Authors: Daniele OritiAbstract:In this contribution, we introduce the group field theory (GFT) formalism for Quantum Gravity [1], mainly from the point of view of loop Quantum Gravity, arguing why it represents, in our opinion, a most promising setting for future developments. We describe the kinematical Hilbert space and its relation to the LQG one, and how the GFT Quantum dynamics connects to the canonical one as well as completes spin foam models. We also discuss the problem of defining the continuum limit of such theories and of extracting effective continuum physics, highlighting the important role that GFTs can play in this respect. This is not an in-depth introduction, nor a complete review of the literature. We only outline the foundations of the formalism, survey recent results and offer a perspective on future developments. An historical prelude - Group field theories can be approached from different angles, coming from different lines of research in Quantum Gravity. Historically, their first appearance [2, 3] came as a development of tensor models [4] (themselves a generalisation of matrix models [5], which provided a successful quantisation of (pure) 2d Gravity), allowing to make contact with state sum formulations of 3d Quantum Gravity (Ponzano-Regge and Turaev-Viro model), whose relation with simplicial Quantum Gravity, e.g. Quantum Regge calculus [6], was already known, and more generally topological BF theory in any dimension. These first models were obtained by taking the simplest tensor model for 3d simplicial Gravity and: 1) replacing the domain set for the tensor indices with a group manifold (SU(2)); 2) adding a gauge invariance property to the field (tensor), with the effect of introducing a gauge connection on the lattices generated by the perturbative expansion of the model. The triviality of the kinetic and interaction kernels (simple delta functions on the group) in the GFT action resulted in the amplitudes being exactly those of BF theory discretised on the same lattices (imposing flatness of the connection). Written in terms of group representations, the same amplitudes took the form of the mentioned state sums. This is the first way to understand group field theories: GFTs can be seen as tensor models enriched by algebraic data with a Quantum geometric interpretation (allowing a nice encoding of discrete Gravity degrees of freedom), or, equivalently, as more general class of combinatorially non-local field theories of tensorial type. The relation between state sum models of topological field theory, and their GFT formulation, and loop Quantum Gravity was soon pointed out in [7] (where the link to the dynamical triangulations approach [8] was also mentioned): the boundary states of such models matched the newly developed loop representation for Quantum Gravity [9]. Indeed, spin networks (introduced in LQG immediately afterwards) describe also the Hilbert space of GFT models. The latter acquire then a nice interpretation from the LQG perspective: GFTs are Quantum field theories for spin networks, providing them with a covariant dynamics. This covariant definition started being developed a few years later [10–12]. Indeed, more interest in GFTs as Quantum Gravity models came with the realisation that they provide a complete definition of spin foam models for 4d Gravity [13]: they capture the same Quantum amplitudes as Feynman amplitudes,
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group field theory and loop Quantum Gravity
arXiv: General Relativity and Quantum Cosmology, 2014Co-Authors: Daniele OritiAbstract: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.
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the group field theory approach to Quantum Gravity
arXiv: General Relativity and Quantum Cosmology, 2006Co-Authors: Daniele OritiAbstract:Introduction and motivation Group field theories (GFTs) were developed at first as a generalization of matrix models for 2d Quantum Gravity to 3 and 4 spacetime dimensions to produce a lattice formulation of topological theories. More recently, they have been developed further in the context of spin foam models for Quantum Gravity, as a tool to overcome the limitations of working with a fixed lattice in the non-topological case. In our opinion, however, GFTs should be seen as a fundamental formulation of Quantum Gravity and not just as an auxiliary tool. The bottom line of this perspective, here only tentatively outlined and still to be fully realized, hopefully, after much more work, can be summarized as follows: GFTs are Quantum field theories of spacetime (as opposed to QFTs on spacetime), that describe the dynamics of both its topology and geometry in local, simplicial, covariant, algebraic terms, and that encompass ideas and insights from most of the other approaches to non-perturbative Quantum Gravity. We have just began to explore the structure of these models, but there is already some evidence, in our opinion, that in the GFT framework lies the potential for important developments. The idea of defining a Quantum field theory of geometry, i.e. a QFT on superspace (the space of 3-geometries) for given spatial topology, say S 3 , was already explored in the past. The context was then a global or “Quantum cosmology” one.
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deformed special relativity as an effective flat limit of Quantum Gravity
Nuclear Physics, 2005Co-Authors: Florian Girelli, Etera R. Livine, Daniele OritiAbstract:Abstract We argue that a (slightly) curved space–time probed with a finite resolution, equivalently a finite minimal length, is effectively described by a flat non-commutative space–time. More precisely, a small cosmological constant (so a constant curvature) leads the κ -deformed Poincare flat space–time of deformed special relativity (DSR) theories. This point of view eventually helps understanding some puzzling features of DSR. It also explains how DSR can be considered as an effective flat (low energy) limit of a (true) Quantum Gravity theory. This point of view leads us to consider a possible generalization of DSR to arbitrary curvature in momentum space and to speculate about a possible formulation of an effective Quantum Gravity model in these terms. It also leads us to suggest a doubly deformed special relativity framework for describing particle kinematics in an effective low energy description of Quantum Gravity.
John W Barrett - One of the best experts on this subject based on the ideXlab platform.
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feynman diagrams coupled to three dimensional Quantum Gravity
Classical and Quantum Gravity, 2006Co-Authors: John W BarrettAbstract:A framework for Quantum field theory coupled to three-dimensional Quantum Gravity is proposed. The coupling with Quantum Gravity regulates the Feynman diagrams. One recovers the usual Feynman amplitudes in the limit as the cosmological constant tends to zero.
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relativistic spin networks and Quantum Gravity
Journal of Mathematical Physics, 1998Co-Authors: John W Barrett, Louis CraneAbstract:Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2)×SU(2). Relativistic Quantum spins are related to the geometry of the two-dimensional faces of a 4-simplex. This extends the idea of Ponzano and Regge that SU(2) spins are related to the geometry of the edges of a 3-simplex. This leads us to suggest that there may be a four-dimensional state sum model for Quantum Gravity based on relativistic spin networks that parallels the construction of three-dimensional Quantum Gravity from ordinary spin networks.
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relativistic spin networks and Quantum Gravity
arXiv: General Relativity and Quantum Cosmology, 1997Co-Authors: John W Barrett, Louis CraneAbstract:Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) times SU(2). Relativistic Quantum spins are related to the geometry of the 2-dimensional faces of a 4-simplex. This extends the idea of Ponzano and Regge that SU(2) spins are related to the geometry of the edges of a 3-simplex. This leads us to suggest that there may be a 4-dimensional state sum model for Quantum Gravity based on relativistic spin networks which parallels the construction of 3-dimensional Quantum Gravity from ordinary spin networks.
Gianmassimo Tasinato - One of the best experts on this subject based on the ideXlab platform.
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gravitational wave luminosity distance in Quantum Gravity
Physics Letters B, 2019Co-Authors: Gianluca Calcagni, Sachiko Kuroyanagi, Sylvain Marsat, Mairi Sakellariadou, Nicola Tamanini, Gianmassimo TasinatoAbstract:Abstract Dimensional flow, the scale dependence of the dimensionality of spacetime, is a feature shared by many theories of Quantum Gravity (QG). We present the first study of the consequences of QG dimensional flow for the luminosity distance scaling of gravitational waves in the frequency ranges of LIGO and LISA. We find generic modifications with respect to the standard general-relativistic scaling, largely independent of specific QG proposals. We constrain these effects using two examples of multimessenger standard sirens, the binary neutron-star merger GW170817 and a simulated supermassive black-hole merger event detectable with LISA. We apply these constraints to various QG candidates, finding that the Quantum geometries of group field theory, spin foams and loop Quantum Gravity can give rise to observable signals in the gravitational-wave spin-2 sector. Our results complement and improve GW propagation-speed bounds on modified dispersion relations. Under more model-dependent assumptions, we also show that bounds on Quantum geometry can be strengthened by solar-system tests.
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Quantum Gravity and gravitational wave astronomy
Journal of Cosmology and Astroparticle Physics, 2019Co-Authors: Gianluca Calcagni, Sachiko Kuroyanagi, Sylvain Marsat, Mairi Sakellariadou, Nicola Tamanini, Gianmassimo TasinatoAbstract:We investigate possible signatures of Quantum Gravity which could be tested with current and future gravitational-wave (GW) observations. In particular, we analyze how Quantum Gravity can influence the GW luminosity distance, the time dependence of the effective Planck mass and the instrumental strain noise of interferometers. Using both model-dependent and model-independent formulae, we show that these quantities can encode a non-perturbative effect typical of all Quantum-Gravity theories, namely the way the dimension of spacetime changes with the probed scale. Effects associated with such dimensional flow might be tested with GW observations and constrained significantly in theories with a microscopically discrete spacetime geometry, more strongly than from propagation-speed constraints. Making use of public LIGO data as well as of a simulated higher-redshift LISA source, we impose the first, respectively, actual and mock constraints on Quantum-Gravity parameters affecting the GW luminosity distance and discuss specific theoretical examples. If also the Newtonian potential is modified but light geodesics are not, then solar-system bounds may be stronger than GW ones. Yet, for some theories GW astronomy can give unique information not available from solar-system tests.
Simone Speziale - One of the best experts on this subject based on the ideXlab platform.
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polyhedra in loop Quantum Gravity
Physical Review D, 2011Co-Authors: Eugenio Bianchi, Pietro Dona, Simone SpezialeAbstract:Interwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in 3 : a polyhedron is uniquely described by the areas and normals to its faces. We provide a reconstruction of the geometry of the polyhedron: we give formulas for the edge lengths, the volume and the adjacency of its faces. At the Quantum level, this correspondence allows us to identify an intertwiner with the state of a Quantum polyhedron, thus generalizing the notion of Quantum tetrahedron familiar in the loop Quantum Gravity literature. Moreover, coherent intertwiners result to be peaked on the classical geometry of polyhedra. We discuss the relevance of this result for loop Quantum Gravity. In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra. Furthermore, we introduce an operator that measures the volume of a Quantum polyhedron and examine its relation with the standard volume operator of loop Quantum Gravity. We also comment on the semiclassical limit of spinfoams with non-simplicial graphs.
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geometry of loop Quantum Gravity on a graph
Physical Review D, 2010Co-Authors: Carlo Rovelli, Simone SpezialeAbstract: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.
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graviton propagator in loop Quantum Gravity
arXiv: General Relativity and Quantum Cosmology, 2006Co-Authors: Eugenio Bianchi, Carlo Rovelli, Leonardo Modesto, Simone SpezialeAbstract: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.
