International Nuclear Information System (INIS)
Pullin, J.
2015-01-01
Loop quantum gravity is one of the approaches that are being studied to apply the rules of quantum mechanics to the gravitational field described by the theory of General Relativity . We present an introductory summary of the main ideas and recent results. (Author)
Directory of Open Access Journals (Sweden)
Rovelli Carlo
1998-01-01
Full Text Available The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a mathematically well-defined, non-perturbative and background independent quantization of general relativity, with its conventional matter couplings. Research in loop quantum gravity today forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained are: (i The computation of the physical spectra of geometrical quantities such as area and volume, which yields quantitative predictions on Planck-scale physics. (ii A derivation of the Bekenstein-Hawking black hole entropy formula. (iii An intriguing physical picture of the microstructure of quantum physical space, characterized by a polymer-like Planck scale discreteness. This discreteness emerges naturally from the quantum theory and provides a mathematically well-defined realization of Wheeler's intuition of a spacetime ``foam''. Long standing open problems within the approach (lack of a scalar product, over-completeness of the loop basis, implementation of reality conditions have been fully solved. The weak part of the approach is the treatment of the dynamics: at present there exist several proposals, which are intensely debated. Here, I provide a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.
Rovelli, Carlo
2008-01-01
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.
Directory of Open Access Journals (Sweden)
Rovelli Carlo
2008-07-01
Full Text Available 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.
Newtonian gravity in loop quantum gravity
Smolin, Lee
2010-01-01
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.
Towards conformal loop quantum gravity
International Nuclear Information System (INIS)
Wang, Charles H-T
2006-01-01
A discussion is given of recent developments in canonical gravity that assimilates the conformal analysis of gravitational degrees of freedom. The work is motivated by the problem of time in quantum gravity and is carried out at the metric and the triad levels. At the metric level, it is shown that by extending the Arnowitt-Deser-Misner (ADM) phase space of general relativity (GR), a conformal form of geometrodynamics can be constructed. In addition to the Hamiltonian and Diffeomorphism constraints, an extra first class constraint is introduced to generate conformal transformations. This phase space consists of York's mean extrinsic curvature time, conformal three-metric and their momenta. At the triad level, the phase space of GR is further enlarged by incorporating spin-gauge as well as conformal symmetries. This leads to a canonical formulation of GR using a new set of real spin connection variables. The resulting gravitational constraints are first class, consisting of the Hamiltonian constraint and the canonical generators for spin-gauge and conformorphism transformations. The formulation has a remarkable feature of being parameter-free. Indeed, it is shown that a conformal parameter of the Barbero-Immirzi type can be absorbed by the conformal symmetry of the extended phase space. This gives rise to an alternative approach to loop quantum gravity that addresses both the conceptual problem of time and the technical problem of functional calculus in quantum gravity
Cosmological footprints of loop quantum gravity.
Grain, J; Barrau, A
2009-02-27
The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum effects in the early universe. We show that the associated corrections should modify the potential seen by gravitational waves during the inflationary amplification. The resulting power spectrum should exhibit a characteristic tilt. This opens a new window for cosmological tests of quantum gravity.
Transition probability spaces in loop quantum gravity
Guo, Xiao-Kan
2018-03-01
We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability spaces. This is exemplified by first checking such structures in covariant quantum mechanics and then identifying the transition probability spaces in spin foam models via a simplified version of general boundary formulation. The transition probability space thus defined gives a simple way to reconstruct the discrete analog of the Hilbert space of the canonical theory and the relevant quantum logical structures. Second, we show that the transition probability space and in particular the spin foam model are 2-categories. Then we discuss how to realize in spin foam models two proposals by Crane about the mathematical structures of quantum gravity, namely, the quantum topos and causal sites. We conclude that transition probability spaces provide us with an alternative framework to understand various foundational questions of loop quantum gravity.
Anomaly freedom in perturbative loop quantum gravity
International Nuclear Information System (INIS)
Bojowald, Martin; Hossain, Golam Mortuza; Kagan, Mikhail; Shankaranarayanan, S.
2008-01-01
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a consistent deformation of the classical system, which shows that the discreteness in loop quantum gravity can be implemented in effective equations without spoiling space-time covariance. Nevertheless, nontrivial quantum corrections do arise in the constraint algebra. Since correction terms must appear in tightly controlled forms to avoid anomalies, detailed insights for the correct implementation of constraint operators can be gained. The procedures of this article thus provide a clear link between fundamental quantum gravity and phenomenology.
Topspin networks in loop quantum gravity
International Nuclear Information System (INIS)
Duston, Christopher L
2012-01-01
We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert space of cylindrical functions. We will also discuss the area and Hamiltonian operators, and show how they depend on the topology. This extends the idea of ‘background independence’ in loop quantum gravity to include topology as well as geometry. It is hoped this work will confirm the usefulness of the topspin network formalism and open up several new avenues for research into quantum gravity. (paper)
Fundamental Structure of Loop Quantum Gravity
Han, Muxin; Ma, Yongge; Huang, Weiming
In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, non-perturbative quantum theory for a Lorentzian gravitational field on a four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete on the fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory. In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of the kinematical Ashtekar-Isham-Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to
Holonomy loops, spectral triples and quantum gravity
DEFF Research Database (Denmark)
Johannes, Aastrup; Grimstrup, Jesper Møller; Nest, Ryszard
2009-01-01
We review the motivation, construction and physical interpretation of a semi-finite spectral triple obtained through a rearrangement of central elements of loop quantum gravity. The triple is based on a countable set of oriented graphs and the algebra consists of generalized holonomy loops...
Loop-quantum-gravity vertex amplitude.
Engle, Jonathan; Pereira, Roberto; Rovelli, Carlo
2007-10-19
Spin foam models are hoped to provide the dynamics of loop-quantum gravity. However, the most popular of these, the Barrett-Crane model, does not have the good boundary state space and there are indications that it fails to yield good low-energy n-point functions. We present an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly. Its state space matches the SO(3) loop gravity one and it yields an SO(4)-covariant vertex amplitude for Euclidean loop gravity.
Loop quantum gravity; Gravedad cuantica de lazos
Energy Technology Data Exchange (ETDEWEB)
Pullin, J.
2015-07-01
Loop quantum gravity is one of the approaches that are being studied to apply the rules of quantum mechanics to the gravitational field described by the theory of General Relativity . We present an introductory summary of the main ideas and recent results. (Author)
Particle Scattering in Loop Quantum Gravity
International Nuclear Information System (INIS)
Modesto, Leonardo; Rovelli, Carlo
2005-01-01
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
A new vacuum for loop quantum gravity
International Nuclear Information System (INIS)
Dittrich, Bianca; Geiller, Marc
2015-01-01
We construct a new vacuum and representation for loop quantum gravity. Because the new vacuum is based on BF theory, it is physical for (2+1)-dimensional gravity, and much closer to the spirit of spin foam quantization in general. To construct this new vacuum and the associated representation of quantum observables, we introduce a modified holonomy–flux algebra that is cylindrically consistent with respect to the notion of refinement by time evolution suggested in Dittrich and Steinhaus (2013 arXiv:1311.7565). This supports the proposal for a construction of the physical vacuum made in Dittrich and Steinhaus (2013 arXiv:1311.7565) and Dittrich (2012 New J. Phys. 14 123004), and for (3+1)-dimensional gravity. We expect that the vacuum introduced here will facilitate the extraction of large scale physics and cosmological predictions from loop quantum gravity. (fast track communication)
Loop quantum gravity in asymptotically flat spaces
International Nuclear Information System (INIS)
Arnsdorf, M.
2000-01-01
This thesis describes applications and extensions of the loop variable approach to non-perturbative quantum gravity. The common theme of the work presented, is the need to generalise loop quantum gravity to be applicable in cases where space is asymptotically flat, and no longer compact as is usually assumed. This is important for the study of isolated gravitational systems. It also presents a natural context in which to search for the semi-classical limit, one of the main outstanding problems in loop quantum gravity. In the first part of the thesis we study how isolated gravitational systems can be attributed particle-like properties. In particular, we show how spinorial states can arise in pure loop quantum gravity if spatial topology is non-trivial, thus confirming an old conjecture of Friedman and Sorkin. Heuristically, this corresponds to the idea that we can rotate isolated regions of spatial topology relative to the environment at infinity, and that only a 4π-rotation will take us back to the original configuration. To do this we extend the standard loop quantum gravity formalism by introducing a compactification of our non-compact spatial manifold, and study the knotting of embedded graphs. The second part of the thesis takes a more systematic approach to the study of loop quantum gravity on non-compact spaces. We look for new representations of the loop algebra, which give rise to quantum theories that are inequivalent to the standard one. These theories naturally describe excitations of a fiducial background state, which is specified via the choice of its vacuum expectation values. In particular, we can choose background states that describe the geometries of non-compact manifolds. We also discuss how suitable background states can be constructed that can approximate classical phase space data, in our case holonomies along embedded paths and geometrical quantities related to areas and volumes. These states extend the notion of the weave and provide a
Semiclassical analysis of loop quantum gravity
International Nuclear Information System (INIS)
Conrady, F.
2005-01-01
In this Ph.D. thesis, we explore and develop new methods that should help in determining an effective semiclassical description of canonical loop quantum gravity and spin foam gravity. A brief introduction to loop quantum gravity is followed by three research papers that present the results of the Ph.D. project. In the first article, we deal with the problem of time and a new proposal for implementing proper time as boundary conditions in a sum over histories: we investigate a concrete realization of this formalism for free scalar field theory. In the second article, we translate semiclassical states of linearized gravity into states of loop quantum gravity. The properties of the latter indicate how semiclassicality manifests itself in the loop framework, and how this may be exploited for doing semiclassical expansions. In the third part, we propose a new formulation of spin foam models that is fully triangulation- and background-independent: by means of a symmetry condition, we identify spin foam models whose triangulation-dependence can be naturally removed. (orig.)
Semiclassical analysis of loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Conrady, F.
2005-10-17
In this Ph.D. thesis, we explore and develop new methods that should help in determining an effective semiclassical description of canonical loop quantum gravity and spin foam gravity. A brief introduction to loop quantum gravity is followed by three research papers that present the results of the Ph.D. project. In the first article, we deal with the problem of time and a new proposal for implementing proper time as boundary conditions in a sum over histories: we investigate a concrete realization of this formalism for free scalar field theory. In the second article, we translate semiclassical states of linearized gravity into states of loop quantum gravity. The properties of the latter indicate how semiclassicality manifests itself in the loop framework, and how this may be exploited for doing semiclassical expansions. In the third part, we propose a new formulation of spin foam models that is fully triangulation- and background-independent: by means of a symmetry condition, we identify spin foam models whose triangulation-dependence can be naturally removed. (orig.)
Loop quantum gravity: an outside view
International Nuclear Information System (INIS)
Nicolai, Hermann; Peeters, Kasper; Zamaklar, Marija
2005-01-01
We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasize that the off-shell ('strong') closure of the constraint algebra is a crucial test of quantum spacetime covariance, and thereby of the consistency, of the theory. Special attention is paid to the appearance of a large number of ambiguities, in particular in the formulation of the Hamiltonian constraint. Developing suitable approximation methods to establish a connection with classical gravity on the one hand, and with the physics of elementary particles on the other, remains a major challenge. (topical review)
Black holes in loop quantum gravity.
Perez, Alejandro
2017-12-01
This is a review of results on black hole physics in the context of loop quantum gravity. The key feature underlying these results is the discreteness of geometric quantities at the Planck scale predicted by this approach to quantum gravity. Quantum discreteness follows directly from the canonical quantization prescription when applied to the action of general relativity that is suitable for the coupling of gravity with gauge fields, and especially with fermions. Planckian discreteness and causal considerations provide the basic structure for the understanding of the thermal properties of black holes close to equilibrium. Discreteness also provides a fresh new look at more (at the moment) speculative issues, such as those concerning the fate of information in black hole evaporation. The hypothesis of discreteness leads, also, to interesting phenomenology with possible observational consequences. The theory of loop quantum gravity is a developing program; this review reports its achievements and open questions in a pedagogical manner, with an emphasis on quantum aspects of black hole physics.
Regularization ambiguities in loop quantum gravity
International Nuclear Information System (INIS)
Perez, Alejandro
2006-01-01
One of the main achievements of loop quantum gravity is the consistent quantization of the analog of the Wheeler-DeWitt equation which is free of ultraviolet divergences. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem--the existence of well-behaved regularization of the constraints--is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities is the one associated to the SU(2) unitary representation used in the diffeomorphism covariant 'point-splitting' regularization of the nonlinear functionals of the connection. This ambiguity is labeled by a half-integer m and, here, it is referred to as the m ambiguity. The aim of this paper is to investigate the important implications of this ambiguity. We first study 2+1 gravity (and more generally BF theory) quantized in the canonical formulation of loop quantum gravity. Only when the regularization of the quantum constraints is performed in terms of the fundamental representation of the gauge group does one obtain the usual topological quantum field theory as a result. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear-cut choice in the quantization of the constraints in 2+1 loop quantum gravity. We then analyze the effects of the ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for higher representation quantizations of the Hamiltonian constraint. Although the analysis is not complete in 3+1 dimensions - due to the difficulties associated to the definition of the physical inner product - it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is SO(3) we find
Dilaton gravity, Poisson sigma models and loop quantum gravity
International Nuclear Information System (INIS)
Bojowald, Martin; Reyes, Juan D
2009-01-01
Spherically symmetric gravity in Ashtekar variables coupled to Yang-Mills theory in two dimensions and its relation to dilaton gravity and Poisson sigma models are discussed. After introducing its loop quantization, quantum corrections for inverse triad components are shown to provide a consistent deformation without anomalies. The relation to Poisson sigma models provides a covariant action principle of the quantum-corrected theory with effective couplings. Results are also used to provide loop quantizations of spherically symmetric models in arbitrary D spacetime dimensions.
Radiation from quantum weakly dynamical horizons in loop quantum gravity.
Pranzetti, Daniele
2012-07-06
We provide a statistical mechanical analysis of quantum horizons near equilibrium in the grand canonical ensemble. By matching the description of the nonequilibrium phase in terms of weakly dynamical horizons with a local statistical framework, we implement loop quantum gravity dynamics near the boundary. The resulting radiation process provides a quantum gravity description of the horizon evaporation. For large black holes, the spectrum we derive presents a discrete structure which could be potentially observable.
Symmetry reduction of loop quantum gravity
International Nuclear Information System (INIS)
Brunnemann, Johannes; Koslowski, Tim A
2011-01-01
The relation between standard loop quantum cosmology (LQC) and full loop quantum gravity (LQG) fails already at the first nontrivial step: the configuration space of LQC cannot be embedded into the configuration space of full LQG due to a topological obstruction. We investigate this obstruction in detail, because many topological obstructions are the source of physical effects. For this, we derive the topology of a large class of subspaces of the LQG configuration space. This allows us to find the extension of the standard LQC configuration space that admits an embedding in agreement with Fleischhack (arXiv:1010.0449v1 [math-ph]). We then construct the embedding for flat FRW LQC and find the reassuring result that it coincides asymptotically with standard LQC. (paper)
The loop quantum gravity black hole
Pullin, Jorge; Gambini, Rodolfo
2013-04-01
We study the quantization of vacuum spherically symmetric space-times. We use variables adapted to spherical symmetry but do not fix the gauge further. One is left with a diffeomorphism constraint and a Hamiltonian constraint. Rescaling the latter turns the constraint algebra into a true Lie algebra and allows to implement the Dirac quantization procedure. We find exactly the physical states annihilated by all constraints using loop quantum gravity techniques. The space-time metric can be recovered as an evolving constant of the motion in terms of Dirac observables. The singularity is resolved as was anticipated in previous semiclassical studies. The quantum theory has new observables with respect to the classical theory that may play a role in discussions of ``firewalls'' during black hole evaporation.
Towards cosmological dynamics from loop quantum gravity
Li, Bao-Fei; Singh, Parampreet; Wang, Anzhong
2018-04-01
We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the Lorentzian term explicit in the Hamiltonian constraint. We show that quantum geometric effects result in higher than quadratic corrections in energy density in comparison to LQC, causing a nonsingular bounce. Dynamics can be described by the Hamilton or Friedmann-Raychaudhuri equations, but the map between the two descriptions is not one to one. A careful analysis resolves the tension on symmetric versus asymmetric bounce in this model, showing that the bounce must be asymmetric and symmetric bounce is physically inconsistent, in contrast to the standard LQC. In addition, the current observations only allow a scenario where the prebounce branch is asymptotically de Sitter, similar to a quantization of the Schwarzschild interior in LQC, and the postbounce branch yields the classical general relativity. For a quadratic potential, we find that a slow-roll inflation generically happens after the bounce, which is quite similar to what happens in LQC.
Area law from loop quantum gravity
Hamma, Alioscia; Hung, Ling-Yan; Marcianò, Antonino; Zhang, Mingyi
2018-03-01
We explore the constraints following from requiring the area law in the entanglement entropy in the context of loop quantum gravity. We find a unique solution to the single-link wave function in the large j limit, believed to be appropriate in the semiclassical limit. We then generalize our considerations to multilink coherent states, and find that the area law is preserved very generically using our single-link wave function as a building block. Finally, we develop the framework that generates families of multilink states that preserve the area law while avoiding macroscopic entanglement, the space-time analogue of "Schrödinger's cat." We note that these states, defined on a given set of graphs, are the ground states of some local Hamiltonian that can be constructed explicitly. This can potentially shed light on the construction of the appropriate Hamiltonian constraints in the LQG framework.
Loop quantum gravity and black hole entropy quantization
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity,the minimum horizon area gap is obtained.Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization.The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi.
Eigenvalues of the volume operator in loop quantum gravity
International Nuclear Information System (INIS)
Meissner, Krzysztof A
2006-01-01
We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins, which turns out to be of a very simple form. The results can be useful for example in the statistical approach to quantum gravity
Background-free propagation in loop quantum gravity
Speziale, Simone
2008-01-01
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.
Extension of loop quantum gravity to f(R) theories.
Zhang, Xiangdong; Ma, Yongge
2011-04-29
The four-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real su(2) connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the nonperturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.
Relating loop quantum cosmology to loop quantum gravity: symmetric sectors and embeddings
International Nuclear Information System (INIS)
Engle, J
2007-01-01
In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity. First, we introduce a rigorous formulation of an embedding proposed by Bojowald and Kastrup, of LQC states into loop quantum gravity. Then, using certain holomorphic representations, a new class of embeddings, called b-embeddings, are constructed, following the ideas of Engle (2006 Quantum field theory and its symmetry reduction Class. Quantum Gravity 23 2861-94). We exhibit a class of operators preserving each of these embeddings, and show their consistency with the LQC quantization. In the b-embedding case, the classical analogues of these operators separate points in phase space. Embedding at the gauge and diffeomorphism invariant level is discussed briefly in the conclusions
One-loop quantum gravity repulsion in the early Universe.
Broda, Bogusław
2011-03-11
Perturbative quantum gravity formalism is applied to compute the lowest order corrections to the classical spatially flat cosmological Friedmann-Lemaître-Robertson-Walker solution (for the radiation). The presented approach is analogous to the approach applied to compute quantum corrections to the Coulomb potential in electrodynamics, or rather to the approach applied to compute quantum corrections to the Schwarzschild solution in gravity. In the framework of the standard perturbative quantum gravity, it is shown that the corrections to the classical deceleration, coming from the one-loop graviton vacuum polarization (self-energy), have (UV cutoff free) opposite to the classical repulsive properties which are not negligible in the very early Universe. The repulsive "quantum forces" resemble those known from loop quantum cosmology.
Non-commutative flux representation for loop quantum gravity
Baratin, A.; Dittrich, B.; Oriti, D.; Tambornino, J.
2011-09-01
The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this non-commutativity prevents a dual flux (or triad) representation of loop quantum gravity to exist. We show here, instead, that such a representation can be explicitly defined, by means of a non-commutative Fourier transform defined on the loop gravity state space. In this dual representation, flux operators act by sstarf-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.
An ambiguity in one-loop quantum gravity
International Nuclear Information System (INIS)
Capper, D.M.; Kimber, D.P.
1980-01-01
It is argued that the application of the dimensional regularisation technique to one-loop quantum gravity calculations is ambiguous. However, for the calculation of on-mass-shell S-matrix elements, this ambiguity can be resolved by requiring consistency with results obtained from other regularisation schemes. Some discussion is also given of the implications of this work for recent attempts to use higher derivative Lagrangians to solve the renormalisability problem in quantum gravity. (author)
New Hamiltonian constraint operator for loop quantum gravity
Directory of Open Access Journals (Sweden)
Jinsong Yang
2015-12-01
Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
New Hamiltonian constraint operator for loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Yang, Jinsong, E-mail: yangksong@gmail.com [Department of Physics, Guizhou university, Guiyang 550025 (China); Institute of Physics, Academia Sinica, Taiwan (China); Ma, Yongge, E-mail: mayg@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)
2015-12-17
A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Dirac fields in loop quantum gravity and big bang nucleosynthesis
International Nuclear Information System (INIS)
Bojowald, Martin; Das, Rupam; Scherrer, Robert J.
2008-01-01
Big bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions. Several corrections to equation of state parameters arise from classical and quantum physics, which are derived here from a canonical perspective. In particular, loop quantum gravity allows one to compute quantum gravity corrections for Maxwell and Dirac fields. Although the classical actions are very different, quantum corrections to the equation of state are remarkably similar. To lowest order, these corrections take the form of an overall expansion-dependent multiplicative factor in the total density. We use these results, along with the predictions of big bang nucleosynthesis, to place bounds on these corrections and especially the patch size of discrete quantum gravity states.
Black hole state degeneracy in loop quantum gravity
International Nuclear Information System (INIS)
Agullo, Ivan; Diaz-Polo, Jacobo; Fernandez-Borja, Enrique
2008-01-01
The combinatorial problem of counting the black hole quantum states within the isolated horizon framework in loop quantum gravity is analyzed. A qualitative understanding of the origin of the band structure shown by the degeneracy spectrum, which is responsible for the black hole entropy quantization, is reached. Even when motivated by simple considerations, this picture allows to obtain analytical expressions for the most relevant quantities associated to this effect
Constraining the loop quantum gravity parameter space from phenomenology
Directory of Open Access Journals (Sweden)
Suddhasattwa Brahma
2018-03-01
Full Text Available Development of quantum gravity theories rarely takes inputs from experimental physics. In this letter, we take a small step towards correcting this by establishing a paradigm for incorporating putative quantum corrections, arising from canonical quantum gravity (QG theories, in deriving falsifiable modified dispersion relations (MDRs for particles on a deformed Minkowski space–time. This allows us to differentiate and, hopefully, pick between several quantization choices via testable, state-of-the-art phenomenological predictions. Although a few explicit examples from loop quantum gravity (LQG (such as the regularization scheme used or the representation of the gauge group are shown here to establish the claim, our framework is more general and is capable of addressing other quantization ambiguities within LQG and also those arising from other similar QG approaches.
Constraining the loop quantum gravity parameter space from phenomenology
Brahma, Suddhasattwa; Ronco, Michele
2018-03-01
Development of quantum gravity theories rarely takes inputs from experimental physics. In this letter, we take a small step towards correcting this by establishing a paradigm for incorporating putative quantum corrections, arising from canonical quantum gravity (QG) theories, in deriving falsifiable modified dispersion relations (MDRs) for particles on a deformed Minkowski space-time. This allows us to differentiate and, hopefully, pick between several quantization choices via testable, state-of-the-art phenomenological predictions. Although a few explicit examples from loop quantum gravity (LQG) (such as the regularization scheme used or the representation of the gauge group) are shown here to establish the claim, our framework is more general and is capable of addressing other quantization ambiguities within LQG and also those arising from other similar QG approaches.
Probing loop quantum gravity with evaporating black holes.
Barrau, A; Cailleteau, T; Cao, X; Diaz-Polo, J; Grain, J
2011-12-16
This Letter aims at showing that the observation of evaporating black holes should allow the usual Hawking behavior to be distinguished from loop quantum gravity (LQG) expectations. We present a full Monte Carlo simulation of the evaporation in LQG and statistical tests that discriminate between competing models. We conclude that contrarily to what was commonly thought, the discreteness of the area in LQG leads to characteristic features that qualify evaporating black holes as objects that could reveal quantum gravity footprints. © 2011 American Physical Society
Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map.
Sahlmann, Hanno; Thiemann, Thomas
2012-03-16
We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Lie algebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups.
Gravitational interaction to one loop in effective quantum gravity
International Nuclear Information System (INIS)
Akhundov, A.
1996-10-01
The authors carry out the first step of a program conceived, in order to build a realistic model, having the particle spectrum of the standard model and renormalized masses, interaction terms and coupling, etc. which include the class of quantum gravity corrections, obtained by handling gravity as an effective theory. This provides an adequate picture at low energies, i.e. much less than the scale of strong gravity (the Planck mass). Hence the results are valid, irrespectively of any proposal for the full quantum gravity as a fundamental theory. The authors consider only non-analytic contributions to the one-loop scattering matrix elements, which provide the dominant quantum effect at long distance. These contributions are finite and independent from the finite value of the renormalization counter terms of the effective Lagrangian. The authors calculate the interaction of two heavy scalar particles, i.e. close to rest, due to the effective quantum gravity to the one loop order and compare with similar results in the literature
Gravitational interaction to one loop in effective quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Akhundov, A. [Universitaet-gesamthochschule Siegen (Germany)]|[Azerbaijan Academy of Sciences, Baku (Azerbaijan). Institute of Physics; Bellucci, S. [INFN, Laboratori Nazionali di Frascati, Rome (Italy); Shiekh, A. [International Centre for Theoretical Physics, Trieste (Italy)
1996-10-01
The authors carry out the first step of a program conceived, in order to build a realistic model, having the particle spectrum of the standard model and renormalized masses, interaction terms and coupling, etc. which include the class of quantum gravity corrections, obtained by handling gravity as an effective theory. This provides an adequate picture at low energies, i.e. much less than the scale of strong gravity (the Planck mass). Hence the results are valid, irrespectively of any proposal for the full quantum gravity as a fundamental theory. The authors consider only non-analytic contributions to the one-loop scattering matrix elements, which provide the dominant quantum effect at long distance. These contributions are finite and independent from the finite value of the renormalization counter terms of the effective Lagrangian. The authors calculate the interaction of two heavy scalar particles, i.e. close to rest, due to the effective quantum gravity to the one loop order and compare with similar results in the literature.
Hawking radiation from a spherical loop quantum gravity black hole
International Nuclear Information System (INIS)
Gambini, Rodolfo; Pullin, Jorge
2014-01-01
We introduce quantum field theory on quantum space-times techniques to characterize the quantum vacua as a first step toward studying black hole evaporation in spherical symmetry in loop quantum gravity and compute the Hawking radiation. We use as quantum space-time the recently introduced exact solution of the quantum Einstein equations in vacuum with spherical symmetry and consider a spherically symmetric test scalar field propagating on it. The use of loop quantum gravity techniques in the background space-time naturally regularizes the matter content, solving one of the main obstacles to back-reaction calculations in more traditional treatments. The discreteness of area leads to modifications of the quantum vacua, eliminating the trans-Planckian modes close to the horizon, which in turn eliminates all singularities from physical quantities, like the expectation value of the stress–energy tensor. Apart from this, the Boulware, Hartle–Hawking and Unruh vacua differ little from the treatment on a classical space-time. The asymptotic modes near scri are reproduced very well. We show that the Hawking radiation can be computed, leading to an expression similar to the conventional one but with a high frequency cutoff. Since many of the conclusions concern asymptotic behavior, where the spherical mode of the field behaves in a similar way as higher multipole modes do, the results can be readily generalized to non spherically symmetric fields. (paper)
Scalar material reference systems and loop quantum gravity
International Nuclear Information System (INIS)
Giesel, K; Thiemann, T
2015-01-01
In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasized frequently. This idea has been picked up more recently in loop quantum gravity with the aim to perform a reduced phase space quantization of the theory, thus possibly avoiding problems with the (Dirac) operator constraint quantization method for a constrained system. In this work, we review the models that have been studied on the classical and/or the quantum level and parametrize the space of theories considered so far. We then describe the quantum theory of a model that, to the best of our knowledge, has only been considered classically so far. This model could arguably be called the optimal one in this class of models considered as it displays the simplest possible true Hamiltonian, while at the same time reducing all constraints of general relativity. (paper)
Toward explaining black hole entropy quantization in loop quantum gravity
International Nuclear Information System (INIS)
Sahlmann, Hanno
2007-01-01
In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this steplike behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking
PREFACE: Loops 11: Non-Perturbative / Background Independent Quantum Gravity
Mena Marugán, Guillermo A.; Barbero G, J. Fernando; Garay, Luis J.; Villaseñor, Eduardo J. S.; Olmedo, Javier
2012-05-01
Loops 11 The international conference LOOPS'11 took place in Madrid from the 23-28 May 2011. It was hosted by the Instituto de Estructura de la Materia (IEM), which belongs to the Consejo Superior de Investigaciones Cientĺficas (CSIC). Like previous editions of the LOOPS meetings, it dealt with a wealth of state-of-the-art topics on Quantum Gravity, with special emphasis on non-perturbative background-independent approaches to spacetime quantization. The main topics addressed at the conference ranged from the foundations of Quantum Gravity to its phenomenological aspects. They encompassed different approaches to Loop Quantum Gravity and Cosmology, Polymer Quantization, Quantum Field Theory, Black Holes, and discrete approaches such as Dynamical Triangulations, amongst others. In addition, this edition celebrated the 25th anniversary of the introduction of the now well-known Ashtekar variables and the Wednesday morning session was devoted to this silver jubilee. The structure of the conference was designed to reflect the current state and future prospects of research on the different topics mentioned above. Plenary lectures that provided general background and the 'big picture' took place during the mornings, and the more specialised talks were distributed in parallel sessions during the evenings. To be more specific, Monday evening was devoted to Shape Dynamics and Phenomenology Derived from Quantum Gravity in Parallel Session A, and to Covariant Loop Quantum Gravity and Spin foams in Parallel Session B. Tuesday's three Parallel Sessions dealt with Black Hole Physics and Dynamical Triangulations (Session A), the continuation of Monday's session on Covariant Loop Quantum Gravity and Spin foams (Session B) and Foundations of Quantum Gravity (Session C). Finally, Thursday and Friday evenings were devoted to Loop Quantum Cosmology (Session A) and to Hamiltonian Loop Quantum Gravity (Session B). The result of the conference was very satisfactory and enlightening. Not
Towards loop quantum gravity without the time gauge.
Cianfrani, Francesco; Montani, Giovanni
2009-03-06
The Hamiltonian formulation of the Holst action is reviewed and it provides a solution of second-class constraints corresponding to a generic local Lorentz frame. Within this scheme the form of rotation constraints can be reduced to a Gauss-like one by a proper generalization of Ashtekar-Barbero-Immirzi connections. This result emphasizes that the loop quantum gravity quantization procedure can be applied when the time-gauge condition does not stand.
Approaches to quantum gravity. Loop quantum gravity, spinfoams and topos approach
International Nuclear Information System (INIS)
Flori, Cecilia
2010-01-01
One of the main challenges in theoretical physics over the last five decades has been to reconcile quantum mechanics with general relativity into a theory of quantum gravity. However, such a theory has been proved to be hard to attain due to i) conceptual difficulties present in both the component theories (General Relativity (GR) and Quantum Theory); ii) lack of experimental evidence, since the regimes at which quantum gravity is expected to be applicable are far beyond the range of conceivable experiments. Despite these difficulties, various approaches for a theory of Quantum Gravity have been developed. In this thesis we focus on two such approaches: Loop Quantum Gravity and the Topos theoretic approach. The choice fell on these approaches because, although they both reject the Copenhagen interpretation of quantum theory, their underpinning philosophical approach to formulating a quantum theory of gravity are radically different. In particular LQG is a rather conservative scheme, inheriting all the formalism of both GR and Quantum Theory, as it tries to bring to its logical extreme consequences the possibility of combining the two. On the other hand, the Topos approach involves the idea that a radical change of perspective is needed in order to solve the problem of quantum gravity, especially in regard to the fundamental concepts of 'space' and 'time'. Given the partial successes of both approaches, the hope is that it might be possible to find a common ground in which each approach can enrich the other. This thesis is divided in two parts: in the first part we analyse LQG, paying particular attention to the semiclassical properties of the volume operator. Such an operator plays a pivotal role in defining the dynamics of the theory, thus testing its semiclassical limit is of uttermost importance. We then proceed to analyse spin foam models (SFM), which are an attempt at a covariant or path integral formulation of canonical Loop Quantum Gravity (LQG). In
Approaches to quantum gravity. Loop quantum gravity, spinfoams and topos approach
Energy Technology Data Exchange (ETDEWEB)
Flori, Cecilia
2010-07-23
One of the main challenges in theoretical physics over the last five decades has been to reconcile quantum mechanics with general relativity into a theory of quantum gravity. However, such a theory has been proved to be hard to attain due to i) conceptual difficulties present in both the component theories (General Relativity (GR) and Quantum Theory); ii) lack of experimental evidence, since the regimes at which quantum gravity is expected to be applicable are far beyond the range of conceivable experiments. Despite these difficulties, various approaches for a theory of Quantum Gravity have been developed. In this thesis we focus on two such approaches: Loop Quantum Gravity and the Topos theoretic approach. The choice fell on these approaches because, although they both reject the Copenhagen interpretation of quantum theory, their underpinning philosophical approach to formulating a quantum theory of gravity are radically different. In particular LQG is a rather conservative scheme, inheriting all the formalism of both GR and Quantum Theory, as it tries to bring to its logical extreme consequences the possibility of combining the two. On the other hand, the Topos approach involves the idea that a radical change of perspective is needed in order to solve the problem of quantum gravity, especially in regard to the fundamental concepts of 'space' and 'time'. Given the partial successes of both approaches, the hope is that it might be possible to find a common ground in which each approach can enrich the other. This thesis is divided in two parts: in the first part we analyse LQG, paying particular attention to the semiclassical properties of the volume operator. Such an operator plays a pivotal role in defining the dynamics of the theory, thus testing its semiclassical limit is of uttermost importance. We then proceed to analyse spin foam models (SFM), which are an attempt at a covariant or path integral formulation of canonical Loop Quantum
Projective loop quantum gravity. I. State space
Lanéry, Suzanne; Thiemann, Thomas
2016-12-01
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 a latter work by Okolów, 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.
On the embedding of quantum field theory on curved spacetimes into loop quantum gravity
International Nuclear Information System (INIS)
Stottmeister, Alexander
2015-01-01
The main theme of this thesis is an investigation into possible connections between loop quantum gravity and quantum field theory on curved spacetimes: On the one hand, we aim for the formulation of a general framework that allows for a derivation of quantum field theory on curved spacetimes in a semi-classical limit. On the other hand, we discuss representation-theoretical aspects of loop quantum gravity and quantum field theory on curved spacetimes as both of the latter presumably influence each other in the aforesaid semi-classical limit. Regarding the first point, we investigate the possible implementation of the Born-Oppenheimer approximation in the sense of space-adiabatic perturbation theory in models of loop quantum gravity-type. In the course of this, we argue for the need of a Weyl quantisation and an associated symbolic calculus for loop quantum gravity, which we then successfully define, at least to a certain extent. The compactness of the Lie groups, which models a la loop quantum gravity are based on, turns out to be a main obstacle to a fully satisfactory definition of a Weyl quantisation. Finally, we apply our findings to some toy models of linear scalar quantum fields on quantum cosmological spacetimes and discuss the implementation of space-adiabatic perturbation theory therein. In view of the second point, we start with a discussion of the microlocal spectrum condition for quantum fields on curved spacetimes and how it might be translated to a background-independent Hamiltonian quantum theory of gravity, like loop quantum gravity. The relevance of this lies in the fact that the microlocal spectrum condition selects a class of physically relevant states of the quantum matter fields and is, therefore, expected to play an important role in the aforesaid semi-classical limit of gravity-matter systems. Following this, we switch our perspective and analyse the representation theory of loop quantum gravity. We find some intriguing relations between the
Group field theories for all loop quantum gravity
Oriti, Daniele; Ryan, James P.; Thürigen, Johannes
2015-02-01
Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.
Secular effects on inflation from one-loop quantum gravity
International Nuclear Information System (INIS)
Cabrer, J.A.; Espriu, D.
2008-01-01
In this Letter we revisit and extend a previous analysis where the possible relevance of quantum gravity effects in a cosmological setup was studied. The object of interest are non-local (logarithmic) terms generated in the effective action of gravity due to the exchange in loops of massless modes (such as photons or the gravitons themselves). We correct one mistake existing in the previous work and discuss the issue in a more general setting in different cosmological scenarios. We obtain the one-loop quantum-corrected evolution equations for the cosmological scale factor up to a given order in a derivative expansion in two particular cases: a matter dominated universe with vanishing cosmological constant, and in a de Sitter universe. We show that the quantum corrections, albeit tiny, may have a secular effect that eventually modifies the expansion rate. For a de Sitter universe they tend to slow down the rate of the expansion, while the effect may be the opposite in a matter dominated universe
Renormalization and Coarse-graining of Loop Quantum Gravity
Charles, Christoph
2017-01-01
The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will investigate some coarse-graining methods that should become helpful in this enterprise. We concentrate on two aspects of the theory's coarse-graining: finding natural large scale observables on one hand and studying how the dynamics of varying graphs could...
Semiclassical Loop Quantum Gravity and Black Hole Thermodynamics
Directory of Open Access Journals (Sweden)
Arundhati Dasgupta
2013-02-01
Full Text Available In this article we explore the origin of black hole thermodynamics using semiclassical states in loop quantum gravity. We re-examine the case of entropy using a density matrix for a coherent state and describe correlations across the horizon due to SU(2 intertwiners. We further show that Hawking radiation is a consequence of a non-Hermitian term in the evolution operator, which is necessary for entropy production or depletion at the horizon. This non-unitary evolution is also rooted in formulations of irreversible physics.
On the UV Dimensions of Loop Quantum Gravity
Directory of Open Access Journals (Sweden)
Michele Ronco
2016-01-01
Full Text Available Planck-scale dynamical dimensional reduction is attracting more and more interest in the quantum-gravity literature since it seems to be a model independent effect. However, different studies base their results on different concepts of space-time dimensionality. Most of them rely on the spectral dimension; others refer to the Hausdorff dimension; and, very recently, the thermal dimension has also been introduced. We here show that all these distinct definitions of dimension give the same outcome in the case of the effective regime of Loop Quantum Gravity (LQG. This is achieved by deriving a modified dispersion relation from the hypersurface-deformation algebra with quantum corrections. Moreover, we also observe that the number of UV dimensions can be used to constrain the ambiguities in the choice of these LQG-based modifications of the Dirac space-time algebra. In this regard, introducing the polymerization of connections, that is, K→sinδK/δ, we find that the leading quantum correction gives dUV=2.5. This result may indicate that the running to the expected value of two dimensions is ongoing, but it has not been completed yet. Finding dUV at ultrashort distances would require going beyond the effective approach we here present.
2D quantum gravity at three loops: A counterterm investigation
Directory of Open Access Journals (Sweden)
Lætitia Leduc
2016-02-01
Full Text Available We analyze the divergences of the three-loop partition function at fixed area in 2D quantum gravity. Considering the Liouville action in the Kähler formalism, we extract the coefficient of the leading divergence ∼AΛ2(lnAΛ22. This coefficient is non-vanishing. We discuss the counterterms one can and must add and compute their precise contribution to the partition function. This allows us to conclude that every local and non-local divergence in the partition function can be balanced by local counterterms, with the only exception of the maximally non-local divergence (lnAΛ23. Yet, this latter is computed and does cancel between the different three-loop diagrams. Thus, requiring locality of the counterterms is enough to renormalize the partition function. Finally, the structure of the new counterterms strongly suggests that they can be understood as a renormalization of the measure action.
The perturbative Regge-calculus regime of loop quantum gravity
International Nuclear Information System (INIS)
Bianchi, Eugenio; Modesto, Leonardo
2008-01-01
The relation between loop quantum gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In this paper we study a semiclassical regime of loop quantum gravity and show that it admits an effective description in terms of perturbative area-Regge-calculus. The regime of interest is identified by a class of states given by superpositions of four-valent spin networks, peaked on large spins. As a probe of the dynamics in this regime, we compute explicitly two- and three-area correlation functions at the vertex amplitude level. We find that they match with the ones computed perturbatively in area-Regge-calculus with a single 4-simplex, once a specific perturbative action and measure have been chosen in the Regge-calculus path integral. Correlations of other geometric operators and the existence of this regime for other models for the dynamics are briefly discussed
Fusion basis for lattice gauge theory and loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Delcamp, Clement [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Department of Physics Astronomy and Guelph-Waterloo Physics Institute, University of Waterloo,Waterloo, Ontario N2L 3G1 (Canada); Dittrich, Bianca; Riello, Aldo [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)
2017-02-10
We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2+1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel’d double of the gauge group, and can be readily “fused” together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi-local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse-graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin-network basis, in which it is much more complicated to account for electric excitations, i.e. for Gauß constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi-scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2+1) gravity coupled to point particles. In a follow-up work, we have exploited this notion to provide a new definition of entanglement entropy for these theories.
Fusion basis for lattice gauge theory and loop quantum gravity
International Nuclear Information System (INIS)
Delcamp, Clement; Dittrich, Bianca; Riello, Aldo
2017-01-01
We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2+1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel’d double of the gauge group, and can be readily “fused” together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi-local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse-graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin-network basis, in which it is much more complicated to account for electric excitations, i.e. for Gauß constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi-scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2+1) gravity coupled to point particles. In a follow-up work, we have exploited this notion to provide a new definition of entanglement entropy for these theories.
Computing black hole entropy in loop quantum gravity from a conformal field theory perspective
International Nuclear Information System (INIS)
Agulló, Iván; Borja, Enrique F.; Díaz-Polo, Jacobo
2009-01-01
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
Analytic continuation of black hole entropy in Loop Quantum Gravity
International Nuclear Information System (INIS)
Jibril, Ben Achour; Mouchet, Amaury; Noui, Karim
2015-01-01
We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter γ. This construction deeply relies on the link between black holes and Chern-Simons theory. Technically, the key point consists in writing the number of microstates as an integral in the complex plane of a holomorphic function, and to make use of complex analysis techniques to perform the analytic continuation. Then, we study the thermodynamical properties of the corresponding system (the black hole is viewed as a gas of indistinguishable punctures) in the framework of the grand canonical ensemble where the energy is defined à la Frodden-Gosh-Perez from the point of view of an observer located close to the horizon. The semi-classical limit occurs at the Unruh temperature T U associated to this local observer. When γ=±i, the entropy reproduces at the semi-classical limit the area law with quantum corrections. Furthermore, the quantum corrections are logarithmic provided that the chemical potential is fixed to the simple value μ=2T U .
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
Directory of Open Access Journals (Sweden)
Jacobo Diaz-Polo
2012-08-01
Full Text Available We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on the quasi-local definition of a black hole encoded in the isolated horizon formalism. We show, by means of the covariant phase space framework, the appearance in the conserved symplectic structure of a boundary term corresponding to a Chern-Simons theory on the horizon and present its quantization both in the U(1 gauge fixed version and in the fully SU(2 invariant one. We then describe the boundary degrees of freedom counting techniques developed for an infinite value of the Chern-Simons level case and, less rigorously, for the case of a finite value. This allows us to perform a comparison between the U(1 and SU(2 approaches and provide a state of the art analysis of their common features and different implications for the entropy calculations. In particular, we comment on different points of view regarding the nature of the horizon degrees of freedom and the role played by the Barbero-Immirzi parameter. We conclude by presenting some of the most recent results concerning possible observational tests for theory.
Oriented matroids—combinatorial structures underlying loop quantum gravity
Brunnemann, Johannes; Rideout, David
2010-10-01
We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator (Ashtekar A and Lewandowski J 1998 Adv. Theor. Math. Phys. 1 388) in loop quantum gravity (LQG). These structures encode geometrical information of the embedding of arbitrary valence vertices of a graph in three-dimensional Riemannian space and can be represented by sign strings containing relative orientations of embedded edges. We demonstrate that these signature factors are a special representation of the general mathematical concept of an oriented matroid (Ziegler G M 1998 Electron. J. Comb.; Björner A et al 1999 Oriented Matroids (Cambridge: Cambridge University Press)). Moreover, we show that oriented matroids can also be used to describe the topology (connectedness) of directed graphs. Hence, the mathematical methods developed for oriented matroids can be applied to the difficult combinatorics of embedded graphs underlying the construction of LQG. As a first application we revisit the analysis of Brunnemann and Rideout (2008 Class. Quantum Grav. 25 065001 and 065002), and find that enumeration of all possible sign configurations used there is equivalent to enumerating all realizable oriented matroids of rank 3 (Ziegler G M 1998 Electron. J. Comb.; Björner A et al 1999 Oriented Matroids (Cambridge: Cambridge University Press)), and thus can be greatly simplified. We find that for 7-valent vertices having no coplanar triples of edge tangents, the smallest non-zero eigenvalue of the volume spectrum does not grow as one increases the maximum spin jmax at the vertex, for any orientation of the edge tangents. This indicates that, in contrast to the area operator, considering large jmax does not necessarily imply large volume eigenvalues. In addition we give an outlook to possible starting points for rewriting the combinatorics of LQG in terms of oriented matroids.
Two-loop renormalization of quantum gravity simplified
Bern, Zvi; Chi, Huan-Hang; Dixon, Lance; Edison, Alex
2017-02-01
The coefficient of the dimensionally regularized two-loop R3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. We explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.
Loop quantum gravity effects on inflation and the CMB
International Nuclear Information System (INIS)
Tsujikawa, Shinji; Singh, Parampreet; Maartens, Roy
2004-01-01
In loop quantum cosmology, the universe avoids a big bang singularity and undergoes an early and short super-inflation phase. During super-inflation, non-perturbative quantum corrections to the dynamics drive an inflaton field up its potential hill, thus setting the initial conditions for standard inflation. We show that this effect can raise the inflaton high enough to achieve sufficient e-foldings in the standard inflation era. We analyse the cosmological perturbations generated when slow-roll is violated after super-inflation and show that loop quantum effects can in principle leave an indirect signature on the largest scales in the CMB, with some loss of power and running of the spectral index
International Nuclear Information System (INIS)
Bodendorfer, N; Zipfel, A
2016-01-01
Building on a recent proposal for a quantum reduction to spherical symmetry from full loop quantum gravity, we investigate the relation between a quantisation of spherically symmetric general relativity and a reduction at the quantum level. To this end, we generalise the previously proposed quantum reduction by dropping the gauge fixing condition on the radial diffeomorphisms, thus allowing us to make direct contact with previous work on reduced quantisation. A dictionary between spherically symmetric variables and observables with respect to the reduction constraints in the full theory is discussed, as well as an embedding of reduced quantum states to a subsector of the quantum symmetry reduced full theory states. On this full theory subsector, the quantum algebra of the mentioned observables is computed and shown to qualitatively reproduce the quantum algebra of the reduced variables in the large quantum number limit for a specific choice of regularisation. Insufficiencies in recovering the reduced algebra quantitatively from the full theory are attributed to the oversimplified full theory quantum states we use. (paper)
Amaral, Marcelo M.; Aschheim, Raymond; Bubuianu, Laurenţiu; Irwin, Klee; Vacaru, Sergiu I.; Woolridge, Daniel
2017-09-01
The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/aperiodic/fractal/stochastic/(super) cluster/filament/polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off-diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi-Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.
Phase space and black-hole entropy of higher genus horizons in loop quantum gravity
International Nuclear Information System (INIS)
Kloster, S; Brannlund, J; DeBenedictis, A
2008-01-01
In the context of loop quantum gravity, we construct the phase space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the dimension of the corresponding phase space is calculated including the genus cycles as degrees of freedom. From this, the black-hole entropy can be calculated by counting the microstates which correspond to a black hole of fixed area. We find that the leading term agrees with the A/4 law and that the sub-leading contribution is modified by the genus cycles
Three-dimensional loop quantum gravity: towards a self-gravitating quantum field theory
International Nuclear Information System (INIS)
Noui, Karim
2007-01-01
In a companion paper, we have emphasized the role of the Drinfeld double DSU(2) in the context of three-dimensional Riemannian loop quantum gravity coupled to massive spinless point particles. We make use of this result to propose a model for a self-gravitating quantum field theory (massive spinless non-causal scalar field) in three-dimensional Riemannian space. We start by constructing the Fock space of the free self-gravitating field: the vacuum is the unique DSU(2) invariant state, one-particle states correspond to DSU(2) unitary irreducible simple representations and any multi-particles states are obtained as the symmetrized tensor product between simple representations. The associated quantum field is defined by the usual requirement of covariance under DSU(2). Then, we introduce a DSU(2)-invariant self-interacting potential (the obtained model is a group field theory) and explicitly compute the lowest order terms (in the self-interaction coupling constant λ) of the propagator and of the three-point function. Finally, we compute the lowest order quantum gravity corrections (in the Newton constant G) to the propagator and to the three-point function
Extension of Loop Quantum Gravity to Metric Theories beyond General Relativity
International Nuclear Information System (INIS)
Ma Yongge
2012-01-01
The successful background-independent quantization of Loop Quantum Gravity relies on the key observation that classical General Relativity can be cast into the connection-dynamical formalism with the structure group of SU(2). Due to this particular formalism, Loop Quantum Gravity was generally considered as a quantization scheme that applies only to General Relativity. However, we will show that the nonperturbative quantization procedure of Loop Quantum Gravity can be extended to a rather general class of metric theories of gravity, which have received increased attention recently due to motivations coming form cosmology and astrophysics. In particular, we will first introduce how to reformulate the 4-dimensional metric f(R) theories of gravity, as well as Brans-Dicke theory, into connection-dynamical formalism with real SU(2) connections as configuration variables. Through these formalisms, we then outline the nonpertubative canonical quantization of the f(R) theories and Brans-Dicke theory by extending the loop quantization scheme of General Relativity.
Black Hole Entropy with and without Log Correction in Loop Quantum Gravity
International Nuclear Information System (INIS)
Mitra, P.
2014-01-01
Earlier calculations of black hole entropy in loop quantum gravity have given a term proportional to the area with a correction involving the logarithm of the area when the area eigenvalue is close to the classical area. However the calculations yield an entropy proportional to the area eigenvalue with no such correction when the area eigenvalue is large compared to the classical area
Testing the master constraint programme for loop quantum gravity: V. Interacting field theories
International Nuclear Information System (INIS)
Dittrich, B; Thiemann, T
2006-01-01
This is the fifth and final paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. Here we consider interacting quantum field theories, specifically we consider the non-Abelian Gauss constraints of Einstein-Yang-Mills theory and 2 + 1 gravity. Interestingly, while Yang-Mills theory in 4D is not yet rigorously defined as an ordinary (Wightman) quantum field theory on Minkowski space, in background-independent quantum field theories such as loop quantum gravity (LQG) this might become possible by working in a new, background-independent representation. While for the Gauss constraint the master constraint can be solved explicitly, for the 2 + 1 theory we are only able to rigorously define the master constraint operator. We show that the, by other methods known, physical Hilbert is contained in the kernel of the master constraint, however, to systematically derive it by only using spectral methods is as complicated as for 3 + 1 gravity and we therefore leave the complete analysis for 3 + 1 gravity
A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity
Cattaneo, Alberto S.; Perez, Alejandro
2017-05-01
We show that the non-Abelian nature of geometric fluxes—the corner-stone in the definition of quantum geometry in the framework of loop quantum gravity (LQG)—follows directly form the continuum canonical commutations relations of gravity in connection variables and the validity of the Gauss law. The present treatment simplifies previous formulations and thus identifies more clearly the root of the discreteness of geometric operators in LQG. Our statement generalizes to arbitrary gauge theories and relies only on the validity of the Gauss law.
Surface state decoherence in loop quantum gravity, a first toy model
International Nuclear Information System (INIS)
Feller, Alexandre; Livine, Etera R
2017-01-01
The quantum-to-classical transition through decoherence is a major facet of the semi-classical analysis of quantum models that are supposed to admit a classical regime, as quantum gravity should be. A particular problem of interest is the decoherence of black hole horizons and holographic screens induced by the bulk-boundary coupling with interior degrees of freedom. Here in this paper we present a first toy-model, in the context of loop quantum gravity, for the dynamics of a surface geometry as an open quantum system. We discuss the resulting decoherence and recoherence and compare the exact density matrix evolution to the commonly used master equation approximation à la Lindblad underlining its merits and limitations. The prospect of this study is to have a clearer understanding of the boundary decoherence of black hole horizons seen by outside observers. (paper)
Simplicity constraints: A 3D toy model for loop quantum gravity
Charles, Christoph
2018-05-01
In loop quantum gravity, tremendous progress has been made using the Ashtekar-Barbero variables. These variables, defined in a gauge fixing of the theory, correspond to a parametrization of the solutions of the so-called simplicity constraints. Their geometrical interpretation is however unsatisfactory as they do not constitute a space-time connection. It would be possible to resolve this point by using a full Lorentz connection or, equivalently, by using the self-dual Ashtekar variables. This leads however to simplicity constraints or reality conditions which are notoriously difficult to implement in the quantum theory. We explore in this paper the possibility of using completely degenerate actions to impose such constraints at the quantum level in the context of canonical quantization. To do so, we define a simpler model, in 3D, with similar constraints by extending the phase space to include an independent vielbein. We define the classical model and show that a precise quantum theory by gauge unfixing can be defined out of it, completely equivalent to the standard 3D Euclidean quantum gravity. We discuss possible future explorations around this model as it could help as a stepping stone to define full-fledged covariant loop quantum gravity.
Black hole state counting in loop quantum gravity: a number-theoretical approach.
Agulló, Iván; Barbero G, J Fernando; Díaz-Polo, Jacobo; Fernández-Borja, Enrique; Villaseñor, Eduardo J S
2008-05-30
We give an efficient method, combining number-theoretic and combinatorial ideas, to exactly compute black hole entropy in the framework of loop quantum gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and explicitly determine the number of solutions to the projection constraint. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum.
Black holes in loop quantum gravity: the complete space-time.
Gambini, Rodolfo; Pullin, Jorge
2008-10-17
We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semiclassical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordström space-time including a Cauchy horizon is suggested.
International Nuclear Information System (INIS)
Romney, B.; Barrau, A.; Vidotto, F.; Le Meur, H.; Noui, K.
2011-01-01
The loop quantum gravity is the only theory that proposes a quantum description of space-time and therefore of gravitation. This theory predicts that space is not infinitely divisible but that is has a granular structure at the Planck scale (10 -35 m). Another feature of loop quantum gravity is that it gets rid of the Big-Bang singularity: our expanding universe may come from the bouncing of a previous contracting universe, in this theory the Big-Bang is replaced with a big bounce. The loop quantum theory predicts also the huge number of quantum states that accounts for the entropy of large black holes. (A.C.)
U(N) tools for loop quantum gravity: the return of the spinor
Borja, Enrique F.; Freidel, Laurent; Garay, Iñaki; Livine, Etera R.
2011-03-01
We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity and describe the corresponding phase space in terms of spinors with the appropriate constraints. We show how its quantization leads back to the standard Hilbert space of intertwiner states defined as holomorphic functionals. We then explain how to glue these intertwiners states in order to construct spin network states as wavefunctions on the spinor phase space. In particular, we translate the usual loop gravity holonomy observables to our classical framework. Finally, we propose how to derive our phase space structure from an action principle which induces non-trivial dynamics for the spin network states. We conclude by applying explicitly our framework to states living on the simple 2-vertex graph and discuss the properties of the resulting Hamiltonian.
Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Yang, Jinsong [Guizhou University, Department of Physics, Guiyang (China); Academia Sinica, Institute of Physics, Taipei (China); Ma, Yongge [Beijing Normal University, Department of Physics, Beijing (China)
2017-04-15
To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature. (orig.)
Fine-grained state counting for black holes in loop quantum gravity.
Ghosh, A; Mitra, P
2009-04-10
A state of a black hole in loop quantum gravity is given by a distribution of spins on punctures on the horizon. The distribution is of the Boltzmann type, with the area playing the role of the energy. In investigations where the total area was kept approximately constant, there was a kind of thermal equilibrium between the spins which have the same analogue temperature and the entropy was proportional to the area. If the area is precisely fixed, however, multiple constraints appear, different spins have different analogue temperatures and the entropy is not strictly linear in the area, but is bounded by a linear rise.
The kinematical Hilbert space of loop quantum gravity from BF theories
International Nuclear Information System (INIS)
Cianfrani, Francesco
2011-01-01
In this work, it is demonstrated how the kinematical Hilbert space of loop quantum gravity (LQG) can be inferred from the configuration space of BF theories via the imposition of the Hamiltonian constraints. In particular, it is outlined how the projection to the representations associated with Ashtekar-Barbero connections provides the correct procedure to implement second-class constraints and the corresponding nontrivial induced symplectic structure. Then, the reduction to SU(2) invariant intertwiners is analyzed and the properties of LQG states under Lorentz transformations are discussed.
A Non-Polynomial Gravity Formulation for Loop Quantum Cosmology Bounce
Directory of Open Access Journals (Sweden)
Stefano Chinaglia
2017-09-01
Full Text Available Recently the so-called mimetic gravity approach has been used to obtain corrections to the Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists of adding geometric non-polynomial higher derivative terms to Hilbert–Einstein action, which are nonetheless polynomials and lead to a second-order differential equation in Friedmann–Lemaître–Robertson–Walker space-times. Our explicit action turns out to be a realization of the Helling proposal of effective action with an infinite number of terms. The model is also investigated in the presence of a non-vanishing cosmological constant, and a new exact bounce solution is found and studied.
Beyond-one-loop quantum gravity action yielding both inflation and late-time acceleration
Directory of Open Access Journals (Sweden)
E. Elizalde
2017-08-01
Full Text Available A unified description of early-time inflation with the current cosmic acceleration is achieved by means of a new theory that uses a quadratic model of gravity, with the inclusion of an exponential F(R-gravity contribution for dark energy. High-curvature corrections of the theory come from higher-derivative quantum gravity and yield an effective action that goes beyond the one-loop approximation. It is shown that, in this theory, viable inflation emerges in a natural way, leading to a spectral index and tensor-to-scalar ratio that are in perfect agreement with the most reliable Planck results. At low energy, late-time accelerated expansion takes place. As exponential gravity, for dark energy, must be stabilized during the matter and radiation eras, we introduce a curing term in order to avoid nonphysical singularities in the effective equation of state parameter. The results of our analysis are confirmed by accurate numerical simulations, which show that our model does fit the most recent cosmological data for dark energy very precisely.
The graviton vacuum as a distributional state in kinematic loop quantum gravity
International Nuclear Information System (INIS)
Varadarajan, Madhavan
2005-01-01
The quantum behaviour of weak gravitational fields admits an adequate, albeit approximate, description by those graviton states in which the expectation values and fluctuations of the linearized gravitational field are small. Such states must approximate corresponding states in full quantum gravity. We analyse the nature of this approximation for the graviton vacuum state in the context of kinematical loop quantum gravity (LQG) wherein the constraints are ignored. We identify the graviton vacuum state with kinematically non-normalizable, distributional states in LQG by demanding that relations between linearized operator actions on the former are mirrored by those of their nonlinear counterparts on the latter. We define a semi-norm on the space of kinematical distributions and show that the identification is approximate up to distributions which are small in this semi-norm. We argue that our candidate states are annihilated by the linearized constraints (expressed as operators in the full theory) to leading order in the parameter characterizing the approximation. This suggests the possibility, in a scheme such as ours, of solving the full constraints order by order in this parameter. The main drawback of our considerations is that they depend on certain auxilliary constructions which, though mathematically well defined, do not arise from physical insight. Our work is an attempt to implement an earlier proposal of Iwasaki and Rovelli
International Nuclear Information System (INIS)
Markov, M.A.; West, P.C.
1984-01-01
This book discusses the state of the art of quantum gravity, quantum effects in cosmology, quantum black-hole physics, recent developments in supergravity, and quantum gauge theories. Topics considered include the problems of general relativity, pregeometry, complete cosmological theories, quantum fluctuations in cosmology and galaxy formation, a new inflationary universe scenario, grand unified phase transitions and the early Universe, the generalized second law of thermodynamics, vacuum polarization near black holes, the relativity of vacuum, black hole evaporations and their cosmological consequences, currents in supersymmetric theories, the Kaluza-Klein theories, gauge algebra and quantization, and twistor theory. This volume constitutes the proceedings of the Second Seminar on Quantum Gravity held in Moscow in 1981
On the computation of black hole entropy in loop quantum gravity
International Nuclear Information System (INIS)
Fernando Barbero G, J; Villasenor, Eduardo J S
2009-01-01
We discuss some issues related to the computation of black hole entropy in loop quantum gravity from the novel point of view provided by the recent number-theoretical methods introduced by the authors and their collaborators. In particular we give exact expressions, in the form of integral transforms, for the black hole entropy in terms of the area. We do this by following several approaches based both on our combinatorial techniques and on functional equations similar to those employed by Meissner in his pioneering work on this subject. To put our results in perspective, we compare them with those of Meissner. We will show how our methods confirm some of his findings, extend the validity of others and correct some mistakes. At the end of the paper, we will discuss the delicate issue of the asymptotics of black hole entropy.
Evidence for maximal acceleration and singularity resolution in covariant loop quantum gravity.
Rovelli, Carlo; Vidotto, Francesca
2013-08-30
A simple argument indicates that covariant loop gravity (spin foam 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.
Odintsov, S. D.; Oikonomou, V. K.; Saridakis, Emmanuel N.
2015-12-01
We investigate the realization of two bouncing paradigms, namely of the superbounce and the loop quantum cosmological ekpyrosis, in the framework of various modified gravities. In particular, we focus on the F(R) , F(G) and F(T) gravities, and we reconstruct their specific subclasses which lead to such universe evolutions. These subclasses constitute from power laws, polynomials, or hypergeometric ansatzes, which can be approximated by power laws. The qualitative similarity of the different effective gravities which realize the above two bouncing cosmologies, indicates that a universality might be lying behind the bounce. Finally, performing a linear perturbation analysis, we show that the obtained solutions are conditionally or fully stable.
International Nuclear Information System (INIS)
Giribet, G E
2005-01-01
Claus Kiefer presents his book, Quantum Gravity, with his hope that '[the] book will convince readers of [the] outstanding problem [of unification and quantum gravity] and encourage them to work on its solution'. With this aim, the author presents a clear exposition of the fundamental concepts of gravity and the steps towards the understanding of its quantum aspects. The main part of the text is dedicated to the analysis of standard topics in the formulation of general relativity. An analysis of the Hamiltonian formulation of general relativity and the canonical quantization of gravity is performed in detail. Chapters four, five and eight provide a pedagogical introduction to the basic concepts of gravitational physics. In particular, aspects such as the quantization of constrained systems, the role played by the quadratic constraint, the ADM decomposition, the Wheeler-de Witt equation and the problem of time are treated in an expert and concise way. Moreover, other specific topics, such as the minisuperspace approach and the feasibility of defining extrinsic times for certain models, are discussed as well. The ninth chapter of the book is dedicated to the quantum gravitational aspects of string theory. Here, a minimalistic but clear introduction to string theory is presented, and this is actually done with emphasis on gravity. It is worth mentioning that no hard (nor explicit) computations are presented, even though the exposition covers the main features of the topic. For instance, black hole statistical physics (within the framework of string theory) is developed in a pedagogical and concise way by means of heuristical arguments. As the author asserts in the epilogue, the hope of the book is to give 'some impressions from progress' made in the study of quantum gravity since its beginning, i.e., since the end of 1920s. In my opinion, Kiefer's book does actually achieve this goal and gives an extensive review of the subject. (book review)
International Nuclear Information System (INIS)
Isham, C.
1989-01-01
Gravitational effects are seen as arising from a curvature in spacetime. This must be reconciled with gravity's apparently passive role in quantum theory to achieve a satisfactory quantum theory of gravity. The development of grand unified theories has spurred the search, with forces being of equal strength at a unification energy of 10 15 - 10 18 GeV, with the ''Plank length'', Lp ≅ 10 -35 m. Fundamental principles of general relativity and quantum mechanics are outlined. Gravitons are shown to have spin-0, as mediators of gravitation force in the classical sense or spin-2 which are related to the quantisation of general relativity. Applying the ideas of supersymmetry to gravitation implies partners for the graviton, especially the massless spin 3/2 fermion called a gravitino. The concept of supersymmetric strings is introduced and discussed. (U.K.)
Bojowald, Martin
2008-01-01
Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time. Supplementary material is available for this article at 10.12942/lrr-2008-4.
Directory of Open Access Journals (Sweden)
Bojowald Martin
2008-07-01
Full Text Available Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time.
Directory of Open Access Journals (Sweden)
Bojowald Martin
2005-12-01
Full Text Available Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical space-time inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding space-time is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend space-time beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.
Barbero-Immirzi parameter as a scalar field: K-inflation from loop quantum gravity?
International Nuclear Information System (INIS)
Taveras, Victor; Yunes, Nicolas
2008-01-01
We consider a loop-quantum gravity inspired modification of general relativity, where the Holst action is generalized by making the Barbero-Immirzi (BI) parameter a scalar field, whose value could be dynamically determined. The modified theory leads to a nonzero torsion tensor that corrects the field equations through quadratic first derivatives of the BI field. Such a correction is equivalent to general relativity in the presence of a scalar field with nontrivial kinetic energy. This stress energy of this field is automatically covariantly conserved by its own dynamical equations of motion, thus satisfying the strong equivalence principle. Every general relativistic solution remains a solution to the modified theory for any constant value of the BI field. For arbitrary time-varying BI fields, a study of cosmological solutions reduces the scalar-field stress energy to that of a pressureless perfect fluid in a comoving reference frame, forcing the scale-factor dynamics to be equivalent to those of a stiff equation of state. Upon ultraviolet completion, this model could provide a natural mechanism for k inflation, where the role of the inflaton is played by the BI field and inflation is driven by its nontrivial kinetic energy instead of a potential.
Higher dimensional loop quantum cosmology
International Nuclear Information System (INIS)
Zhang, Xiangdong
2016-01-01
Loop quantum cosmology (LQC) is the symmetric sector of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogeneous cosmological model in n + 1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n + 1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n + 1 dimensional model and the 3 + 1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers the possibility to investigate quantum gravity effects in higher dimensional cosmology. (orig.)
Singularity resolution in quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity program, and is based on an alternative to the Schroedinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute 'singularity resolution' in quantum gravity
Alvarez, Enrique
2004-01-01
Gravitons should have momentum just as photons do; and since graviton momentum would cause compression rather than elongation of spacetime outside of matter; it does not appear that gravitons are compatible with Swartzchild's spacetime curvature. Also, since energy is proportional to mass, and mass is proportional to gravity; the energy of matter is proportional to gravity. The energy of matter could thus contract space within matter; and because of the inter-connectedness of space, cause the...
Energy Technology Data Exchange (ETDEWEB)
Lamon, Raphael
2010-06-29
Quantum gravity is an attempt to unify general relativity with quantum mechanics which are the two highly successful fundamental theories of theoretical physics. The main difficulty in this unification arises from the fact that, while general relativity describes gravity as a macroscopic geometrical theory, quantum mechanics explains microscopic phenomena. As a further complication, not only do both theories describe different scales but also their philosophical ramifications and the mathematics used to describe them differ in a dramatic way. Consequently, one possible starting point of an attempt at a unification is quantum mechanics, i.e. particle physics, and try to incorporate gravitation. This pathway has been chosen by particle physicists which led to string theory. On the other hand, loop quantum gravity (LQG) chooses the other possibility, i.e. it takes the geometrical aspects of gravity seriously and quantizes geometry. The first part of this thesis deals with a generalization of loop quantum cosmology (LQC) to toroidal topologies. LQC is a quantization of homogenous solutions of Einstein's field equations using tools from LQG. First the general concepts of closed topologies is introduced with special emphasis on Thurston's theorem and its consequences. It is shown that new degrees of freedom called Teichmueller parameters come into play and their dynamics can be described by a Hamiltonian. Several numerical solutions for a toroidal universe are presented and discussed. Following the guidelines of LQG this dynamics are rewritten using the Ashtekar variables and numerical solutions are shown. However, in order to find a suitable Hilbert space a canonical transformation must be performed. On the other hand this transformation makes the quantization of geometrical quantities less tractable such that two different ways are presented. It is shown that in both cases the spectrum of such geometrical operators depends on the initial value problem
International Nuclear Information System (INIS)
Lamon, Raphael
2010-01-01
Quantum gravity is an attempt to unify general relativity with quantum mechanics which are the two highly successful fundamental theories of theoretical physics. The main difficulty in this unification arises from the fact that, while general relativity describes gravity as a macroscopic geometrical theory, quantum mechanics explains microscopic phenomena. As a further complication, not only do both theories describe different scales but also their philosophical ramifications and the mathematics used to describe them differ in a dramatic way. Consequently, one possible starting point of an attempt at a unification is quantum mechanics, i.e. particle physics, and try to incorporate gravitation. This pathway has been chosen by particle physicists which led to string theory. On the other hand, loop quantum gravity (LQG) chooses the other possibility, i.e. it takes the geometrical aspects of gravity seriously and quantizes geometry. The first part of this thesis deals with a generalization of loop quantum cosmology (LQC) to toroidal topologies. LQC is a quantization of homogenous solutions of Einstein's field equations using tools from LQG. First the general concepts of closed topologies is introduced with special emphasis on Thurston's theorem and its consequences. It is shown that new degrees of freedom called Teichmueller parameters come into play and their dynamics can be described by a Hamiltonian. Several numerical solutions for a toroidal universe are presented and discussed. Following the guidelines of LQG this dynamics are rewritten using the Ashtekar variables and numerical solutions are shown. However, in order to find a suitable Hilbert space a canonical transformation must be performed. On the other hand this transformation makes the quantization of geometrical quantities less tractable such that two different ways are presented. It is shown that in both cases the spectrum of such geometrical operators depends on the initial value problem. Furthermore, we
de Haro, Jaume; Amorós, Jaume
2018-03-01
We consider the Arnowitt-Deser-Misner formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond general relativity modifying the gravitational sector. Once a preferred slicing, which we choose based on the matter content of the Universe following the spirit of Weyl's postulate, has been fixed, f theories depending on the extrinsic and intrinsic curvature of the slicing are covariant for all the reference frames preserving the foliation; i.e., the constraint and dynamical equations have the same form for all these observers. Moreover, choosing multivalued f functions, bouncing backgrounds emerge in a natural way. In fact, the simplest is the one corresponding to holonomy corrected loop quantum cosmology. The final goal of this work is to provide the equations of perturbations which, unlike the full equations, become gauge invariant in this theory, and apply them to the so-called matter bounce scenario.
Amelino-Camelia, Giovanni
2003-01-01
Comment: 9 pages, LaTex. These notes were prepared while working on an invited contribution to the November 2003 issue of Physics World, which focused on quantum gravity. They intend to give a non-technical introduction (accessible to readers from outside quantum gravity) to "Quantum Gravity Phenomenology"
Perturbations in loop quantum cosmology
International Nuclear Information System (INIS)
Nelson, W; Agullo, I; Ashtekar, A
2014-01-01
The era of precision cosmology has allowed us to accurately determine many important cosmological parameters, in particular via the CMB. Confronting Loop Quantum Cosmology with these observations provides us with a powerful test of the theory. For this to be possible, we need a detailed understanding of the generation and evolution of inhomogeneous perturbations during the early, quantum gravity phase of the universe. Here, we have described how Loop Quantum Cosmology provides a completion of the inflationary paradigm, that is consistent with the observed power spectra of the CMB
Loop quantum cosmology: Recent progress
Indian Academy of Sciences (India)
Aspects of the full theory of loop quantum gravity can be studied in a simpler .... group) 1-forms and vector fields and Λ is an SO(3)-matrix indicating the internal ... are p and c which are related to the more familiar scale factor by the relations.
Induced quantum conformal gravity
International Nuclear Information System (INIS)
Novozhilov, Y.V.; Vassilevich, D.V.
1988-11-01
Quantum gravity is considered as induced by matter degrees of freedom and related to the symmetry breakdown in the low energy region of a non-Abelian gauge theory of fundamental fields. An effective action for quantum conformal gravity is derived where both the gravitational constant and conformal kinetic term are positive. Relation with induced classical gravity is established. (author). 15 refs
International Nuclear Information System (INIS)
Schoutens, K.; van Nieuwenhuizen, P.; State Univ. of New York, Stony Brook, NY
1991-11-01
We briefly review some results in the theory of quantum W 3 gravity in the chiral gauge. We compare them with similar results in the analogous but simpler cases of d = 2 induced gauge theories and d = 2 induced gravity
International Nuclear Information System (INIS)
Vega, H.J. de
1990-01-01
One of the main challenges in theoretical physics today is the unification of all interactions including gravity. At present, string theories appear as the most promising candidates to achieve such a unification. However, gravity has not completely been incorporated in string theory, many technical and conceptual problems remain and a full quantum theory of gravity is still non-existent. Our aim is to properly understand strings in the context of quantum gravity. Attempts towards this are reviewed. (author)
New 'phase' of quantum gravity.
Wang, Charles H-T
2006-12-15
The emergence of loop quantum gravity over the past two decades has stimulated a great resurgence of interest in unifying general relativity and quantum mechanics. Among a number of appealing features of this approach is the intuitive picture of quantum geometry using spin networks and powerful mathematical tools from gauge field theory. However, the present form of loop quantum gravity suffers from a quantum ambiguity, owing to the presence of a free (Barbero-Immirzi) parameter. Following the recent progress on conformal decomposition of gravitational fields, we present a new phase space for general relativity. In addition to spin-gauge symmetry, the new phase space also incorporates conformal symmetry making the description parameter free. The Barbero-Immirzi ambiguity is shown to occur only if the conformal symmetry is gauge fixed prior to quantization. By withholding its full symmetries, the new phase space offers a promising platform for the future development of loop quantum gravity. This paper aims to provide an exposition, at a reduced technical level, of the above theoretical advances and their background developments. Further details are referred to cited references.
Loop quantum cosmology and singularities.
Struyve, Ward
2017-08-15
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.
Flipped spinfoam vertex and loop gravity
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Engle, Jonathan; Pereira, Roberto [CPT, CNRS Case 907, Universite de la Mediterranee, F-13288 Marseille (France); Rovelli, Carlo [CPT, CNRS Case 907, Universite de la Mediterranee, F-13288 Marseille (France)], E-mail: rovelli@cpt.univ-mrs.fr
2008-07-21
We introduce a vertex amplitude for 4d loop quantum gravity. We derive it from a conventional quantization of a Regge discretization of euclidean general relativity. This yields a spinfoam sum that corrects some difficulties of the Barrett-Crane theory. The second class simplicity constraints are imposed weakly, and not strongly as in Barrett-Crane theory. Thanks to a flip in the quantum algebra, the boundary states turn out to match those of SO(3) loop quantum gravity-the two can be identified as eigenstates of the same physical quantities-providing a solution to the problem of connecting the covariant SO(4) spinfoam formalism with the canonical SO(3) spin-network one. The vertex amplitude is SO(3) and SO(4)-covariant. It rectifies the triviality of the intertwiner dependence of the Barrett-Crane vertex, which is responsible for its failure to yield the correct propagator tensorial structure. The construction provides also an independent derivation of the kinematics of loop quantum gravity and of the result that geometry is quantized.
Quantum gravity and quantum cosmology
Papantonopoulos, Lefteris; Siopsis, George; Tsamis, Nikos
2013-01-01
Quantum gravity has developed into a fast-growing subject in physics and it is expected that probing the high-energy and high-curvature regimes of gravitating systems will shed some light on how to eventually achieve an ultraviolet complete quantum theory of gravity. Such a theory would provide the much needed information about fundamental problems of classical gravity, such as the initial big-bang singularity, the cosmological constant problem, Planck scale physics and the early-time inflationary evolution of our Universe. While in the first part of this book concepts of quantum gravity are introduced and approached from different angles, the second part discusses these theories in connection with cosmological models and observations, thereby exploring which types of signatures of modern and mathematically rigorous frameworks can be detected by experiments. The third and final part briefly reviews the observational status of dark matter and dark energy, and introduces alternative cosmological models. ...
One-loop pure-gravity contributions to a black-hole geometry with quantum fluctuations
International Nuclear Information System (INIS)
Peterkin, R.E.
1985-01-01
A black-hole is unstable to zero-means quantum fluctuations of its metric. These quantum fluctuations break the degeneracy of the locations of the event-horizon and the apparent-horizon for a Schwarzschild black-hole. The path-integral in spacetime with Euclidean signature is calculated from the ADM action to second order in the variations. It is found that the second-order term of this perturbation expansion gives the same contribution to the path-integral as the zeroth-order term for these particular fluctuations. A surface near the black-hole event-horizon is correctly treated as a boundary, and this surface makes a substantial contribution to the path-integral. One may treat this path-integral as a partition function and calculate thermodynamic quantities. The entropy of this black-hole, for example, is found to be close to the accepted value of A/4h, where A is the black-hole surface area. The meaning of these particular fluctuations and the importance of the boundary near the event-horizon is discussed
International Nuclear Information System (INIS)
Williams, Ruth M
2006-01-01
A review is given of a number of approaches to discrete quantum gravity, with a restriction to those likely to be relevant in four dimensions. This paper is dedicated to Rafael Sorkin on the occasion of his sixtieth birthday
Directory of Open Access Journals (Sweden)
J. Ambjørn
1995-07-01
Full Text Available The 2-point function is the natural object in quantum gravity for extracting critical behavior: The exponential falloff of the 2-point function with geodesic distance determines the fractal dimension dH of space-time. The integral of the 2-point function determines the entropy exponent γ, i.e. the fractal structure related to baby universes, while the short distance behavior of the 2-point function connects γ and dH by a quantum gravity version of Fisher's scaling relation. We verify this behavior in the case of 2d gravity by explicit calculation.
BOOK REVIEW: Quantum Gravity: third edition Quantum Gravity: third edition
Rovelli, Carlo
2012-09-01
The request by Classical and Quantum Gravity to review the third edition of Claus Kiefer's 'Quantum Gravity' puts me in a slightly awkward position. This is a remarkably good book, which every person working in quantum gravity should have on the shelf. But in my opinion quantum gravity has undergone some dramatic advances in the last few years, of which the book makes no mention. Perhaps the omission only attests to the current vitality of the field, where progress is happening fast, but it is strange for me to review a thoughtful, knowledgeable and comprehensive book on my own field of research, which ignores what I myself consider the most interesting results to date. Kiefer's book is unique as a broad introduction and a reliable overview of quantum gravity. There are numerous books in the field which (often notwithstanding titles) focus on a single approach. There are also countless conference proceedings and article collections aiming to be encyclopaedic, but offering disorganized patchworks. Kiefer's book is a careful and thoughtful presentation of all aspects of the immense problem of quantum gravity. Kiefer is very learned, and brings together three rare qualities: he is pedagogical, he is capable of simplifying matter to the bones and capturing the essential, and he offers a serious and balanced evaluation of views and ideas. In a fractured field based on a major problem that does not yet have a solution, these qualities are precious. I recommend Kiefer's book to my students entering the field: to work in quantum gravity one needs a vast amount of technical knowledge as well as a grasp of different ideas, and Kiefer's book offers this with remarkable clarity. This novel third edition simplifies and improves the presentation of several topics, but also adds very valuable new material on quantum gravity phenomenology, loop quantum cosmology, asymptotic safety, Horava-Lifshitz gravity, analogue gravity, the holographic principle, and more. This is a testament
Directory of Open Access Journals (Sweden)
Cahill R. T.
2015-10-01
Full Text Available A new quantum gravity experiment is reported with the data confirming the generali- sation of the Schrödinger equation to include the interaction of the wave function with dynamical space. Dynamical space turbulence, via this interaction process, raises and lowers the energy of the electron wave function, which is detected by observing conse- quent variations in the electron quantum barrier tunnelling rate in reverse-biased Zener diodes. This process has previously been reported and enabled the measurement of the speed of the dynamical space flow, which is consistent with numerous other detection experiments. The interaction process is dependent on the angle between the dynamical space flow velocity and the direction of the electron flow in the diode, and this depen- dence is experimentally demonstrated. This interaction process explains gravity as an emergent quantum process, so unifying quantum phenomena and gravity. Gravitational waves are easily detected.
Quantum Gravity Effects in Cosmology
Directory of Open Access Journals (Sweden)
Gu Je-An
2018-01-01
Full Text Available Within the geometrodynamic approach to quantum cosmology, we studied the quantum gravity effects in cosmology. The Gibbons-Hawking temperature is corrected by quantum gravity due to spacetime fluctuations and the power spectrum as well as any probe field will experience the effective temperature, a quantum gravity effect.
On Spectral Triples in Quantum Gravity I
DEFF Research Database (Denmark)
Aastrup, Johannes; M. Grimstrup, Jesper; Nest, Ryszard
2009-01-01
This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator....... The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly......, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations...
Quantum space loop quantum gravity and the search for the structure of space, time, and the universe
Baggott, Jim
2018-01-01
Today we are blessed with two extraordinarily successful theories of physics. The first is Albert Einstein's general theory of relativity, which describes the large-scale behaviour of matter in a curved spacetime. This theory is the basis for the standard model of big bang cosmology. The discovery of gravitational waves at the LIGO observatory in the US (and then Virgo, in Italy) is only the most recent of this theory's many triumphs. The second is quantum mechanics. This theory describes the properties and behaviour of matter and radiation at their smallest scales. It is the basis for the standard model of particle physics, which builds up all the visible constituents of the universe out of collections of quarks, electrons and force-carrying particles such as photons. The discovery of the Higgs boson at CERN in Geneva is only the most recent of this theory's many triumphs. But, while they are both highly successful, these two structures leave a lot of important questions unanswered. They are also based on ...
International Nuclear Information System (INIS)
Husain, Viqar
2008-01-01
There has been a flurry of books on quantum gravity in the past few years. The first edition of Kiefer's book appeared in 2004, about the same time as Carlo Rovelli's book with the same title. This was soon followed by Thomas Thiemann's 'Modern Canonical Quantum General Relativity'. Although the main focus of each of these books is non-perturbative and non-string approaches to the quantization of general relativity, they are quite orthogonal in temperament, style, subject matter and mathematical detail. Rovelli and Thiemann focus primarily on loop quantum gravity (LQG), whereas Kiefer attempts a broader introduction and review of the subject that includes chapters on string theory and decoherence. Kiefer's second edition attempts an even wider and somewhat ambitious sweep with 'new sections on asymptotic safety, dynamical triangulation, primordial black holes, the information-loss problem, loop quantum cosmology, and other topics'. The presentation of these current topics is necessarily brief given the size of the book, but effective in encapsulating the main ideas in some cases. For instance the few pages devoted to loop quantum cosmology describe how the mini-superspace reduction of the quantum Hamiltonian constraint of LQG becomes a difference equation, whereas the discussion of 'dynamical triangulations', an approach to defining a discretized Lorentzian path integral for quantum gravity, is less detailed. The first few chapters of the book provide, in a roughly historical sequence, the covariant and canonical metric variable approach to the subject developed in the 1960s and 70s. The problem(s) of time in quantum gravity are nicely summarized in the chapter on quantum geometrodynamics, followed by a detailed and effective introduction of the WKB approach and the semi-classical approximation. These topics form the traditional core of the subject. The next three chapters cover LQG, quantization of black holes, and quantum cosmology. Of these the chapter on LQG is
Discrete Lorentzian quantum gravity
Loll, R.
2000-01-01
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and that therefore also the lattice theory must be formulated
International Nuclear Information System (INIS)
Meszaros, A.
1984-05-01
In case the graviton has a very small non-zero mass, the existence of six additional massive gravitons with very big masses leads to a finite quantum gravity. There is an acausal behaviour on the scales that is determined by the masses of additional gravitons. (author)
International Nuclear Information System (INIS)
Williams, J.W.
1992-01-01
After a brief introduction to Regge calculus, some examples of its application is quantum gravity are described in this paper. In particular, the earliest such application, by Ponzano and Regge, is discussed in some detail and it is shown how this leads naturally to current work on invariants of three-manifolds
International Nuclear Information System (INIS)
Hartle, J.B.
1985-01-01
Simplicial approximation and the ideas associated with the Regge calculus provide a concrete way of implementing a sum over histories formulation of quantum gravity. A simplicial geometry is made up of flat simplices joined together in a prescribed way together with an assignment of lengths to their edges. A sum over simplicial geometries is a sum over the different ways the simplices can be joined together with an integral over their edge lengths. The construction of the simplicial Euclidean action for this approach to quantum general relativity is illustrated. The recovery of the diffeomorphism group in the continuum limit is discussed. Some possible classes of simplicial complexes with which to define a sum over topologies are described. In two dimensional quantum gravity it is argued that a reasonable class is the class of pseudomanifolds
Stepping out of homogeneity in loop quantum cosmology
International Nuclear Information System (INIS)
Rovelli, Carlo; Vidotto, Francesca
2008-01-01
We explore the extension of quantum cosmology outside the homogeneous approximation using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for describing general fluctuations of quantum geometry near the initial singularity. We show that the dynamical structure of the model reduces to that of loop quantum cosmology in the Born-Oppenheimer approximation. This result corroborates the assumptions that ground loop cosmology sheds some light on the physical and mathematical relation between loop cosmology and full loop quantum gravity, and on the nature of the cosmological approximation. Finally, we show that the non-graph-changing Hamiltonian constraint considered in the context of algebraic quantum gravity provides a viable effective dynamics within this approximation
Gomberoff, Andres
2006-01-01
The 2002 Pan-American Advanced Studies Institute School on Quantum Gravity was held at the Centro de Estudios Cientificos (CECS),Valdivia, Chile, January 4-14, 2002. The school featured lectures by ten speakers, and was attended by nearly 70 students from over 14 countries. A primary goal was to foster interaction and communication between participants from different cultures, both in the layman’s sense of the term and in terms of approaches to quantum gravity. We hope that the links formed by students and the school will persist throughout their professional lives, continuing to promote interaction and the essential exchange of ideas that drives research forward. This volume contains improved and updated versions of the lectures given at the School. It has been prepared both as a reminder for the participants, and so that these pedagogical introductions can be made available to others who were unable to attend. We expect them to serve students of all ages well.
International Nuclear Information System (INIS)
Rumpf, H.
1987-01-01
We begin with a naive application of the Parisi-Wu scheme to linearized gravity. This will lead into trouble as one peculiarity of the full theory, the indefiniteness of the Euclidean action, shows up already at this level. After discussing some proposals to overcome this problem, Minkowski space stochastic quantization will be introduced. This will still not result in an acceptable quantum theory of linearized gravity, as the Feynman propagator turns out to be non-causal. This defect will be remedied only after a careful analysis of general covariance in stochastic quantization has been performed. The analysis requires the notion of a metric on the manifold of metrics, and a natural candidate for this is singled out. With this a consistent stochastic quantization of Einstein gravity becomes possible. It is even possible, at least perturbatively, to return to the Euclidean regime. 25 refs. (Author)
Topics in Theories of Quantum Gravity
International Nuclear Information System (INIS)
Perelstein, M.
2005-01-01
In this thesis, the author addresses several issues involving gravity. The first half of the thesis is devoted to studying quantum properties of Einstein gravity and its supersymmetric extensions in the perturbative regime. String theory suggests that perturbative scattering amplitudes in the theories of gravity are related to the amplitudes in gauge theories. This connection has been studied at classical (tree) level by Kawai, Lewellen and Tye. Here, they will explore the relationship between gravity and gauge theory at quantum (loop) level. This relationship, together with the cut-based approach to computing loop amplitudes, allow us to obtain new non-trivial results for quantum gravity. IN particular, they present two infinite sequences of one-loop n-graviton scattering amplitudes: the maximally helicity violating amplitudes in N = 8 supergravity, and the ''all-plus'' helicity amplitudes in Einstein gravity with any minimally coupled massless matter content. The results for n (le) 6 will be obtained by an explicit calculation, while those for n > 6 is inferred from the soft and collinear properties of the amplitudes. They also present an explicit expression for the two-loop contribution to the four-particle scattering amplitude in N = 8 supergravity, and observe a simple relation between this result and its counterpart in N = 4 super-Yang-Mills theory. Furthermore, the simple structure of the two-particle unitarity cuts in these theories suggests that similar relations exist to all loop orders. If this is the case, the first ultraviolet divergence in N = 8 supergravity should appear at five loops, contrary to the earlier expectation of a three-loop counterterm
Topics in Theories of Quantum Gravity
Energy Technology Data Exchange (ETDEWEB)
Perelstein, M.
2005-04-05
In this thesis, the author addresses several issues involving gravity. The first half of the thesis is devoted to studying quantum properties of Einstein gravity and its supersymmetric extensions in the perturbative regime. String theory suggests that perturbative scattering amplitudes in the theories of gravity are related to the amplitudes in gauge theories. This connection has been studied at classical (tree) level by Kawai, Lewellen and Tye. Here, they will explore the relationship between gravity and gauge theory at quantum (loop) level. This relationship, together with the cut-based approach to computing loop amplitudes, allow us to obtain new non-trivial results for quantum gravity. IN particular, they present two infinite sequences of one-loop n-graviton scattering amplitudes: the maximally helicity violating amplitudes in N = 8 supergravity, and the ''all-plus'' helicity amplitudes in Einstein gravity with any minimally coupled massless matter content. The results for n {le} 6 will be obtained by an explicit calculation, while those for n > 6 is inferred from the soft and collinear properties of the amplitudes. They also present an explicit expression for the two-loop contribution to the four-particle scattering amplitude in N = 8 supergravity, and observe a simple relation between this result and its counterpart in N = 4 super-Yang-Mills theory. Furthermore, the simple structure of the two-particle unitarity cuts in these theories suggests that similar relations exist to all loop orders. If this is the case, the first ultraviolet divergence in N = 8 supergravity should appear at five loops, contrary to the earlier expectation of a three-loop counterterm.
Towards the map of quantum gravity
Mielczarek, Jakub; Trześniewski, Tomasz
2018-06-01
In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Hořava-Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.
Is quantum gravity unpredictable
International Nuclear Information System (INIS)
Gross, D.J.
1984-01-01
An investigation of Hawking's proposal that the inclusion of topologically non-trivial manifolds in the functional integral of quantum gravity leads to the loss of quantum coherence is carried out. We discuss some of the problems associated with Hawking's Dollar-matrix theory, including the breakdown of the connection between symmetry principles and conservation laws. It is proposed to use Kaluza-Klein theories to study this issue, since these theories contain well-defined euclidean instantons. These can be used to perform explicit semiclassical calculations of the effects of space-time foam. A general method is presented for constructing Kaluza-Klein instantons based on solutions of ordinary Yang-Mills theory. It is argued that none of these will lead to a breakdown of quantum mechanics. The physical effects of space-time foam are discussed in some detail using explicit instantons of a four-dimensional Kaluza-Klein theory. (orig.)
Spontaneous compactification in 2D induced quantum gravity
International Nuclear Information System (INIS)
Elizalde, E.; Odintsov, S.D.
1992-01-01
In this paper spontaneous compactification - on a R 1 x S 1 background - in 2D induced quantum gravity (considered as a toy model for more fundamental quantum gravity) is analyzed in the gauge-independent effective action formalism. It is shown that such compactification is stable, in contradistinction to multidimensional quantum gravity on a R degrees x S 1 (D-> 2) background - which is known to be one-loop unstable
A Immirzi-like parameter for 3D quantum gravity
International Nuclear Information System (INIS)
Bonzom, Valentin; Livine, Etera R
2008-01-01
We study an Immirzi-like ambiguity in three-dimensional quantum gravity. It shares some features with the Immirzi parameter of four-dimensional loop quantum gravity: it does not affect the equations of motion, but modifies the Poisson brackets and the constraint algebra at the canonical level. We focus on the length operator and show how to define it through non-commuting fluxes. We compute its spectrum and show the effect of this Immirzi-like ambiguity. Finally, we extend these considerations to 4D gravity and show how the different topological modifications of the action affect the canonical structure of loop quantum gravity
Loop Transfer Matrix and Loop Quantum Mechanics
International Nuclear Information System (INIS)
Savvidy, George K.
2000-01-01
The gonihedric model of random surfaces on a 3d Euclidean lattice has equivalent representation in terms of transfer matrix K(Q i ,Q f ), which describes the propagation of loops Q. We extend the previous construction of the loop transfer matrix to the case of nonzero self-intersection coupling constant κ. We introduce the loop generalization of Fourier transformation which allows to diagonalize transfer matrices, that depend on symmetric difference of loops only and express all eigenvalues of 3d loop transfer matrix through the correlation functions of the corresponding 2d statistical system. The loop Fourier transformation allows to carry out the analogy with quantum mechanics of point particles, to introduce conjugate loop momentum P and to define loop quantum mechanics. We also consider transfer matrix on 4d lattice which describes propagation of memebranes. This transfer matrix can also be diagonalized by using the generalized Fourier transformation, and all its eigenvalues are equal to the correlation functions of the corresponding 3d statistical system. In particular the free energy of the 4d membrane system is equal to the free energy of 3d gonihedric system of loops and is equal to the free energy of 2d Ising model. (author)
Covariant entropy bound and loop quantum cosmology
International Nuclear Information System (INIS)
Ashtekar, Abhay; Wilson-Ewing, Edward
2008-01-01
We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound is violated near the big bang. However, the hope has been that quantum gravity effects would intervene and protect it. Loop quantum cosmology provides a near ideal setting for investigating this issue. For, on the one hand, quantum geometry effects resolve the singularity and, on the other hand, the wave function is sharply peaked at a quantum corrected but smooth geometry, which can supply the structure needed to test the bound. We find that the bound is respected. We suggest that the bound need not be an essential ingredient for a quantum gravity theory but may emerge from it under suitable circumstances.
Martinetti, P.; Wallet, J.-C.; Amelino-Camelia, G.
2015-08-01
The conference Conceptual and Technical Challenges for Quantum Gravity at Sapienza University of Rome, from 8 to 12 September 2014, has provided a beautiful opportunity for an encounter between different approaches and different perspectives on the quantum-gravity problem. It contributed to a higher level of shared knowledge among the quantum-gravity communities pursuing each specific research program. There were plenary talks on many different approaches, including in particular string theory, loop quantum gravity, spacetime noncommutativity, causal dynamical triangulations, asymptotic safety and causal sets. Contributions from the perspective of philosophy of science were also welcomed. In addition several parallel sessions were organized. The present volume collects contributions from the Noncommutative Geometry and Quantum Gravity parallel session4, with additional invited contributions from specialists in the field. Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics: • from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and string theory, • from early considerations on UV-divergencies in quantum field theory to recent models of gauge theories on noncommutative spacetime, • from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. This volume provides an overview of these various topics, interesting for the specialist as well as accessible to the newcomer. 4partially funded by CNRS PEPS /PTI ''Metric aspect of noncommutative geometry: from Monge to Higgs''
Intersecting Quantum Gravity with Noncommutative Geometry - a Review
Directory of Open Access Journals (Sweden)
Johannes Aastrup
2012-03-01
Full Text Available We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a natural class of semiclassical states which entail emerging fermionic degrees of freedom. In the particular semiclassical approximation where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. We end the paper with an extended outlook section.
Is there a quantum theory of gravity
International Nuclear Information System (INIS)
Strominger, A.
1984-01-01
The paper concerns attempts to construct a unitary, renormalizable quantum field theory of gravity. Renormalizability and unitarity in quantum gravity; the 1/N expansion; 1/D expansions; and quantum gravity and particle physics; are all discussed. (U.K.)
New Spin Foam Models of Quantum Gravity
Miković, A.
We give a brief and a critical review of the Barret-Crane spin foam models of quantum gravity. Then we describe two new spin foam models which are obtained by direct quantization of General Relativity and do not have some of the drawbacks of the Barret-Crane models. These are the model of spin foam invariants for the embedded spin networks in loop quantum gravity and the spin foam model based on the integration of the tetrads in the path integral for the Palatini action.
Expectation values in quantum gravity
International Nuclear Information System (INIS)
Jordan, R.D.
1986-01-01
The purpose of this dissertation is to develop new methods for calculating expectation values of field operators, in situations where particle creation is important. The goal is to apply these techniques to quantum gravity, to see if the initial singularity in the universe might be avoided in the quantum theory. Standard effective action theory is modified to produce effective field equations satisfied by the expectation value of the field in an in state, as opposed to the usual in-out amplitude. Diagrammatic rules are found for calculation of the new field equations, and are used to show that the equations are real and causal up to two loop order. The theory also provides a simple check of unitarity, which is carried out, again up to two loops. Just as the standard effective field equations can be derived by analytic continuation from a theory defined in Euclidean space, so can the modified equations be obtained from a modified contour rotation of the Euclidean theory. This result is used to prove a recent conjecture which yields a simple rule for finding the real, causal equations. The new formalism is applied to two gravitational systems. First, the stability of flat space time is studied by finding the equation satisfied by small perturbations of Minkowski space
Fixed points of quantum gravity
Litim, D F
2003-01-01
Euclidean quantum gravity is studied with renormalisation group methods. Analytical results for a non-trivial ultraviolet fixed point are found for arbitrary dimensions and gauge fixing parameter in the Einstein-Hilbert truncation. Implications for quantum gravity in four dimensions are discussed.
Renormalisation in perturbative quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Rodigast, Andreas
2012-07-02
In this thesis, we derive the gravitational one-loop corrections to the propagators and interactions of the Standard Model field. We consider a higher dimensional brane world scenario: Here, gravitons can propagate in the whole D dimensional space-time whereas the matter fields are confined to a d dimensional sub-manifold (brane). In order to determine the divergent part of the one-loop diagrams, we develop a new regularisation scheme which is both sensitive for polynomial divergences and respects the Ward identities of the Yang-Mills theory. We calculate the gravitational contributions to the {beta} functions of non-Abelian gauge theories, the quartic scalar self-interaction and the Yukawa coupling between scalars and fermions. In the physically interesting case of a four dimensional matter brane, the gravitational contributions to the running of the Yang-Mills coupling constant vanish. The leading contributions to the other two couplings are positive. These results do not depend on the number of extra dimensions. We further compute the gravitationally induced one-loop counterterms with higher covariant derivatives for scalars, Dirac fermions and gauge bosons. In is shown that these counterterms do not coincide with the higher derivative terms in the Lee-Wick standard model. A possible connection between quantum gravity and the latter cannot be inferred.
Einstein gravity emerging from quantum weyl gravity
International Nuclear Information System (INIS)
Zee, A.
1983-01-01
We advocate a conformal invariant world described by the sum of the Weyl, Dirac, and Yang-Mills action. Quantum fluctuations bring back Einstein gravity so that the long-distance phenomenology is as observed. Formulas for the induced Newton's constant and Eddington's constant are derived in quantized Weyl gravity. We show that the analogue of the trace anomaly for the Weyl action is structurally similar to that for the Yang-Mills action
Quantum Gravity (Cambridge Monographs on Mathematical Physics)
International Nuclear Information System (INIS)
Kiefer, C
2005-01-01
The most difficult unsolved problem in fundamental theoretical physics is the consistent implementation of the gravitational interaction into a quantum framework, which would lead to a theory of quantum gravity. Although a final answer is still pending, several promising attempts do exist. Despite the general title, this book is about one of them - loop quantum gravity. This approach proceeds from the idea that a direct quantization of Einstein's theory of general relativity is possible. In contrast to string theory, it presupposes that the unification of all interactions is not needed as a prerequisite for quantum gravity. Usually one divides theories of quantum general relativity into covariant and canonical approaches. Covariant theories employ four-dimensional concepts in its formulation, one example being the path integral approach. Canonical theories start from a classical Hamiltonian version of the theory in which spacetime is foliated into spacelike hypersurfaces. Loop quantum gravity is a variant of the canonical approach, the oldest being quantum geometrodynamics where the fundamental configuration variable is the three-metric. Loop quantum gravity has developed from a new choice of canonical variables introduced by Abhay Ashtekar in 1986, the new configuration variable being a connection defined on a three-manifold. Instead of the connection itself, the loop approach employs a non-local version in which the connection is integrated over closed loops. This is similar to the Wilson loops used in gauge theories. Carlo Rovelli is one of the pioneers of loop quantum gravity which he started to develop with Lee Smolin in two papers written in 1988 and 1990. In his book, he presents a comprehensive and competent overview of this approach and provides at the same time the necessary technical background in order to make the treatment self-contained. In fact, half of the book is devoted to 'preparations' giving a detailed account of Hamiltonian mechanics, quantum
Quantum gravity from noncommutative spacetime
International Nuclear Information System (INIS)
Lee, Jungjai; Yang, Hyunseok
2014-01-01
We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.
Quantum gravity from noncommutative spacetime
Energy Technology Data Exchange (ETDEWEB)
Lee, Jungjai [Daejin University, Pocheon (Korea, Republic of); Yang, Hyunseok [Korea Institute for Advanced Study, Seoul (Korea, Republic of)
2014-12-15
We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.
Gravity as Quantum Entanglement Force
Lee, Jae-Weon; Kim, Hyeong-Chan; Lee, Jungjai
2010-01-01
We conjecture that the total quantum entanglement of matter and vacuum in the universe tends to increase with time, like entropy, and that an effective force is associated with this tendency. We also suggest that gravity and dark energy are types of quantum entanglement forces, similar to Verlinde's entropic force, and give holographic dark energy with an equation of state comparable to current observational data. This connection between quantum entanglement and gravity could give some new in...
International Nuclear Information System (INIS)
Pope, C.N.
1980-02-01
The material contained in this thesis is concerned with the functional integral approach to the quantum theory of gravity. It seems to be necessary to work with metrics of positive definite signature (Euclidean metrics) and then analytically continue the result back to the Lorentzian regime. The dominant contributions to the functional integral come from metrics which are stationary points of the action, i.e. classical solutions of the Euclideanized Einstein equations. These are known as Gravitational Instantons. Boundary conditions have to be placed upon the metrics included in the functional integral, and these are determined by the physical problem being considered. Three types of boundary condition have arisen in this context, corresponding to (i) zero temperature physics, and the calculation of particle scattering amplitudes, (ii) finite temperature effects, such as black hole radiance, and (iii) the study of the structure of the gravitational vacuum on Planck length scales. Instantons in the first category are asymptotically flat in all four directions, those in the second are asymptotically flat in three directions and periodic in the fourth, and those which arise in studying the gravitational vacuum are compact without boundaries. Much of the thesis is concerned with considering these various kinds of instanton, and particularly with the effects of their non-trivial topology. One way in which this can be investigated is by means of the various topological index theorems, and these are applied to a variety of situations. Self-dual metrics seem to have particular significance in quantum gravity, and they are discussed in detail. Finally, some recent work on the calculation of the propagation of particles in the gravitational vacuum is described. (author)
International Nuclear Information System (INIS)
Jones, K.R.W.
1995-01-01
We develop a nonlinear quantum theory of Newtonian gravity consistent with an objective interpretation of the wavefunction. Inspired by the ideas of Schroedinger, and Bell, we seek a dimensional reduction procedure to map complex wavefunctions in configuration space onto a family of observable fields in space-time. Consideration of quasi-classical conservation laws selects the reduced one-body quantities as the basis for an explicit quasi-classical coarse-graining. These we interpret as describing the objective reality of the laboratory. Thereafter, we examine what may stand in the role of the usual Copenhagen observer to localise this quantity against macroscopic dispersion. Only a tiny change is needed, via a generically attractive self-potential. A nonlinear treatment of gravitational self-energy is thus advanced. This term sets a scale for all wavepackets. The Newtonian cosmology is thus closed, without need of an external observer. Finally, the concept of quantisation is re-interpreted as a nonlinear eigenvalue problem. To illustrate, we exhibit an elementary family of gravitationally self-bound solitary waves. Contrasting this theory with its canonically quantised analogue, we find that the given interpretation is empirically distinguishable, in principle. This result encourages deeper study of nonlinear field theories as a testable alternative to canonically quantised gravity. (author). 46 refs., 5 figs
Nonperturbative quantum gravity
International Nuclear Information System (INIS)
Ambjørn, J.; Görlich, A.; Jurkiewicz, J.; Loll, R.
2012-01-01
Asymptotic safety describes a scenario in which general relativity can be quantized as a conventional field theory, despite being nonrenormalizable when expanding it around a fixed background geometry. It is formulated in the framework of the Wilsonian renormalization group and relies crucially on the existence of an ultraviolet fixed point, for which evidence has been found using renormalization group equations in the continuum. “Causal Dynamical Triangulations” (CDT) is a concrete research program to obtain a nonperturbative quantum field theory of gravity via a lattice regularization, and represented as a sum over spacetime histories. In the Wilsonian spirit one can use this formulation to try to locate fixed points of the lattice theory and thereby provide independent, nonperturbative evidence for the existence of a UV fixed point. We describe the formalism of CDT, its phase diagram, possible fixed points and the “quantum geometries” which emerge in the different phases. We also argue that the formalism may be able to describe a more general class of Hořava–Lifshitz gravitational models.
Natural inflation and quantum gravity.
de la Fuente, Anton; Saraswat, Prashant; Sundrum, Raman
2015-04-17
Cosmic inflation provides an attractive framework for understanding the early Universe and the cosmic microwave background. It can readily involve energies close to the scale at which quantum gravity effects become important. General considerations of black hole quantum mechanics suggest nontrivial constraints on any effective field theory model of inflation that emerges as a low-energy limit of quantum gravity, in particular, the constraint of the weak gravity conjecture. We show that higher-dimensional gauge and gravitational dynamics can elegantly satisfy these constraints and lead to a viable, theoretically controlled and predictive class of natural inflation models.
Time and a physical Hamiltonian for quantum gravity.
Husain, Viqar; Pawłowski, Tomasz
2012-04-06
We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. © 2012 American Physical Society
Loop quantum cosmology: a status report
International Nuclear Information System (INIS)
Ashtekar, Abhay; Singh, Parampreet
2011-01-01
Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity (LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of LQG. In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low spacetime curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction. In cosmological models, while Einstein's equations hold to an excellent degree of approximation at low curvature, they undergo major modifications in the Planck regime: for matter satisfying the usual energy conditions, any time a curvature invariant grows to the Planck scale, quantum geometry effects dilute it, thereby resolving singularities of general relativity. Quantum geometry corrections become more sophisticated as the models become richer. In particular, in anisotropic models, there are significant changes in the dynamics of shear potentials which tame their singular behavior in striking contrast to older results on anisotropies in bouncing models. Once singularities are resolved, the conceptual paradigm of cosmology changes and one has to revisit many of the standard issues-e.g. the 'horizon problem'-from a new perspective. Such conceptual issues as well as potential observational consequences of the new Planck scale physics are being explored, especially within the inflationary paradigm. These considerations have given rise to a burst of activity in LQC in recent years, with contributions from quantum gravity experts, mathematical physicists and cosmologists. The goal of this review is to provide an overview of the current state of the art in LQC for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general and cosmologists who wish to apply LQC to probe modifications in the standard paradigm of the early universe. In this review, effort has been made to
Infinite degeneracy of states in quantum gravity
International Nuclear Information System (INIS)
Hackett, Jonathan; Wan Yidun
2011-01-01
The setting of Braided Ribbon Networks is used to present a general result in spin-networks embedded in manifolds: the existence of an infinite number of species of conserved quantities. Restricted to three-valent networks the number of such conserved quantities in a given network is shown to be determined by the number of nodes in the network. The implication of these conserved quantities is discussed in the context of Loop Quantum Gravity.
Effective action in multidimensional quantum gravity, and spontaneous compactification
International Nuclear Information System (INIS)
Bagrov, V.G.; Bukhbinder, I.L.; Odintsov, S.D.
1987-01-01
The one-loop effective action (Casimir energy) is obtained for a special form of model of multidimensional quantum gravity and for several variants of d-dimensional quantum R 2 -gravity on the space M 4 x T/sub d//sub -4/, where M 4 is Minkowski space and T/sub d//sub -4/ is the (d-4)-dimensional torus. It is shown that the effective action of the model of multidimensional quantum gravity and R 2 -gravity without the cosmological term and Einstein term leads to instability of the classical compactification. By a numerical calculation it is demonstrated that the effective action of five-dimensional R 2 -gravity with the cosmological term admits a self-consistent spontaneous compactification. The one-loop effective action is also found for five-dimensional Einstein gravity with antisymmetric torsion on the space M 4 x S 1 (S 1 is the one-dimensional sphere)
A quantum Goldman bracket in (2 + 1) quantum gravity
International Nuclear Information System (INIS)
Nelson, J E; Picken, R F
2008-01-01
In the context of quantum gravity for spacetimes of dimension (2 + 1), we describe progress in the construction of a quantum Goldman bracket for intersecting loops on surfaces. Using piecewise linear paths in R 2 (representing loops on the spatial manifold, i.e. the torus) and a quantum connection with noncommuting components, we review how holonomies and Wilson loops for two homotopic paths are related by phases in terms of the signed area between them. Paths rerouted at intersection points with other paths occur on the rhs of the Goldman bracket. To better understand their nature we introduce the concept of integer points inside the parallelogram spanned by two intersecting paths, and show that the rerouted paths must necessarily pass through these integer points
Gravity loop corrections to the standard model Higgs in Einstein gravity
International Nuclear Information System (INIS)
Yugo Abe; Masaatsu Horikoshi; Takeo Inami
2016-01-01
We study one-loop quantum gravity corrections to the standard model Higgs potential V(φ) à la Coleman-Weinberg and examine the stability question of V(φ) in the energy region of Planck mass scale, μ ≃ M_P_l (M_P_l = 1.22x10"1"9 GeV). We calculate the gravity one-loop corrections to V(φ) in Einstein gravity by using the momentum cut-off Λ. We have found that even small gravity corrections compete with the standard model term of V(φ) and affect the stability argument of the latter part alone. This is because the latter part is nearly zero in the energy region of M_P_l. (author)
Dark Matter in Quantum Gravity
Calmet, Xavier; Latosh, Boris
2018-01-01
We show that quantum gravity, whatever its ultra-violet completion might be, could account for dark matter. Indeed, besides the massless gravitational field recently observed in the form of gravitational waves, the spectrum of quantum gravity contains two massive fields respectively of spin 2 and spin 0. If these fields are long-lived, they could easily account for dark matter. In that case, dark matter would be very light and only gravitationally coupled to the standard model particles.
International Nuclear Information System (INIS)
Au, G.
1995-03-01
One of the greatest challenges facing theoretical physics lies in reconciling Einstein's classical theory of gravity - general relativity -with quantum field theory. Although both theories have been experimentally supported in their respective regimes, they are as compatible as a square peg and a round hole. This article summarises the current status of the superstring approach to the problem, the status of the Ashtekar program, and problem of time in quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Au, G
1995-03-01
One of the greatest challenges facing theoretical physics lies in reconciling Einstein`s classical theory of gravity - general relativity -with quantum field theory. Although both theories have been experimentally supported in their respective regimes, they are as compatible as a square peg and a round hole. This article summarises the current status of the superstring approach to the problem, the status of the Ashtekar program, and problem of time in quantum gravity.
Manifestations of quantum gravity in scalar QED phenomena
International Nuclear Information System (INIS)
Elizalde, E.; Odintsov, S.D.; Romeo, A.
1995-01-01
Quantum gravitational corrections to the effective potential, at the one-loop level and in the leading-log approximation, for scalar quantum electrodynamics with higher-derivative gravity, which is taken as an effective theory for quantum gravity (QG), are calculated. We point out the appearance of relevant phenomena caused by quantum gravity, such as dimensional transmutation, QG-driven instabilities of the potential, QG corrections to scalar-to-vector mass ratios, and curvature-induced phase transitions, whose existence is shown by means of analytical and numerical study
Quantum Gravity in Two Dimensions
DEFF Research Database (Denmark)
Ipsen, Asger Cronberg
The topic of this thesis is quantum gravity in 1 + 1 dimensions. We will focus on two formalisms, namely Causal Dynamical Triangulations (CDT) and Dy- namical Triangulations (DT). Both theories regularize the gravity path integral as a sum over triangulations. The difference lies in the class...
Black holes as quantum gravity condensates
Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo
2018-03-01
We model spherically symmetric black holes within the group field theory formalism for quantum gravity via generalized condensate states, involving sums over arbitrarily refined graphs (dual to three-dimensional triangulations). The construction relies heavily on both the combinatorial tools of random tensor models and the quantum geometric data of loop quantum gravity, both part of the group field theory formalism. Armed with the detailed microscopic structure, we compute the entropy associated with the black hole horizon, which turns out to be equivalently the Boltzmann entropy of its microscopic degrees of freedom and the entanglement entropy between the inside and outside regions. We recover the area law under very general conditions, as well as the Bekenstein-Hawking formula. The result is also shown to be generically independent of any specific value of the Immirzi parameter.
Light-like scattering in quantum gravity
International Nuclear Information System (INIS)
Bjerrum-Bohr, N.E.J.; Donoghue, John F.; Holstein, Barry R.; Planté, Ludovic; Vanhove, Pierre
2016-01-01
We consider scattering in quantum gravity and derive long-range classical and quantum contributions to the scattering of light-like bosons and fermions (spin-0, spin-(1/2), spin-1) from an external massive scalar field, such as the Sun or a black hole. This is achieved by treating general relativity as an effective field theory and identifying the non-analytic pieces of the one-loop gravitational scattering amplitude. It is emphasized throughout the paper how modern amplitude techniques, involving spinor-helicity variables, unitarity, and squaring relations in gravity enable much simplified computations. We directly verify, as predicted by general relativity, that all classical effects in our computation are universal (in the context of matter type and statistics). Using an eikonal procedure we confirm the post-Newtonian general relativity correction for light-like bending around large stellar objects. We also comment on treating effects from quantum ℏ dependent terms using the same eikonal method.
Light-like scattering in quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Bjerrum-Bohr, N.E.J. [Niels Bohr International Academy & Discovery Center, Niels Bohr Institute,University of Copenhagen, Blegdamsvej 17, Copenhagen Ø, DK-2100 (Denmark); Donoghue, John F. [Department of Physics-LGRT, University of Massachusetts,Amherst, MA, 01003 (United States); Holstein, Barry R. [Department of Physics-LGRT, University of Massachusetts,Amherst, MA, 01003 (United States); Kavli Institute for Theoretical Physics, University of California,Santa Barbara, CA, 93016 (United States); Planté, Ludovic; Vanhove, Pierre [CEA, DSM, Institut de Physique Théorique, IPhT, CNRS MPPU, URA2306,Saclay, Gif-sur-Yvette, F-91191 (France)
2016-11-21
We consider scattering in quantum gravity and derive long-range classical and quantum contributions to the scattering of light-like bosons and fermions (spin-0, spin-(1/2), spin-1) from an external massive scalar field, such as the Sun or a black hole. This is achieved by treating general relativity as an effective field theory and identifying the non-analytic pieces of the one-loop gravitational scattering amplitude. It is emphasized throughout the paper how modern amplitude techniques, involving spinor-helicity variables, unitarity, and squaring relations in gravity enable much simplified computations. We directly verify, as predicted by general relativity, that all classical effects in our computation are universal (in the context of matter type and statistics). Using an eikonal procedure we confirm the post-Newtonian general relativity correction for light-like bending around large stellar objects. We also comment on treating effects from quantum ℏ dependent terms using the same eikonal method.
Universality of quantum gravity corrections.
Das, Saurya; Vagenas, Elias C
2008-11-28
We show that the existence of a minimum measurable length and the related generalized uncertainty principle (GUP), predicted by theories of quantum gravity, influence all quantum Hamiltonians. Thus, they predict quantum gravity corrections to various quantum phenomena. We compute such corrections to the Lamb shift, the Landau levels, and the tunneling current in a scanning tunneling microscope. We show that these corrections can be interpreted in two ways: (a) either that they are exceedingly small, beyond the reach of current experiments, or (b) that they predict upper bounds on the quantum gravity parameter in the GUP, compatible with experiments at the electroweak scale. Thus, more accurate measurements in the future should either be able to test these predictions, or further tighten the above bounds and predict an intermediate length scale between the electroweak and the Planck scale.
Quantum gravity and quantum nondemolition measurements
International Nuclear Information System (INIS)
Borzeszkowski, H.H. von; Treder, H.J.
1984-01-01
It is shown that in Quantum Gravity, and more general: in Grand Unified Theory incorporating General Relativity on a basic level, there arise necessarily absolute limitations on measurement which one cannot evade by any 'quantum nondemolition measurements'. This fact is demonstrated not to oppose the existence of certain approximations to the full theory where these limitations do not arise. (author)
Quantum gravity extension of the inflationary scenario.
Agullo, Ivan; Ashtekar, Abhay; Nelson, William
2012-12-21
Since the standard inflationary paradigm is based on quantum field theory on classical space-times, it excludes the Planck era. Using techniques from loop quantum gravity, the paradigm is extended to a self-consistent theory from the Planck scale to the onset of slow roll inflation, covering some 11 orders of magnitude in energy density and curvature. This preinflationary dynamics also opens a small window for novel effects, e.g., a source for non-Gaussianities, which could extend the reach of cosmological observations to the deep Planck regime of the early Universe.
Nonperturbative loop quantization of scalar-tensor theories of gravity
International Nuclear Information System (INIS)
Zhang Xiangdong; Ma Yongge
2011-01-01
The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter ω(φ). In the sector of ω(φ)=-(3/2), the feasible theories are restricted and a new primary constraint generating conformal transformations of spacetime is obtained, while in the other sector of ω(φ)≠-(3/2), the canonical structure and constraint algebra of the theories are similar to those of general relativity coupled with a scalar field. By canonical transformations, we further obtain the connection-dynamical formalism of the scalar-tensor theories with real su(2) connections as configuration variables in both sectors. This formalism enables us to extend the scheme of nonperturbative loop quantum gravity to the scalar-tensor theories. The quantum kinematical framework for the scalar-tensor theories is rigorously constructed. Both the Hamiltonian constraint operator and master constraint operator are well defined and proposed to represent quantum dynamics. Thus the loop quantum gravity method is also valid for general scalar-tensor theories.
Renormalization and asymptotic freedom in quantum gravity
International Nuclear Information System (INIS)
Tomboulis, E.T.
1984-01-01
The article reviews some recent attempts to construct satisfactory theories of quantum gravity within the framework of local, continuum field theory. Quantum gravity; the renormalization group and its fixed points; fixed points and dimensional continuation in gravity; and quantum gravity at d=4-the 1/N expansion-asymptotic freedom; are all discussed. (U.K.)
Quantum field theory II introductions to quantum gravity, supersymmetry and string theory
Manoukian, Edouard B
2016-01-01
This book takes a pedagogical approach to explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics. The first part of the book introduces quantum gravity, without requiring previous knowledge of general relativity (GR). The necessary geometrical aspects are derived afresh leading to explicit general Lagrangians for gravity, including that of general relativity. The quantum aspect of gravitation, as described by the graviton, is introduced and perturbative quantum GR is discussed. The Schwinger-DeWitt formalism is developed to compute the one-loop contribution to the theory and renormalizability aspects of the perturbative theory are also discussed. This follows by introducing only the very basics of a non-perturbative, background-independent, formulation of quantum gravity, referred to as “loop quantum gravity”, which gives rise to a quantization of space. In the second part the author in...
Light fermions in quantum gravity
International Nuclear Information System (INIS)
Eichhorn, Astrid; Gies, Holger
2011-01-01
We study the impact of quantum gravity, formulated as a quantum field theory of the metric, on chiral symmetry in a fermionic matter sector. Specifically we address the question of whether metric fluctuations can induce chiral symmetry breaking and bound state formation. Our results based on the functional renormalization group indicate that chiral symmetry is left intact even at strong gravitational coupling. In particular, we found that asymptotically safe quantum gravity where the gravitational couplings approach a non-Gaußian fixed point generically admits universes with light fermions. Our results thus further support quantum gravity theories built on fluctuations of the metric field such as the asymptotic-safety scenario. A study of chiral symmetry breaking through gravitational quantum effects may also serve as a significant benchmark test for other quantum gravity scenarios, since a completely broken chiral symmetry at the Planck scale would not be in accordance with the observation of light fermions in our universe. We demonstrate that this elementary observation already imposes constraints on a generic UV completion of gravity. (paper)
Can chaos be observed in quantum gravity?
International Nuclear Information System (INIS)
Dittrich, Bianca; Höhn, Philipp A.; Koslowski, Tim A.; Nelson, Mike I.
2017-01-01
Full general relativity is almost certainly ‘chaotic’. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.
Can chaos be observed in quantum gravity?
Energy Technology Data Exchange (ETDEWEB)
Dittrich, Bianca, E-mail: bdittrich@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5 (Canada); Höhn, Philipp A., E-mail: p.hoehn@univie.ac.at [Vienna Center for Quantum Science and Technology, and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna (Austria); Koslowski, Tim A., E-mail: koslowski@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, México D.F. 04510 (Mexico); Nelson, Mike I., E-mail: mike@aims.edu.gh [African Institute for Mathematical Sciences, P.O Box LG 197, Legon, Accra (Ghana)
2017-06-10
Full general relativity is almost certainly ‘chaotic’. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.
Knot theory and a physical state of quantum gravity
International Nuclear Information System (INIS)
Liko, Tomas; Kauffman, Louis H
2006-01-01
We discuss the theory of knots, and describe how knot invariants arise naturally in gravitational physics. The focus of this review is to delineate the relationship between knot theory and the loop representation of non-perturbative canonical quantum general relativity (loop quantum gravity). This leads naturally to a discussion of the Kodama wavefunction, a state which is conjectured to be the ground state of the gravitational field with positive cosmological constant. This review can serve as a self-contained introduction to loop quantum gravity and related areas. Our intent is to make the paper accessible to a wider audience that may include topologists, knot theorists, and other persons innocent of the physical background to this approach to quantum gravity. (topical review)
Effective action in multidimensional quantum gravity and spontaneous compactification
International Nuclear Information System (INIS)
Bagrov, V.G.; Bukhbinder, I.L.; Odintsov, S.D.
1987-01-01
One-loop effective action (the Casimir energy) is obtained for a special model of multidimensional quantum gravity and several variants of the d-dimensional quantum R 2 gravity in the space M 4 xT d-4 , where M 4 is the Minkowski space and T d-4 is the (d-4)-dimensional torus. It is shown that the effective action for the conformal gravity and the R 2 gravity without cosmological and Einstein's terms lead to an instability of the classical compactification. A numerical calculation reveals that the effective action for the five-dimensional R 2 gravity with the cosmological term is compatible with a self-consistent spontaneous compactification. The one-loop effective action is also obtained for the five dimensional Einstein gravity with the antisymmetrical torsion in the space M 4 xS 1 , where S 1 is the one-dimensional sphere
Thermodynamics in Loop Quantum Cosmology
International Nuclear Information System (INIS)
Li, L.F.; Zhu, J.Y.
2009-01-01
Loop quantum cosmology (LQC) is very powerful to deal with the behavior of early universe. Moreover, the effective loop quantum cosmology gives a successful description of the universe in the semiclassical region. We consider the apparent horizon of the Friedmann-Robertson-Walker universe as a thermodynamical system and investigate the thermodynamics of LQC in the semiclassical region. The effective density and effective pressure in the modified Friedmann equation from LQC not only determine the evolution of the universe in LQC scenario but also are actually found to be the thermodynamic quantities. This result comes from the energy definition in cosmology (the Misner-Sharp gravitational energy) and is consistent with thermodynamic laws. We prove that within the framework of loop quantum cosmology, the elementary equation of equilibrium thermodynamics is still valid.
The Kauffman bracket and the Jones polynomial in quantum gravity
International Nuclear Information System (INIS)
Griego, J.
1996-01-01
In the loop representation the quantum states of gravity are given by knot invariants. From general arguments concerning the loop transform of the exponential of the Chern-Simons form, a certain expansion of the Kauffman bracket knot polynomial can be formally viewed as a solution of the Hamiltonian constraint with a cosmological constant in the loop representation. The Kauffman bracket is closely related to the Jones polynomial. In this paper the operation of the Hamiltonian on the power expansions of the Kauffman bracket and Jones polynomials is analyzed. It is explicitly shown that the Kauffman bracket is a formal solution of the Hamiltonian constraint to third order in the cosmological constant. We make use of the extended loop representation of quantum gravity where the analytic calculation can be thoroughly accomplished. Some peculiarities of the extended loop calculus are considered and the significance of the results to the case of the conventional loop representation is discussed. (orig.)
Steps towards a quantum theory of gravity
International Nuclear Information System (INIS)
Unruh, W.G.
1984-01-01
The paper concerns simple experiments in quantum gravity. 'Schroedinger's Cat' experiment to test semiclassical quantum gravity, and the gravitational single slit experiment to demonstrate the wave-particle duality for photons, are both described and discussed. (U.K.)
A new class of group field theories for 1st order discrete quantum gravity
Oriti, D.; Tlas, T.
2008-01-01
Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any choice of spacetime dimension and signature, whose Feynman
Spin Entanglement Witness for Quantum Gravity
Bose, Sougato; Mazumdar, Anupam; Morley, Gavin W.; Ulbricht, Hendrik; Toros, Marko; Paternostro, Mauro; Geraci, Andrew A.; Barker, Peter F.; Kim, M. S.; Milburn, Gerard
2017-01-01
Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no
Foundations of quantum gravity
Lindesay, James
2013-01-01
Exploring how the subtleties of quantum coherence can be consistently incorporated into Einstein’s theory of gravitation, this book is ideal for researchers interested in the foundations of relativity and quantum physics. The book examines those properties of coherent gravitating systems that are most closely connected to experimental observations. Examples of consistent co-gravitating quantum systems whose overall effects upon the geometry are independent of the coherence state of each constituent are provided, and the properties of the trapping regions of non-singular black objects, black holes, and a dynamic de Sitter cosmology are discussed analytically, numerically, and diagrammatically. The extensive use of diagrams to summarise the results of the mathematics enables readers to bypass the need for a detailed understanding of the steps involved. Assuming some knowledge of quantum physics and relativity, the book provides textboxes featuring supplementary information for readers particularly interested ...
Algebraic quantum gravity (AQG): I. Conceptual setup
International Nuclear Information System (INIS)
Giesel, K; Thiemann, T
2007-01-01
We introduce a new top down approach to canonical quantum gravity, called algebraic quantum gravity (AQG). The quantum kinematics of AQG is determined by an abstract *-algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single master constraint operator. While AQG is inspired by loop quantum gravity (LQG), it differs drastically from it because in AQG there is fundamentally no topology or differential structure. A natural Hilbert space representation acquires the structure of an infinite tensor product (ITP) whose separable strong equivalence class Hilbert subspaces (sectors) are left invariant by the quantum dynamics. The missing information about the topology and differential structure of the spacetime manifold as well as about the background metric to be approximated is supplied by coherent states. Given such data, the corresponding coherent state defines a sector in the ITP which can be identified with a usual QFT on the given manifold and background. Thus, AQG contains QFT on all curved spacetimes at once, possibly has something to say about topology change and provides the contact with the familiar low energy physics. In particular, in two companion papers we develop semiclassical perturbation theory for AQG and LQG and thereby show that the theory admits a semiclassical limit whose infinitesimal gauge symmetry agrees with that of general relativity. In AQG everything is computable with sufficient precision and no UV divergences arise due to the background independence of the fundamental combinatorial structure. Hence, in contrast to lattice gauge theory on a background metric, no continuum limit has to be taken. There simply is no lattice regulator that must be sent to zero
Is Quantum Gravity a Super-Quantum Theory?
Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; Takeuchi, Tatsu
2013-01-01
We argue that quantum gravity should be a super-quantum theory, that is, a theory whose non-local correlations are stronger than those of canonical quantum theory. As a super-quantum theory, quantum gravity should display distinct experimentally observable super-correlations of entangled stringy states.
Quantum gravity as Escher's dragon
International Nuclear Information System (INIS)
Smilga, A.V.
2003-01-01
The main obstacle in attempts to construct a consistent quantum gravity is the absence of independent flat time. This can in principle be cured by going out to higher dimensions. The modern paradigm assumes that the fundamental theory of everything is some form of string theory living in space of more than four dimensions. We advocate another possibility that the fundamental theory is a form of D = 4 higher derivative gravity. This class of theories has a nice feature of renormalizability, so that perturbative calculations are feasible. There are also finite N = 4 supersymmetric conformal supergravity theories. This possibility is particularly attractive. Einstein's gravity is obtained in a natural way as an effective low-energy theory. The N= 1 supersymmetric version of the theory has a natural higher dimensional interpretation due to V.I. Ogievetsky and E.S. Sokatchev, which involves embedding our curved Minkowski spacetime manifold into flat eight-dimensional space. Assuming that a variant of the finite N = 4 theory also admits a similar interpretation, this may eventually allow one to construct consistent quantum theory of gravity. We argue, however, that, even though future gravity theory will probably use higher dimensions as construction scaffolds, its physical content and meaning should refer to four dimensions, where an observer lives
The ultraviolet behavior of quantum gravity
Anselmi, Damiano; Piva, Marco
2018-05-01
A theory of quantum gravity has been recently proposed by means of a novel quantization prescription, which is able to turn the poles of the free propagators that are due to the higher derivatives into fakeons. The classical Lagrangian contains the cosmological term, the Hilbert term, √{-g}{R}_{μ ν }{R}^{μ ν } and √{-g}{R}^2 . In this paper, we compute the one-loop renormalization of the theory and the absorptive part of the graviton self energy. The results illustrate the mechanism that makes renormalizability compatible with unitarity. The fakeons disentangle the real part of the self energy from the imaginary part. The former obeys a renormalizable power counting, while the latter obeys the nonrenormalizable power counting of the low energy expansion and is consistent with unitarity in the limit of vanishing cosmological constant. The value of the absorptive part is related to the central charge c of the matter fields coupled to gravity.
Loop amplitudes in an extended gravity theory
Dunbar, David C.; Godwin, John H.; Jehu, Guy R.; Perkins, Warren B.
2018-05-01
We extend the S-matrix of gravity by the addition of the minimal three-point amplitude or equivalently adding R3 terms to the Lagrangian. We demonstrate how Unitarity can be used to simply examine the renormalisability of this theory and determine the R4 counter-terms that arise at one-loop. We find that the combination of R4 terms that arise in the extended theory is complementary to the R4 counter-term associated with supersymmetric Lagrangians.
Proposal for testing quantum gravity in the lab
International Nuclear Information System (INIS)
Ali, Ahmed Farag; Das, Saurya; Vagenas, Elias C.
2011-01-01
Attempts to formulate a quantum theory of gravitation are collectively known as quantum gravity. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called generalized uncertainty principle (GUP). We have proposed a GUP consistent with string theory, black hole physics, and doubly special relativity theories and have showed that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it suggests that the space that confines it must be quantized, and in fact that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this may signal the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale. Because this influences all the quantum Hamiltonians in an universal way, it predicts quantum gravity corrections to various quantum phenomena. Therefore, in the present work we compute these corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current in a scanning tunneling microscope.
New directions in quantum gravity
International Nuclear Information System (INIS)
Penrose, Roger
1988-01-01
There has been much work over the past thirty years or so, concerned with trying to discover how Nature is able to achieve unity and harmony in combining two seemingly incompatible collections of phenomena: those of the sub-microscopic world, described by quantum mechanics, and those of the large-scale world, described by general relativity. The essential need for such a quantum gravity theory arose. Numerous heroic attempts to quantize the Einstein theory followed but these eventually foundered on the harsh rocks of non-renormalizability. This impasse led most workers in the field to explore possible modifications of Einstein's theory such as supergravity, increasing the number of space-time dimensions, replacing the standard (Hilbert) action of general relativity theory by something more complicated and superstring theory. Time-asymmetry in space-time singularity structure is discussed. In searching for a time-asymmetric quantum gravity theory the theories of general relativity and quantum mechanics both need to be modified. Then an objective wave-function collapse can occur at a level at which gravitation begins to be involved in a quantum process. (author)
The affine quantum gravity programme
International Nuclear Information System (INIS)
Klauder, John R
2002-01-01
The central principle of affine quantum gravity is securing and maintaining the strict positivity of the matrix { g-hat ab (x)} composed of the spatial components of the local metric operator. On spectral grounds, canonical commutation relations are incompatible with this principle, and they must be replaced by noncanonical, affine commutation relations. Due to the partial second-class nature of the quantum gravitational constraints, it is advantageous to use the recently developed projection operator method, which treats all quantum constraints on an equal footing. Using this method, enforcement of regularized versions of the gravitational operator constraints is formulated quite naturally by means of a novel and relatively well-defined functional integral involving only the same set of variables that appears in the usual classical formulation. It is anticipated that skills and insight to study this formulation can be developed by studying special, reduced-variable models that still retain some basic characteristics of gravity, specifically a partial second-class constraint operator structure. Although perturbatively nonrenormalizable, gravity may possibly be understood nonperturbatively from a hard-core perspective that has proved valuable for specialized models. Finally, developing a procedure to pass to the genuine physical Hilbert space involves several interconnected steps that require careful coordination
Directory of Open Access Journals (Sweden)
Bernard S. Kay
2015-12-01
Full Text Available We give a review, in the style of an essay, of the author’s 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state—entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author’s recent arguments based on this alternative description which suggest that the Anti de Sitter space (AdS/conformal field theory (CFT correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory.
The toroidal Hausdorff dimension of 2d Euclidean quantum gravity
DEFF Research Database (Denmark)
Ambjorn, Jan; Budd, Timothy George
2013-01-01
The lengths of shortest non-contractible loops are studied numerically in 2d Euclidean quantum gravity on a torus coupled to conformal field theories with central charge less than one. We find that the distribution of these geodesic lengths displays a scaling in agreement with a Hausdorff dimension...
Graviton propagator from background-independent quantum gravity.
Rovelli, Carlo
2006-10-13
We study the graviton propagator in Euclidean loop quantum gravity. We use spin foam, boundary-amplitude, and group-field-theory techniques. We compute a component of the propagator to first order, under some approximations, obtaining the correct large-distance behavior. This indicates a way for deriving conventional spacetime quantities from a background-independent theory.
Theories of quantum gravity: Pt. 1
International Nuclear Information System (INIS)
Aragone, C.
1990-01-01
Superstrings continue to be a source of inspiration for the basic understanding of quantum gravity. They seem to provide a more fundamental arena than quantum field theory. Even though we still do not have a theory of everything, string concepts bring a new theoretical richness to research in quantum and classical gravity. Papers presented at the session on this subject are reviewed. (author)
2D quantum gravity from quantum entanglement.
Gliozzi, F
2011-01-21
In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way that allows them to backreact. As a consequence, they become dynamical subsystems whose position, form, and extension are determined by their interaction with the whole system. We analyze, in particular, quantum spin chains described at criticality by a conformal field theory. Its coupling to the Gibbs' ensemble of all possible subsystems is relevant and drives the system into a new fixed point which is argued to be that of the 2D quantum gravity coupled to this system. Numerical experiments on the critical Ising model show that the new critical exponents agree with those predicted by the formula of Knizhnik, Polyakov, and Zamolodchikov.
From quantum cosmology to quantum gravity
International Nuclear Information System (INIS)
Englert, F.
1983-01-01
A theory is proposed which solves the problem of the acausal character of the hot big bang cosmology in general relativity. The initial thermal state is stabilized by constructing a semi-classical solution to the coupled graviation and matter system with zero cosmological constant. This solution is an expanding deSitter in which black holes are created by a quantum process out of the expansion energy. It is argued that the initial nucleation process originates from a quantum metric fluctuation. Universe-like configurations must be added over the path integral metrics. This stabilizes the path integral and saturates it with a ''foam of universes'' where the nonrenormalizability of gravity can be seen as the manifestation of long range interactions within a universe. This description introduces indeterminacy into quantum field theory and suggests that 4-D space-time should be explained by new concepts
Topics in string theory and quantum gravity
Alvarez-Gaume, Luis
1992-01-01
These are the lecture notes for the Les Houches Summer School on Quantum Gravity held in July 1992. The notes present some general critical assessment of other (non-string) approaches to quantum gravity, and a selected set of topics concerning what we have learned so far about the subject from string theory. Since these lectures are long (133 A4 pages), we include in this abstract the table of contents, which should help the user of the bulletin board in deciding whether to latex and print the full file. 1-FIELD THEORETICAL APPROACH TO QUANTUM GRAVITY: Linearized gravity; Supergravity; Kaluza-Klein theories; Quantum field theory and classical gravity; Euclidean approach to Quantum Gravity; Canonical quantization of gravity; Gravitational Instantons. 2-CONSISTENCY CONDITIONS: ANOMALIES: Generalities about anomalies; Spinors in 2n dimensions; When can we expect to find anomalies?; The Atiyah-Singer Index Theorem and the computation of anomalies; Examples: Green-Schwarz cancellation mechanism and Witten's SU(2) ...
Newtonian gravity on quantum spacetime
Directory of Open Access Journals (Sweden)
Majid Shahn
2014-04-01
Full Text Available The bicrossproduct model λ-Minkowski (or ‘κ-Minkowski’ quantum space-time has an anomaly for the action of the Poincaré quantum group which was resolved by an extra cotangent direction θ’ not visible classically. We show that gauging a coefficient of θ′ introduces gravity into the model. We solve and analyse the model nonrelativisticaly in a 1/r potential, finding an induced constant term in the effective potential energy and a weakening and separation of the effective gravitational and inertial masses as the test particle Klein-Gordon mass increases. The present work is intended as a proof of concept but the approach could be relevant to an understanding of dark energy and possibly to macroscopic quantum systems.
The affine quantum gravity programme
Klauder, J R
2002-01-01
The central principle of affine quantum gravity is securing and maintaining the strict positivity of the matrix left brace g-hat sub a sub b (x)right brace composed of the spatial components of the local metric operator. On spectral grounds, canonical commutation relations are incompatible with this principle, and they must be replaced by noncanonical, affine commutation relations. Due to the partial second-class nature of the quantum gravitational constraints, it is advantageous to use the recently developed projection operator method, which treats all quantum constraints on an equal footing. Using this method, enforcement of regularized versions of the gravitational operator constraints is formulated quite naturally by means of a novel and relatively well-defined functional integral involving only the same set of variables that appears in the usual classical formulation. It is anticipated that skills and insight to study this formulation can be developed by studying special, reduced-variable models that sti...
Dimensional reduction in quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Hooft, G [Rijksuniversiteit Utrecht (Netherlands). Inst. voor Theoretische Fysica
1994-12-31
The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable degrees of freedom can best be described as if they were Boolean variables defined on a two- dimensional lattice, evolving with time. This observation, deduced from not much more than unitarity, entropy and counting arguments, implies severe restrictions on possible models of quantum gravity. Using cellular automata as an example it is argued that this dimensional reduction implies more constraints than the freedom we have in constructing models. This is the main reason why so-far no completely consistent mathematical models of quantum black holes have been found. (author). 13 refs, 2 figs.
Quantum Gravity Mathematical Models and Experimental Bounds
Fauser, Bertfried; Zeidler, Eberhard
2007-01-01
The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on ...
Focus on quantum Einstein gravity Focus on quantum Einstein gravity
Ambjorn, Jan; Reuter, Martin; Saueressig, Frank
2012-09-01
The gravitational asymptotic safety program summarizes the attempts to construct a consistent and predictive quantum theory of gravity within Wilson's generalized framework of renormalization. Its key ingredient is a non-Gaussian fixed point of the renormalization group flow which controls the behavior of the theory at trans-Planckian energies and renders gravity safe from unphysical divergences. Provided that the fixed point comes with a finite number of ultraviolet-attractive (relevant) directions, this construction gives rise to a consistent quantum field theory which is as predictive as an ordinary, perturbatively renormalizable one. This opens up the exciting possibility of establishing quantum Einstein gravity as a fundamental theory of gravity, without introducing supersymmetry or extra dimensions, and solely based on quantization techniques that are known to work well for the other fundamental forces of nature. While the idea of gravity being asymptotically safe was proposed by Steven Weinberg more than 30 years ago [1], the technical tools for investigating this scenario only emerged during the last decade. Here a key role is played by the exact functional renormalization group equation for gravity, which allows the construction of non-perturbative approximate solutions for the RG-flow of the gravitational couplings. Most remarkably, all solutions constructed to date exhibit a suitable non-Gaussian fixed point, lending strong support to the asymptotic safety conjecture. Moreover, the functional renormalization group also provides indications that the central idea of a non-Gaussian fixed point providing a safe ultraviolet completion also carries over to more realistic scenarios where gravity is coupled to a suitable matter sector like the standard model. These theoretical successes also triggered a wealth of studies focusing on the consequences of asymptotic safety in a wide range of phenomenological applications covering the physics of black holes, early
Cosmic censorship in quantum Einstein gravity
Bonanno, A.; Koch, B.; Platania, A.
2017-05-01
We study the quantum gravity modification of the Kuroda-Papapetrou model induced by the running of the Newton’s constant at high energy in quantum Einstein gravity. We argue that although the antiscreening character of the gravitational interaction favours the formation of a naked singularity, quantum gravity effects turn the classical singularity into a ‘whimper’ singularity which remains naked for a finite amount of advanced time.
The Bianchi IX model in loop quantum cosmology
International Nuclear Information System (INIS)
Bojowald, Martin; Date, Ghanashyam; Hossain, Golam Mortuza
2004-01-01
The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behaviour. The way this is realized, independently of quantization ambiguities, suggests a new look at initial and final singularities
Continuum-regularized quantum gravity
International Nuclear Information System (INIS)
Chan Huesum; Halpern, M.B.
1987-01-01
The recent continuum regularization of d-dimensional Euclidean gravity is generalized to arbitrary power-law measure and studied in some detail as a representative example of coordinate-invariant regularization. The weak-coupling expansion of the theory illustrates a generic geometrization of regularized Schwinger-Dyson rules, generalizing previous rules in flat space and flat superspace. The rules are applied in a non-trivial explicit check of Einstein invariance at one loop: the cosmological counterterm is computed and its contribution is included in a verification that the graviton mass is zero. (orig.)
Group field theory and simplicial quantum gravity
International Nuclear Information System (INIS)
Oriti, D
2010-01-01
We present a new group field theory for 4D quantum gravity. It incorporates the constraints that give gravity from BF theory and has quantum amplitudes with the explicit form of simplicial path integrals for first-order gravity. The geometric interpretation of the variables and of the contributions to the quantum amplitudes is manifest. This allows a direct link with other simplicial gravity approaches, like quantum Regge calculus, in the form of the amplitudes of the model, and dynamical triangulations, which we show to correspond to a simple restriction of the same.
Quantum state correction of relic gravitons from quantum gravity
Rosales, Jose-Luis
1996-01-01
The semiclassical approach to quantum gravity would yield the Schroedinger formalism for the wave function of metric perturbations or gravitons plus quantum gravity correcting terms in pure gravity; thus, in the inflationary scenario, we should expect correcting effects to the relic graviton (Zel'dovich) spectrum of the order (H/mPl)^2.
Measurement analysis and quantum gravity
International Nuclear Information System (INIS)
Albers, Mark; Kiefer, Claus; Reginatto, Marcel
2008-01-01
We consider the question of whether consistency arguments based on measurement theory show that the gravitational field must be quantized. Motivated by the argument of Eppley and Hannah, we apply a DeWitt-type measurement analysis to a coupled system that consists of a gravitational wave interacting with a mass cube. We also review the arguments of Eppley and Hannah and of DeWitt, and investigate a second model in which a gravitational wave interacts with a quantized scalar field. We argue that one cannot conclude from the existing gedanken experiments that gravity has to be quantized. Despite the many physical arguments which speak in favor of a quantum theory of gravity, it appears that the justification for such a theory must be based on empirical tests and does not follow from logical arguments alone.
State sum models for quantum gravity
Barrett, John W.
2000-01-01
This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.
Does time exist in quantum gravity?
Directory of Open Access Journals (Sweden)
Claus Kiefer
2015-12-01
Full Text Available Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a “problem of time”. In my essay, I investigate those consequences for the concept of time that may be drawn without a detailed knowledge of quantum gravity. The only assumptions are the experimentally supported universality of the linear structure of quantum theory and the recovery of general relativity in the classical limit. Among the consequences are the fundamental timelessness of quantum gravity, the approximate nature of a semiclassical time, and the correlation of entropy with the size of the Universe.
Fractal universe and quantum gravity.
Calcagni, Gianluca
2010-06-25
We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.
Spin Entanglement Witness for Quantum Gravity.
Bose, Sougato; Mazumdar, Anupam; Morley, Gavin W; Ulbricht, Hendrik; Toroš, Marko; Paternostro, Mauro; Geraci, Andrew A; Barker, Peter F; Kim, M S; Milburn, Gerard
2017-12-15
Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no feasible ideas yet to test its quantum coherent behavior directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple spin correlation measurements.
Perturbative quantum gravity as a double copy of gauge theory.
Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik
2010-08-06
In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.
A quantum kinematics for asymptotically flat gravity
Campiglia, Miguel; Varadarajan, Madhavan
2015-07-01
We construct a quantum kinematics for asymptotically flat gravity based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying loop quantum gravity (LQG) which supports, in addition to the usual LQG operators, the action of ‘background exponential operators’, which are connection dependent operators labelled by ‘background’ su(2) electric fields. KS states have, in addition to the LQG state label corresponding to one dimensional excitations of the triad, a label corresponding to a ‘background’ electric field that describes three dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields that label the states and the background electric fields that label the operators. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We show that KS states can be realised as wave functions on a quantum configuration space of generalized connections and that the asymptotic behaviour of each such generalized connection is determined by that of the background electric fields which label the background exponential operators. Similar to the spatially compact case, the Gauss law and diffeomorphism constraints are then imposed through group averaging techniques to obtain a large sector of gauge invariant states. It is shown that this sector supports a unitary action of the group of asymptotic rotations and translations and that, as anticipated by Friedman and Sorkin, for appropriate spatial topology, this sector contains states that display fermionic behaviour under 2π rotations.
Ehrenfest's principle in quantum gravity
International Nuclear Information System (INIS)
Greensite, J.
1991-01-01
The Ehrenfest principle d t = is proposed as (part of) a definition of the time variable in canonical quantum gravity. This principle selects a time direction in superspace, and provides a conserved, positive definite probability measure. An exact solution of the Ehrenfest condition is obtained, which leads to constant-time surfaces in superspace generated by the operator d/dτ=ΛθxΛ, where Λ is the gradient operator in superspace, and θ is the phase of the Wheeler-DeWitt wavefunction Φ; the constant-time surfaces are determined by this solution up to a choice of initial t=0 surface. This result holds throughout superspace, including classically forbidden regions and in the neighborhood of caustics; it also leads to ordinary quantum field theory and classical gravity in regions of superspace where the phase satisfies vertical stroked t θvertical stroke>>vertical stroked t ln(Φ * Φ)vertical stroke and (d t θ) 2 >>vertical stroked t 2 θvertical stroke. (orig.)
Inflationary cosmology from quantum conformal gravity
International Nuclear Information System (INIS)
Jizba, Petr; Kleinert, Hagen; Scardigli, Fabio
2015-01-01
We analyze the functional integral for quantum conformal gravity and show that, with the help of a Hubbard-Stratonovich transformation, the action can be broken into a local quadratic-curvature theory coupled to a scalar field. A one-loop effective-action calculation reveals that strong fluctuations of the metric field are capable of spontaneously generating a dimensionally transmuted parameter which, in the weak-field sector of the broken phase, induces a Starobinsky-type f(R)-model with a gravi-cosmological constant. A resulting non-trivial relation between Starobinsky's parameter and the gravi-cosmological constant is highlighted and implications for cosmic inflation are briefly discussed and compared with the recent PLANCK and BICEP2 data. (orig.)
New Hamiltonians for loop quantum cosmology with arbitrary spin representations
Ben Achour, Jibril; Brahma, Suddhasattwa; Geiller, Marc
2017-04-01
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the fundamental representation, and very little is known about the physics associated with higher spin labels. This constitutes an ambiguity of which the understanding, we believe, is fundamental for connecting loop quantum cosmology to full theories of quantum gravity like loop quantum gravity, its spin foam formulation, or cosmological group field theory. We take a step in this direction by providing here a new closed formula for the Hamiltonian of flat Friedmann-Lemaître-Robertson-Walker models regularized in a representation of arbitrary spin. This expression is furthermore polynomial in the basic variables which correspond to well-defined operators in the quantum theory, takes into account the so-called inverse-volume corrections, and treats in a unified way two different regularization schemes for the curvature. After studying the effective classical dynamics corresponding to single and multiple-spin Hamiltonians, we study the behavior of the critical density when the number of representations is increased and the stability of the difference equations in the quantum theory.
Numerical analysis of the big bounce in loop quantum cosmology
International Nuclear Information System (INIS)
Laguna, Pablo
2007-01-01
Loop quantum cosmology (LQC) homogeneous models with a massless scalar field show that the big-bang singularity can be replaced by a big quantum bounce. To gain further insight on the nature of this bounce, we study the semidiscrete loop quantum gravity Hamiltonian constraint equation from the point of view of numerical analysis. For illustration purposes, we establish a numerical analogy between the quantum bounces and reflections in finite difference discretizations of wave equations triggered by the use of nonuniform grids or, equivalently, reflections found when solving numerically wave equations with varying coefficients. We show that the bounce is closely related to the method for the temporal update of the system and demonstrate that explicit time-updates in general yield bounces. Finally, we present an example of an implicit time-update devoid of bounces and show back-in-time, deterministic evolutions that reach and partially jump over the big-bang singularity
Quantum Kinematics of Bosonic Vortex Loops
International Nuclear Information System (INIS)
Goldin, G.A.; Owczarek, R.; Sharp, D.H.
1999-01-01
Poisson structure for vortex filaments (loops and arcs) in 2D ideal incompressible fluid is analyzed in detail. Canonical coordinates and momenta on coadjoint orbits of the area-preserving diffeomorphism group, associated with such vortices, are found. The quantum space of states in the simplest case of ''bosonic'' vortex loops is built within a geometric quantization approach to the description of a quantum fluid. Fock-like structure and non-local creation and annihilation operators of quantum vortex filaments are introduced
Loss of quantum coherence from discrete quantum gravity
International Nuclear Information System (INIS)
Gambini, Rodolfo; Porto, Rafael A; Pullin, Jorge
2004-01-01
We show that a recent proposal for the quantization of gravity based on discrete spacetime implies a modification of standard quantum mechanics that naturally leads to a loss of coherence in quantum states of the type discussed by Milburn. The proposal overcomes the energy conservation problem of previously proposed decoherence mechanisms stemming from quantum gravity. Mesoscopic quantum systems (as Bose-Einstein condensates) appear as the most promising testing grounds for an experimental verification of the mechanism. (letter to the editor)
From quantum gravity to quantum field theory via noncommutative geometry
International Nuclear Information System (INIS)
Aastrup, Johannes; Grimstrup, Jesper Møller
2014-01-01
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction, which encodes the kinematics of quantum gravity, we construct semi-classical states which, in a semi-classical limit, give a system of interacting fermions in an ambient gravitational field. The emergent interaction involves flux tubes of the gravitational field. In the additional limit, where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. (paper)
Gravity-matter entanglement in Regge quantum gravity
International Nuclear Information System (INIS)
Paunković, Nikola; Vojinović, Marko
2016-01-01
We argue that Hartle-Hawking states in the Regge quantum gravity model generically contain non-trivial entanglement between gravity and matter fields. Generic impossibility to talk about “matter in a point of space” is in line with the idea of an emergent spacetime, and as such could be taken as a possible candidate for a criterion for a plausible theory of quantum gravity. Finally, this new entanglement could be seen as an additional “effective interaction”, which could possibly bring corrections to the weak equivalence principle. (paper)
The Euclidean three-point function in loop and perturbative gravity
International Nuclear Information System (INIS)
Rovelli, Carlo; Zhang Mingyi
2011-01-01
We compute the leading order of the three-point function in loop quantum gravity, using the vertex expansion of the Euclidean version of the new spin foam dynamics, in the region of γ < 1. We find results consistent with Regge calculus in the limit γ → 0, j → ∞. We also compute the tree-level three-point function of perturbative quantum general relativity in position space and discuss the possibility of directly comparing the two results.
On a Continuum Limit for Loop Quantum Cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose Antonio
2008-01-01
The use of non-regular representations of the Heisenberg-Weyl commutation relations has proved to be useful for studying conceptual and technical issues in quantum gravity. Of particular relevance is the study of Loop Quantum Cosmology (LQC), symmetry reduced theory that is related to Loop Quantum Gravity, and that is based on a non-regular, polymeric representation. Recently, a soluble model was used by Ashtekar, Corichi and Singh to study the relation between Loop Quantum Cosmology and the standard Wheeler-DeWitt theory and, in particular, the passage to the limit in which the auxiliary parameter (interpreted as ''quantum geometry discreetness'') is sent to zero in hope to get rid of this 'regulator' that dictates the LQC dynamics at each 'scale'. In this note we outline the first steps toward reformulating this question within the program developed by the authors for studying the continuum limit of polymeric theories, which was successfully applied to simple systems such as a Simple Harmonic Oscillator
Loop quantum cosmology with self-dual variables
Wilson-Ewing, Edward
2015-12-01
Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann space-time coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by choosing a particular inner product for the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomylike operators of which some are well defined; these operators in turn are used in the definition of the Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum theory is closely related, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived which provide a good approximation to the full quantum dynamics for sharply peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects resolve the big-bang and big-crunch singularities and replace them by a nonsingular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.
Generalized uncertainty principle, quantum gravity and Horava-Lifshitz gravity
International Nuclear Information System (INIS)
Myung, Yun Soo
2009-01-01
We investigate a close connection between generalized uncertainty principle (GUP) and deformed Horava-Lifshitz (HL) gravity. The GUP commutation relations correspond to the UV-quantum theory, while the canonical commutation relations represent the IR-quantum theory. Inspired by this UV/IR quantum mechanics, we obtain the GUP-corrected graviton propagator by introducing UV-momentum p i =p 0i (1+βp 0 2 ) and compare this with tensor propagators in the HL gravity. Two are the same up to p 0 4 -order.
Thermodynamics and phases in quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Mann, R B
2009-01-01
We give an approach for studying quantum gravity effects on black hole thermodynamics. This combines a quantum framework for gravitational collapse with quasi-local definitions of energy and surface gravity. Our arguments suggest that (i) the specific heat of a black hole becomes positive after a phase transition near the Planck scale,(ii) its entropy acquires a logarithmic correction and (iii) the mass loss rate is modified such that Hawking radiation stops near the Planck scale. These results are due essentially to a realization of fundamental discreteness in quantum gravity, and are in this sense potentially theory independent.
Loop quantum corrected Einstein Yang-Mills black holes
Protter, Mason; DeBenedictis, Andrew
2018-05-01
In this paper, we study the homogeneous interiors of black holes possessing SU(2) Yang-Mills fields subject to corrections inspired by loop quantum gravity. The systems studied possess both magnetic and induced electric Yang-Mills fields. We consider the system of equations both with and without Wilson loop corrections to the Yang-Mills potential. The structure of the Yang-Mills Hamiltonian, along with the restriction to homogeneity, allows for an anomaly-free effective quantization. In particular, we study the bounce which replaces the classical singularity and the behavior of the Yang-Mills fields in the quantum corrected interior, which possesses topology R ×S2 . Beyond the bounce, the magnitude of the Yang-Mills electric field asymptotically grows monotonically. This results in an ever-expanding R sector even though the two-sphere volume is asymptotically constant. The results are similar with and without Wilson loop corrections on the Yang-Mills potential.
Loop quantum cosmology: from pre-inflationary dynamics to observations
International Nuclear Information System (INIS)
Ashtekar, Abhay; Barrau, Aurélien
2015-01-01
The Planck collaboration has provided us rich information about the early Universe, and a host of new observational missions will soon shed further light on the ‘anomalies’ that appear to exist on the largest angular scales. From a quantum gravity perspective, it is natural to inquire if one can trace back the origin of such puzzling features to Planck scale physics. Loop quantum cosmology provides a promising avenue to explore this issue because of its natural resolution of the big bang singularity. Thanks to advances over the last decade, the theory has matured sufficiently to allow concrete calculations of the phenomenological consequences of its pre-inflationary dynamics. In this article we summarize the current status of the ensuing two-way dialog between quantum gravity and observations. (paper)
Perturbative Quantum Gravity from Gauge Theory
Carrasco, John Joseph
In this dissertation we present the graphical techniques recently developed in the construction of multi-loop scattering amplitudes using the method of generalized unitarity. We construct the three-loop and four-loop four-point amplitudes of N = 8 supergravity using these methods and the Kawaii, Lewellen and Tye tree-level relations which map tree-level gauge theory amplitudes to tree-level gravity theory amplitudes. We conclude by extending a tree-level duality between color and kinematics, generic to gauge theories, to a loop level conjecture, allowing the easy relation between loop-level gauge and gravity kinematics. We provide non-trivial evidence for this conjecture at three-loops in the particular case of maximal supersymmetry.
Measure problem in slow roll inflation and loop quantum cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Karami, Asieh
2011-01-01
We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered. Contrary to the standard expectation, the probability of having enough inflation, that is close to 1 in LQC, grows and tends to 1 as one approaches the GR limit. We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture. As we show, the conflicting results stem from different choices of initial conditions for the computation of probability. The singularity-free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.
Quantum loop corrections of a charged de Sitter black hole
Naji, J.
2018-03-01
A charged black hole in de Sitter (dS) space is considered and logarithmic corrected entropy used to study its thermodynamics. Logarithmic corrections of entropy come from thermal fluctuations, which play a role of quantum loop correction. In that case we are able to study the effect of quantum loop on black hole thermodynamics and statistics. As a black hole is a gravitational object, it helps to obtain some information about the quantum gravity. The first and second laws of thermodynamics are investigated for the logarithmic corrected case and we find that it is only valid for the charged dS black hole. We show that the black hole phase transition disappears in the presence of logarithmic correction.
Spin foam models for quantum gravity
Perez, Alejandro
The definition of a quantum theory of gravity is explored following Feynman's path-integral approach. The aim is to construct a well defined version of the Wheeler-Misner- Hawking ``sum over four geometries'' formulation of quantum general relativity (GR). This is done by means of exploiting the similarities between the formulation of GR in terms of tetrad-connection variables (Palatini formulation) and a simpler theory called BF theory. One can go from BF theory to GR by imposing certain constraints on the BF-theory configurations. BF theory contains only global degrees of freedom (topological theory) and it can be exactly quantized á la Feynman introducing a discretization of the manifold. Using the path integral for BF theory we define a path integration for GR imposing the BF-to-GR constraints on the BF measure. The infinite degrees of freedom of gravity are restored in the process, and the restriction to a single discretization introduces a cut- off in the summed-over configurations. In order to capture all the degrees of freedom a sum over discretization is implemented. Both the implementation of the BF-to-GR constraints and the sum over discretizations are obtained by means of the introduction of an auxiliary field theory (AFT). 4-geometries in the path integral for GR are given by the Feynman diagrams of the AFT which is in this sense dual to GR. Feynman diagrams correspond to 2-complexes labeled by unitary irreducible representations of the internal gauge group (corresponding to tetrad rotation in the connection to GR). A model for 4-dimensional Euclidean quantum gravity (QG) is defined which corresponds to a different normalization of the Barrett-Crane model. The model is perturbatively finite; divergences appearing in the Barrett-Crane model are cured by the new normalization. We extend our techniques to the Lorentzian sector, where we define two models for four-dimensional QG. The first one contains only time-like representations and is shown to be
Approximating the physical inner product of loop quantum cosmology
International Nuclear Information System (INIS)
Bahr, Benjamin; Thiemann, Thomas
2007-01-01
In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity
Quantum gravity phenomenology. Achievements and challenges
Energy Technology Data Exchange (ETDEWEB)
Liberati, S. [International School for Advanced Study (SISSA), Trieste (Italy); INFN, Sezione di Trieste (Italy); Maccione, L. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2011-05-15
Motivated by scenarios of quantum gravity, Planck-suppressed deviations from Lorentz invariance are expected at observable energies. Ultra-High-Energy Cosmic Rays, the most energetic particles ever observed in nature, yielded in the last two years strong constraints on deviations suppressed by O(E{sup 2}/M{sup 2}{sub Pl}) and also, for the first time, on space-time foam, stringy inspired models of quantum gravity. We review the most important achievements and discuss future outlooks. (orig.)
Superrenormalizable quantum gravity with complex ghosts
Directory of Open Access Journals (Sweden)
Leonardo Modesto
2016-04-01
Full Text Available We suggest and briefly review a new sort of superrenormalizable models of higher derivative quantum gravity. The higher derivative terms in the action can be introduced in such a way that all the unphysical massive states have complex poles. According to the literature on Lee–Wick quantization, in this case the theory can be formulated as unitary, since all massive ghosts-like degrees of freedom are unstable. Keywords: Quantum gravity, Higher derivatives, Complex poles
Quantum Gravity phenomenology: achievements and challenges
International Nuclear Information System (INIS)
Liberati, S; Maccione, L
2011-01-01
Motivated by scenarios of quantum gravity, Planck-suppressed deviations from Lorentz invariance are expected at observable energies. Ultra-High-Energy Cosmic Rays, the most energetic particles ever observed in nature, yielded in the last two years strong constraints on deviations suppressed by O(E 2 /M 2 Pl ) and also, for the first time, on space-time foam, stringy inspired models of quantum gravity. We review the most important achievements and discuss future outlooks.
Feynman diagrams coupled to three-dimensional quantum gravity
International Nuclear Information System (INIS)
Barrett, John W
2006-01-01
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
Applications of quantum information theory to quantum gravity
International Nuclear Information System (INIS)
Smolin, L.
2005-01-01
Full text: I describe work by and with Fotini Markopoulou and Olaf Dreyeron the application of quantum information theory to quantum gravity. A particular application to black hole physics is described, which treats the black hole horizon as an open system, in interaction with an environment, which are the degrees of freedom in the bulk spacetime. This allows us to elucidate which quantum states of a general horizon contribute to the entropy of a Schwarzchild black hole. This case serves as an example of how methods from quantum information theory may help to elucidate how the classical limit emerges from a background independent quantum theory of gravity. (author)
Spectral dimension in causal set quantum gravity
International Nuclear Information System (INIS)
Eichhorn, Astrid; Mizera, Sebastian
2014-01-01
We evaluate the spectral dimension in causal set quantum gravity by simulating random walks on causal sets. In contrast to other approaches to quantum gravity, we find an increasing spectral dimension at small scales. This observation can be connected to the nonlocality of causal set theory that is deeply rooted in its fundamentally Lorentzian nature. Based on its large-scale behaviour, we conjecture that the spectral dimension can serve as a tool to distinguish causal sets that approximate manifolds from those that do not. As a new tool to probe quantum spacetime in different quantum gravity approaches, we introduce a novel dimensional estimator, the causal spectral dimension, based on the meeting probability of two random walkers, which respect the causal structure of the quantum spacetime. We discuss a causal-set example, where the spectral dimension and the causal spectral dimension differ, due to the existence of a preferred foliation. (paper)
Feynman propagator for spin foam quantum gravity.
Oriti, Daniele
2005-03-25
We link the notion causality with the orientation of the spin foam 2-complex. We show that all current spin foam models are orientation independent. Using the technology of evolution kernels for quantum fields on Lie groups, we construct a generalized version of spin foam models, introducing an extra proper time variable. We prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of quantum field theory (QFT) or as inner products between quantum gravity states; and a new class of causal models, the quantum gravity analogue of the Feynman propagator in QFT, nontrivial function of the orientation data, and implying a notion of "timeless ordering".
Decoherence in quantum gravity: issues and critiques
Energy Technology Data Exchange (ETDEWEB)
Anastopoulos, C [Department of Physics, University of Patras, 26500 Patras (Greece); Hu, B L [Department of Physics, University of Maryland, College Park, Maryland 20742-4111 (United States)
2007-05-15
An increasing number of papers have appeared in recent years on decoherence in quantum gravity at the Planck energy. We discuss the meaning of decoherence in quantum gravity starting from the common notion that quantum gravity is a theory for the microscopic structures of spacetime, and invoking some generic features of quantum decoherence from the open systems viewpoint. We dwell on a range of issues bearing on this process including the relation between statistical and quantum, noise from effective field theory, the meaning of stochasticity, the origin of non-unitarity and the nature of nonlocality in this and related contexts. To expound these issues we critique on two representative theories: One claims that decoherence in quantum gravity scale leads to the violation of CPT symmetry at sub-Planckian energy which is used to explain today's particle phenomenology. The other uses this process in place with the Brownian motion model to prove that spacetime foam behaves like a thermal bath. A companion paper will deal with intrinsic and fundamental decoherence which also bear on issues in classical and quantum gravity.
Decoherence in quantum gravity: issues and critiques
International Nuclear Information System (INIS)
Anastopoulos, C; Hu, B L
2007-01-01
An increasing number of papers have appeared in recent years on decoherence in quantum gravity at the Planck energy. We discuss the meaning of decoherence in quantum gravity starting from the common notion that quantum gravity is a theory for the microscopic structures of spacetime, and invoking some generic features of quantum decoherence from the open systems viewpoint. We dwell on a range of issues bearing on this process including the relation between statistical and quantum, noise from effective field theory, the meaning of stochasticity, the origin of non-unitarity and the nature of nonlocality in this and related contexts. To expound these issues we critique on two representative theories: One claims that decoherence in quantum gravity scale leads to the violation of CPT symmetry at sub-Planckian energy which is used to explain today's particle phenomenology. The other uses this process in place with the Brownian motion model to prove that spacetime foam behaves like a thermal bath. A companion paper will deal with intrinsic and fundamental decoherence which also bear on issues in classical and quantum gravity
Black Hole Interior in Quantum Gravity.
Nomura, Yasunori; Sanches, Fabio; Weinberg, Sean J
2015-05-22
We discuss the interior of a black hole in quantum gravity, in which black holes form and evaporate unitarily. The interior spacetime appears in the sense of complementarity because of special features revealed by the microscopic degrees of freedom when viewed from a semiclassical standpoint. The relation between quantum mechanics and the equivalence principle is subtle, but they are still consistent.
Quantum and gravity. Blend or melange?
Energy Technology Data Exchange (ETDEWEB)
Wuethrich, Christian [University of Geneva (Switzerland)
2016-07-01
Do we need to quantize gravity, as it is tacitly assumed in much of fundamental physics? The standard lore falls short of justifying an affirmative answer. Black hole thermodynamics is widely considered, faint though it may be, our firmest hint at a quantum theory of gravity - despite the failure to date to observe Hawking radiation or any other effect that would require going beyond a classical description of black holes. Hawking radiation hitherto merely enjoys a theoretical derivation in a semi-classical theory combining quantum matter with classical gravity. But how can a semi-classical melange of physical principles possibly justify that the quantum and gravity are blended into a unified fundamental theory when the latter is generally expected to reject at least some of the principles in the former?.
Canonical methods in classical and quantum gravity: An invitation to canonical LQG
Reyes, Juan D.
2018-04-01
Loop Quantum Gravity (LQG) is a candidate quantum theory of gravity still under construction. LQG was originally conceived as a background independent canonical quantization of Einstein’s general relativity theory. This contribution provides some physical motivations and an overview of some mathematical tools employed in canonical Loop Quantum Gravity. First, Hamiltonian classical methods are reviewed from a geometric perspective. Canonical Dirac quantization of general gauge systems is sketched next. The Hamiltonian formultation of gravity in geometric ADM and connection-triad variables is then presented to finally lay down the canonical loop quantization program. The presentation is geared toward advanced undergradute or graduate students in physics and/or non-specialists curious about LQG.
A 'general boundary' formulation for quantum mechanics and quantum gravity
International Nuclear Information System (INIS)
Oeckl, Robert
2003-01-01
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such 'general boundary' quantum theories through a generalized path integral quantization. I show how both, non-relativistic quantum mechanics and quantum field theory can be given a 'general boundary' formulation. Surprisingly, even in the non-relativistic case, features normally associated with quantum field theory emerge from consistency conditions. This includes states with arbitrary particle number and pair creation. I also note how three-dimensional quantum gravity is an example for a realization of both proposals and suggest to apply them to four-dimensional quantum gravity
Quantum chromodynamics as dynamics of loops
International Nuclear Information System (INIS)
Makeenko, Yu.; Migdal, A.A.
1980-01-01
The problem of a possibility of reformulating quantum chromodynamics (QCD) in terms of colourless composite fields instead of coloured quarks and gluons is considered. The role of such fields is played by the gauge invariant loop functionals. The Shwinger equations of motion is derived in the loop space which completely describe dynamics of the loop fields. New manifestly gauge invariant diagram technique in the loop space is developed. These diagrams reproduce asymptotic freedom in the ultraviolet range and are consistent with the confinement law in the infrared range
Invariant measure of the one-loop quantum gravitational backreaction on inflation
Miao, S. P.; Tsamis, N. C.; Woodard, R. P.
2017-06-01
We use dimensional regularization in pure quantum gravity on a de Sitter background to evaluate the one-loop expectation value of an invariant operator which gives the local expansion rate. We show that the renormalization of this nonlocal composite operator can be accomplished using the counterterms of a simple local theory of gravity plus matter, at least at one-loop order. This renormalization completely absorbs the one-loop correction, which accords with the prediction that the lowest secular backreaction should be a two-loop effect.
Physical renormalization schemes and asymptotic safety in quantum gravity
Falls, Kevin
2017-12-01
The methods of the renormalization group and the ɛ -expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ɛ -expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultraviolet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalizable.
Matter Loops Corrected Modified Gravity in Palatini Formulation
International Nuclear Information System (INIS)
Meng Xinhe; Wang Peng
2008-01-01
Recently, corrections to the standard Einstein-Hilbert action were proposed to explain the current cosmic acceleration in stead of introducing dark energy. In the Palatini formulation of those modified gravity models, there is an important observation due to Arkani-Hamed: matter loops will give rise to a correction to the modified gravity action proportional to the Ricci scalar of the metric. In the presence of such a term, we show that the current forms of modified gravity models in Palatini formulation, specifically, the 1/R gravity and ln R gravity, will have phantoms. Then we study the possible instabilities due to the presence of phantom fields. We show that the strong instability in the metric formulation of 1/R gravity indicated by Dolgov and Kawasaki will not appear and the decay timescales for the phantom fields may be long enough for the theories to make sense as effective field theory. On the other hand, if we change the sign of the modification terms to eliminate the phantoms, some other inconsistencies will arise for the various versions of the modified gravity models. Finally, we comment on the universal property of the Palatini formulation of the matter loops corrected modified gravity models and its implications
Discussion of entanglement entropy in quantum gravity
International Nuclear Information System (INIS)
Ma, Chen-Te
2018-01-01
We study entanglement entropy in gravity theory with quantum effects. A simplest model is a two dimensional Einstein gravity theory. We use an n-sheet manifold to obtain an area term of entanglement entropy by summing over all background fields. Based on AdS/CFT correspondence, strongly coupled conformal field theory is expected to describe perturbative quantum gravity theory. An ultraviolet complete quantum gravity theory should not depend on a choice of an entangling surface. To analysis the problem explicitly, we analyze two dimensional conformal field theory. We find that a coefficient of a universal term of entanglement entropy is independent of a choice of an entangling surface in two dimensional conformal field theory for one interval to show a tentative evidence. Finally, we discuss that translational invariance in a quantum system at zero temperature, size goes to infinity and no mass scales, except for cut-off, possibly be a necessary condition in quantum gravity theory by ruing out a volume law of entanglement entropy. (copyright 2018 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Effective spacetime understanding emergence in effective field theory and quantum gravity
Crowther, Karen
2016-01-01
This book discusses the notion that quantum gravity may represent the "breakdown" of spacetime at extremely high energy scales. If spacetime does not exist at the fundamental level, then it has to be considered "emergent", in other words an effective structure, valid at low energy scales. The author develops a conception of emergence appropriate to effective theories in physics, and shows how it applies (or could apply) in various approaches to quantum gravity, including condensed matter approaches, discrete approaches, and loop quantum gravity.
Chiral fermions in asymptotically safe quantum gravity.
Meibohm, J; Pawlowski, J M
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
International Nuclear Information System (INIS)
Govindarajan, T R; Kaul, R K; Suneeta, V
2002-01-01
We study quantum gravity on dS 3 using the Chern-Simons formulation of three-dimensional gravity. We derive an exact expression for the partition function for quantum gravity on dS 3 in a Euclidean path integral approach. We show that the topology of the space relevant for studying de Sitter entropy is a solid torus. The quantum fluctuations of de Sitter space are sectors of configurations of point masses taking a discrete set of values. The partition function gives the correct semiclassical entropy. The sub-leading correction to the entropy is logarithmic in horizon area, with a coefficient -1. We discuss this correction in detail, and show that the sub-leading correction to the entropy from the dS/CFT correspondence agrees with our result. A comparison with the corresponding results for the AdS 3 BTZ black hole is also presented
Flow and instability in quantum gravity
International Nuclear Information System (INIS)
Douglas, M.R.; Seiberg, N.; Shenker, S.H.
1990-01-01
We study the flow from the m=3 multicritical matrix theory, unambiguously defined by Brezin, Marinari and Parisi, to the m=2 pure gravity theory. We find behavior in the flow indicative of a non-perturbative instability in this definition of non-perturbative pure quantum gravity. We expect a similar situation for all m even theories. Other definitions of these theories are briefly discussed. (orig.)
3D quantum gravity and effective noncommutative quantum field theory.
Freidel, Laurent; Livine, Etera R
2006-06-09
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.
Quantum gravity and the renormalisation group
International Nuclear Information System (INIS)
Litim, D.
2011-01-01
The Standard Model of particle physics is remarkably successful in describing three out of the four known fundamental forces of Nature. But what is up with gravity? Attempts to understand quantum gravity on the same footing as the other forces still face problems. Some time ago, it has been pointed out that gravity may very well exist as a fundamental quantum field theory provided its high-energy behaviour is governed by a fixed point under the renormalisation group. In recent years, this 'asymptotic safety' scenario has found significant support thanks to numerous renormalisation group studies, lattice simulations, and new ideas within perturbation theory. The lectures will give an introduction into the renormalisation group approach for quantum gravity, aimed at those who haven't met the topic before. After an introduction and overview, the key ideas and concepts of asymptotic safety for gravity are fleshed out. Results for gravitational high-energy fixed points and scaling exponents are discussed as well as key features of the gravitational phase diagram. The survey concludes with some phenomenological implications of fixed point gravity including the physics of black holes and particle physics beyond the Standard Model. (author)
Random manifolds and quantum gravity
International Nuclear Information System (INIS)
Krzywicki, A.
2000-01-01
The non-perturbative, lattice field theory approach towards the quantization of Euclidean gravity is reviewed. Included is a tentative summary of the most significant results and a presentation of the current state of art
Prima facie questions in quantum gravity
Isham, C. J.
The long history of the study of quantum gravity has thrown up a complex web of ideas and approaches. The aim of this article is to unravel this web a little by analysing some of the {\\em prima facie\\/} questions that can be asked of almost any approach to quantum gravity and whose answers assist in classifying the different schemes. Particular emphasis is placed on (i) the role of background conceptual and technical structure; (ii) the role of spacetime diffeomorphisms; and (iii) the problem of time.
No chiral truncation of quantum log gravity?
Andrade, Tomás; Marolf, Donald
2010-03-01
At the classical level, chiral gravity may be constructed as a consistent truncation of a larger theory called log gravity by requiring that left-moving charges vanish. In turn, log gravity is the limit of topologically massive gravity (TMG) at a special value of the coupling (the chiral point). We study the situation at the level of linearized quantum fields, focussing on a unitary quantization. While the TMG Hilbert space is continuous at the chiral point, the left-moving Virasoro generators become ill-defined and cannot be used to define a chiral truncation. In a sense, the left-moving asymptotic symmetries are spontaneously broken at the chiral point. In contrast, in a non-unitary quantization of TMG, both the Hilbert space and charges are continuous at the chiral point and define a unitary theory of chiral gravity at the linearized level.
A new quantum representation for canonical gravity and SU(2) Yang-Mills theory
International Nuclear Information System (INIS)
Loll, R.
1990-04-01
Starting from Rovelli-Smolin's infinite-dimensional graded Poisson-bracket algebra of loop variables, we propose a new way of constructing a corresponding quantum representation. After eliminating certain quadratic constraints, we 'integrate' an infinite-dimensional subalgebra of loop variables, using a formal group law expansion. With the help of techniques from the representation theory of semidirect-product groups, we find an exact quantum representation of the full classical Poisson-bracket algebra of loop variables, without any higher-order correction terms. This opens new ways of tackling the quantum dynamics for both canonical gravity and Yang-Mills theory. (orig.)
A new quantum representation for canonical gravity and SU(2) Yang-Mills theory
International Nuclear Information System (INIS)
Loll, R.
1991-01-01
Starting from Rovelli-Smolin's infinite-dimensional graded Poisson-bracket algebra of loop variables, we propose a new way of constructing a corresponding quantum representation. After eliminating certain quadratic constraints, we 'integrate' an infinite-dimensional subalgebra of loop variables, using a formal group law expansion. With the help of techniques from the representation theory of semidirect-product groups, we find an exact quantum representation of the full classical Poisson-bracket algebra of loop variables, without any higher-order correction terms. This opens new ways of tackling the quantum dynamics for both canonical gravity and Yang-Mills theory. (orig.)
Critical behaviors of gravity under quantum perturbations
Directory of Open Access Journals (Sweden)
ZHANG Hongsheng
2014-02-01
Full Text Available Phase transition and critical phenomenon is a very interesting topic in thermodynamics and statistical mechanics. Gravity is believed to have deep and inherent relation to thermodynamics. Near the critical point,the perturbation becomes significant. Thus for ordinary matter (governed by interactions besides gravity the critical behavior will become very different if we ignore the perturbations around the critical point,such as mean field theory. We find that the critical exponents for RN-AdS spacetime keep the same values even when we consider the full quantum perturbations. This indicates a key difference between gravity and ordinary thermodynamic system.
Gauge and Gravity Amplitudes from Trees to Loops
DEFF Research Database (Denmark)
Huang, Rijun
This thesis describes two subjects that I mainly work on during my PhD study. They are both about scattering amplitudes, covering gravity and gauge theories, tree and loop level, with or without supersymmetry. The rst subject is Kawai-Lewellen-Tye(KLT) relation in field theory, which mysteriously...
Pressure Profiles in a Loop Heat Pipe under Gravity Influence
Ku, Jentung
2015-01-01
During the operation of a loop heat pipe (LHP), the viscous flow induces pressure drops in various elements of the loop. The total pressure drop is equal to the sum of pressure drops in vapor grooves, vapor line, condenser, liquid line and primary wick, and is sustained by menisci at liquid and vapor interfaces on the outer surface of the primary wick in the evaporator. The menisci will curve naturally so that the resulting capillary pressure matches the total pressure drop. In ground testing, an additional gravitational pressure head may be present and must be included in the total pressure drop when LHP components are placed in a non-planar configuration. Under gravity-neutral and anti-gravity conditions, the fluid circulation in the LHP is driven solely by the capillary force. With gravity assist, however, the flow circulation can be driven by the combination of capillary and gravitational forces, or by the gravitational force alone. For a gravity-assist LHP at a given elevation between the horizontal condenser and evaporator, there exists a threshold heat load below which the LHP operation is gravity driven and above which the LHP operation is capillary force and gravity co-driven. The gravitational pressure head can have profound effects on the LHP operation, and such effects depend on the elevation, evaporator heat load, and condenser sink temperature. This paper presents a theoretical study on LHP operations under gravity-neutral, anti-gravity, and gravity-assist modes using pressure diagrams to help understand the underlying physical processes. Effects of the condenser configuration on the gravitational pressure head and LHP operation are also discussed.
Testing quantum gravity through dumb holes
Energy Technology Data Exchange (ETDEWEB)
Pourhassan, Behnam, E-mail: b.pourhassan@du.ac.ir [School of Physics, Damghan University, Damghan (Iran, Islamic Republic of); Faizal, Mir, E-mail: f2mir@uwaterloo.ca [Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB T1K 3M4 (Canada); Irving K. Barber School of Arts and Sciences, University of British Columbia - Okanagan, Kelowna, BC V1V 1V7 (Canada); Capozziello, Salvatore, E-mail: capozzie@na.infn.it [Dipartimento di Fisica, Università di Napoli ”Frederico II” Complesso Universitario di Monte S. Angelo, Edificio G, Via Cinthia, I-80126 Napoli (Italy); Gran Sasso Science Institute (INFN), Via F. Crispi 7, I-67100 L’ Aquila (Italy)
2017-02-15
We propose a method to test the effects of quantum fluctuations on black holes by analyzing the effects of thermal fluctuations on dumb holes, the analogs for black holes. The proposal is based on the Jacobson formalism, where the Einstein field equations are viewed as thermodynamical relations, and so the quantum fluctuations are generated from the thermal fluctuations. It is well known that all approaches to quantum gravity generate logarithmic corrections to the entropy of a black hole and the coefficient of this term varies according to the different approaches to the quantum gravity. It is possible to demonstrate that such logarithmic terms are also generated from thermal fluctuations in dumb holes. In this paper, we claim that it is possible to experimentally test such corrections for dumb holes, and also obtain the correct coefficient for them. This fact can then be used to predict the effects of quantum fluctuations on realistic black holes, and so it can also be used, in principle, to experimentally test the different approaches to quantum gravity.
In the Beginning Was Quantum Gravity.
Thomsen, Dietrick E.
1983-01-01
Cosmology is the theory by which the structure and history of the universe is described. Discusses the relationship between cosmology, gravity, and quantum mechanics, and whether the relationship can be formulated through Einstein's theory or a modification of it. Also discusses progress made in these scientific areas. (JN)
Conformal constraint in canonical quantum gravity
t Hooft, G.
2010-01-01
Perturbative canonical quantum gravity is considered, when coupled to a renormalizable model for matter fields. It is proposed that the functional integral over the dilaton field should be disentangled from the other integrations over the metric fields. This should generate a conformally invariant
Canonical quantum gravity and consistent discretizations
Indian Academy of Sciences (India)
Abstract. This paper covers some developments in canonical quantum gravity that ... derstanding the real Ashtekar variables four dimensionally [4], or the recent work ... Traditionally, canonical formulations of general relativity considered as canonical variables the metric on a spatial slice qab and a canonically conjugate.
Black holes, strings and quantum gravity
International Nuclear Information System (INIS)
Maldacena, Juan
2001-01-01
Most physical phenomena can be explained by 'Quantum Mechanics' and 'Einstein Theory of Gravity'. Quantum mechanics is needed for descriptions involving small objects (atoms, nuclei, molecules, etc.) whereas gravity is required for understanding big objects (planets, galaxies). Since, usually small objects are light while big ones are heavy, when one theory is called for, the other is not relevant. Interestingly enough, if we pretend to use both theories simultaneously, for instance when small and very heavy objects are considered (as those in the beginning of our universe), we find that they are mutually inconsistent. Thus, a new theory, so called 'Quantum Gravity', is needed. This works comments on above inconsistencies and indicates how the string theory, rather than a pointlike particle theory, could provide us with a quantum theory of gravity. Though a discussion of black holes it shows us how a string theory on certain space, ca be equivalently described by a particle theory on its boundary, like a sort of hologram. (author)
Stochastic quantum gravity-(2+1)-dimensional case
International Nuclear Information System (INIS)
Hosoya, Akio
1991-01-01
At first the amazing coincidences are pointed out in quantum field theory in curved space-time and quantum gravity, when they exhibit stochasticity. To explore the origin of them, the (2+1)-dimensional quantum gravity is considered as a toy model. It is shown that the torus universe in the (2+1)-dimensional quantum gravity is a quantum chaos in a rigorous sense. (author). 15 refs
Quantum gravito-optics: a light route from semiclassical gravity to quantum gravity
International Nuclear Information System (INIS)
Unnikrishnan, C S; Gillies, George T
2015-01-01
Quantum gravity remains an elusive theory, in spite of our thorough understanding of the quantum theory and the general theory of relativity separately, presumably due to the lack of any observational clues. We argue that the theory of quantum gravity has a strong constraining anchor in the sector of gravitational radiation, ensuring reliable physical clues, albeit in a limited observable form. In particular, all types of gravitational waves expected to be observable in LIGO-like advanced detectors are fully quantum mechanical states of radiation. Exact equivalence of the full quantum gravity theory with the familiar semiclassical theory is ensured in the radiation sector, in most real situations where the relevant quantum operator functions are normal ordered, by the analogue of the optical equivalence theorem in quantum optics. We show that this is indeed the case for the detection of the waves from a massive binary system, a single gravitational atom, that emits coherent radiation. The idea of quantum-gravitational optics can assist in guiding along the fuzzy roads to quantum gravity. (paper)
Generalized uncertainty principle and quantum gravity phenomenology
Bosso, Pasquale
The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification in a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical physics. Quantum Gravity Phenomenology (QGP) studies QG effects in low-energy systems. The basis of one such phenomenological model is the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg uncertainty relation and predicts a deformed canonical commutator. In this thesis, we compute Planck-scale corrections to angular momentum eigenvalues, the hydrogen atom spectrum, the Stern-Gerlach experiment, and the Clebsch-Gordan coefficients. We then rigorously analyze the GUP-perturbed harmonic oscillator and study new coherent and squeezed states. Furthermore, we introduce a scheme for increasing the sensitivity of optomechanical experiments for testing QG effects. Finally, we suggest future projects that may potentially test QG effects in the laboratory.
One-loop partition functions of 3D gravity
International Nuclear Information System (INIS)
Giombi, Simone; Yin Xi; Maloney, Alexander
2008-01-01
We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and graviton excitations are computed explicitly using heat kernel techniques. We obtain precisely the result anticipated by Brown and Henneaux: the partition function includes a sum over 'boundary excitations' of AdS 3 , which are the Virasoro descendants of empty Anti-de Sitter space. This result also allows us to compute the one-loop corrections to the Euclidean action of the BTZ black hole as well its higher genus generalizations.
Minimal Length Scale Scenarios for Quantum Gravity.
Hossenfelder, Sabine
2013-01-01
We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize what can be learned from different approaches to a theory of quantum gravity. Then we discuss some models that have been developed to implement a minimal length scale in quantum mechanics and quantum field theory. These models have entered the literature as the generalized uncertainty principle or the modified dispersion relation, and have allowed the study of the effects of a minimal length scale in quantum mechanics, quantum electrodynamics, thermodynamics, black-hole physics and cosmology. Finally, we touch upon the question of ways to circumvent the manifestation of a minimal length scale in short-distance physics.
Minimal Length Scale Scenarios for Quantum Gravity
Directory of Open Access Journals (Sweden)
Sabine Hossenfelder
2013-01-01
Full Text Available We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize what can be learned from different approaches to a theory of quantum gravity. Then we discuss some models that have been developed to implement a minimal length scale in quantum mechanics and quantum field theory. These models have entered the literature as the generalized uncertainty principle or the modified dispersion relation, and have allowed the study of the effects of a minimal length scale in quantum mechanics, quantum electrodynamics, thermodynamics, black-hole physics and cosmology. Finally, we touch upon the question of ways to circumvent the manifestation of a minimal length scale in short-distance physics.
Perturbative Quantum Gravity and its Relation to Gauge Theory
Directory of Open Access Journals (Sweden)
Bern Zvi
2002-01-01
Full Text Available In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on $D$-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input thegravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.
Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators.
Belenchia, Alessio; Benincasa, Dionigi M T; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2016-04-22
Several quantum gravity scenarios lead to physics below the Planck scale characterized by nonlocal, Lorentz invariant equations of motion. We show that such nonlocal effective field theories lead to a modified Schrödinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of optomechanical quantum oscillators is characterized by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the nonlocality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.
Unitarity bounds on low scale quantum gravity
International Nuclear Information System (INIS)
Atkins, Michael; Calmet, Xavier
2010-01-01
We study the unitarity of models with low scale quantum gravity both in four dimensions and in models with a large extra-dimensional volume. We find that models with low scale quantum gravity have problems with unitarity below the scale at which gravity becomes strong. An important consequence of our work is that their first signal at the Large Hadron Collider would not be of a gravitational nature such as graviton emission or small black holes, but rather would be linked to the mechanism which fixes the unitarity problem. We also study models with scalar fields with non-minimal couplings to the Ricci scalar. We consider the strength of gravity in these models and study the consequences for inflation models with non-minimally coupled scalar fields. We show that a single scalar field with a large non-minimal coupling can lower the Planck mass in the TeV region. In that model, it is possible to lower the scale at which gravity becomes strong down to 14 TeV without violating unitarity below that scale. (orig.)
Wilson loops, instantons and quantum mechanics
International Nuclear Information System (INIS)
Schiereck, Marc
2014-05-01
In this thesis we examine two different problems. The first is the computation of vacuum expectation values of Wilson loop operators in ABJM theory, the other problem is finding the instanton series of the refined topological string on certain local Calabi-Yau geometries in the Nekrasov-Shatashvili limit. Based on the description of ABJM theory as a matrix model, it is possible to find a description of it in terms of an ideal Fermi gas with a non-trivial one-particle Hamiltonian. The vacuum-expectation-values of Wilson loop operators in ABJM theory correspond to averages of operators in the statistical-mechanical problem. Using the WKB expansion, it is possible to extract the full 1/N expansion of the vevs, up to exponentially small contributions, for arbitrary Chern-Simons coupling. We compute these vevs for the 1/6 and 1/2 BPS Wilson loops at any winding number. These can be written in terms of the Airy function. The expressions we found reproduce the low genus results previously obtained in the 't Hooft expansion. In another problem we use mirror symmetry, quantum geometry and modularity properties of elliptic curves to calculate the refined free energies, given in terms of an instanton sum, in the Nekrasov-Shatashvili limit on non-compact toric Calabi-Yau manifolds, based on del Pezzo surfaces. Quantum geometry here is to be understood as a quantum deformed version of rigid special geometry, which has its origin in the quantum mechanical behavior of branes in the topological string B-model. We argue that in the Seiberg-Witten picture only the Coulomb parameters lead to quantum corrections, while the mass parameters remain uncorrected. In certain cases we also compute the expansion of the free energies at the orbifold point and the conifold locus. We compute the quantum corrections order by order on ℎ by deriving second order differential operators, which act on the classical periods.
Quantum Gravity Gradiometer Development for Space
Kohel, James M.; Yu, Nan; Kellogg, James R.; Thompson, Robert J.; Aveline, David C.; Maleki, Lute
2006-01-01
Funded by the Advanced Technology Component Program, we have completed the development of a laboratory-based quantum gravity gradiometer based on atom interferometer technology. This is our first step towards a new spaceborne gradiometer instrument, which can significantly contribute to global gravity mapping and monitoring important in the understanding of the solid earth, ice and oceans, and dynamic processes. In this paper, we will briefly review the principles and technical benefits of atom-wave interferometer-based inertial sensors in space. We will then describe the technical implementation of the laboratory setup and report its status. We will also discuss our implementation plan for the next generation instrument.
Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations
International Nuclear Information System (INIS)
Stottmeister, Alexander; Thiemann, Thomas
2016-01-01
This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).
Observational constraints on loop quantum cosmology.
Bojowald, Martin; Calcagni, Gianluca; Tsujikawa, Shinji
2011-11-18
In the inflationary scenario of loop quantum cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to compare with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background and other cosmological experiments, we place bounds on the quantum corrections.
Quantum light in coupled interferometers for quantum gravity tests.
Ruo Berchera, I; Degiovanni, I P; Olivares, S; Genovese, M
2013-05-24
In recent years quantum correlations have received a lot of attention as a key ingredient in advanced quantum metrology protocols. In this Letter we show that they provide even larger advantages when considering multiple-interferometer setups. In particular, we demonstrate that the use of quantum correlated light beams in coupled interferometers leads to substantial advantages with respect to classical light, up to a noise-free scenario for the ideal lossless case. On the one hand, our results prompt the possibility of testing quantum gravity in experimental configurations affordable in current quantum optics laboratories and strongly improve the precision in "larger size experiments" such as the Fermilab holometer; on the other hand, they pave the way for future applications to high precision measurements and quantum metrology.
Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity
Veraguth, Olivier J.; Wang, Charles H.-T.
2017-10-01
Conformal loop quantum gravity provides an approach to loop quantization through an underlying conformal structure i.e. conformally equivalent class of metrics. The property that general relativity itself has no conformal invariance is reinstated with a constrained scalar field setting the physical scale. Conformally equivalent metrics have recently been shown to be amenable to loop quantization including matter coupling. It has been suggested that conformal geometry may provide an extended symmetry to allow a reformulated Immirzi parameter necessary for loop quantization to behave like an arbitrary group parameter that requires no further fixing as its present standard form does. Here, we find that this can be naturally realized via conformal frame transformations in scalar-tensor gravity. Such a theory generally incorporates a dynamical scalar gravitational field and reduces to general relativity when the scalar field becomes a pure gauge. In particular, we introduce a conformal Einstein frame in which loop quantization is implemented. We then discuss how different Immirzi parameters under this description may be related by conformal frame transformations and yet share the same quantization having, for example, the same area gaps, modulated by the scalar gravitational field.
The Asymptotic Safety Scenario in Quantum Gravity.
Niedermaier, Max; Reuter, Martin
2006-01-01
The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.
The Asymptotic Safety Scenario in Quantum Gravity
Directory of Open Access Journals (Sweden)
Niedermaier Max
2006-12-01
Full Text Available The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.
One-loop renormalization of a gravity-scalar system
Energy Technology Data Exchange (ETDEWEB)
Park, I.Y. [Philander Smith College, Department of Applied Mathematics, Little Rock, AR (United States)
2017-05-15
Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the ''mass'' term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information. (orig.)
One-loop renormalization of a gravity-scalar system
International Nuclear Information System (INIS)
Park, I.Y.
2017-01-01
Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the ''mass'' term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information. (orig.)
One-loop renormalization of a gravity-scalar system
Park, I. Y.
2017-05-01
Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the "mass" term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information.
Universal Property of Quantum Gravity implied by Bekenstein-Hawking Entropy and Boltzmann formula
International Nuclear Information System (INIS)
Saida, Hiromi
2013-01-01
We search for a universal property of quantum gravity. By u niversal , we mean the independence from any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on). To do so, we try to put the basis of our discussion on theories established by some experiments. Thus, we focus our attention on thermodynamical and statistical-mechanical basis of the black hole thermodynamics: Let us assume that the Bekenstein-Hawking entropy is given by the Boltzmann formula applied to the underlying theory of quantum gravity. Under this assumption, the conditions justifying Boltzmann formula together with uniqueness of Bekenstein-Hawking entropy imply a reasonable universal property of quantum gravity. The universal property indicates a repulsive gravity at Planck length scale, otherwise stationary black holes can not be regarded as thermal equilibrium states of gravity. Further, in semi-classical level, we discuss a possible correction of Einstein equation which generates repulsive gravity at Planck length scale.
Information theory, spectral geometry, and quantum gravity.
Kempf, Achim; Martin, Robert
2008-01-18
We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well-known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.
The action uncertainty principle and quantum gravity
Mensky, Michael B.
1992-02-01
Results of the path-integral approach to the quantum theory of continuous measurements have been formulated in a preceding paper in the form of an inequality of the type of the uncertainty principle. The new inequality was called the action uncertainty principle, AUP. It was shown that the AUP allows one to find in a simple what outputs of the continuous measurements will occur with high probability. Here a more simple form of the AUP will be formulated, δ S≳ħ. When applied to quantum gravity, it leads in a very simple way to the Rosenfeld inequality for measurability of the average curvature.
Scaling solutions for dilaton quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Henz, T.; Pawlowski, J.M., E-mail: j.pawlowski@thphys.uni-heidelberg.de; Wetterich, C.
2017-06-10
Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between scalar field and renormalization scale k is varied. In the Einstein frame the quantum effective action corresponding to the scaling solutions becomes independent of k. The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity.
Varying constants, black holes, and quantum gravity
International Nuclear Information System (INIS)
Carlip, S.
2003-01-01
Tentative observations and theoretical considerations have recently led to renewed interest in models of fundamental physics in which certain 'constants' vary in time. Assuming fixed black hole mass and the standard form of the Bekenstein-Hawking entropy, Davies, Davis and Lineweaver have argued that the laws of black hole thermodynamics disfavor models in which the fundamental electric charge e changes. I show that with these assumptions, similar considerations severely constrain 'varying speed of light' models, unless we are prepared to abandon cherished assumptions about quantum gravity. Relaxation of these assumptions permits sensible theories of quantum gravity with ''varying constants,'' but also eliminates the thermodynamic constraints, though the black hole mass spectrum may still provide some restrictions on the range of allowable models
Proceeding of the workshop on quantum gravity and topology
International Nuclear Information System (INIS)
Oda, Ichiro
1991-10-01
The workshop on Quantum Gravity and Topology was held at INS on February 21-23, 1991. Several introductory lectures and more than 15 talks were delivered for about 100 participants. The main subjects discussed were i) Topological quantum field theories and topological gravity ii) Low dimensional and four dimensional gravity iii) Topology change iv) Superstring theories etc. (J.P.N.)
Black-hole horizons in modified spacetime structures arising from canonical quantum gravity
International Nuclear Information System (INIS)
Bojowald, Martin; Paily, George M; Reyes, Juan D; Tibrewala, Rakesh
2011-01-01
Several properties of canonical quantum gravity modify spacetime structures, sometimes to the degree that no effective line elements exist to describe the geometry. An analysis of solutions, for instance in the context of black holes, then requires new insights. In this paper, standard definitions of horizons in spherical symmetry are first reformulated canonically, and then evaluated for solutions of equations and constraints modified by inverse-triad corrections of loop quantum gravity. When possible, a spacetime analysis is performed which reveals a mass threshold for black holes and small changes to Hawking radiation. For more general conclusions, canonical perturbation theory is developed to second order to include back-reaction from matter. The results shed light on the questions of whether renormalization of Newton's constant or other modifications of horizon conditions should be taken into account in computations of black-hole entropy in loop quantum gravity.
Quantum fluctuations and spontaneous compactification of eleven-dimensional gravity
International Nuclear Information System (INIS)
Nguen Van Hieu.
1985-01-01
The reduction of the eleven-dimensional pure gravity to the field theory in the four-dimensional Minkowski space-time by means of the spontaneous compactification of the extra dimensions is investigated. The contribution of the quantum fluctuations of the eleven-dimen-- sonal second rank symmetric tensor field to the curvatures of the space-time and the compactified space of the extra dimensions are calculated in the one-loop approximation. It is shown that there exist the values of the cosmological constant for which tachions are absent. As a result, self-consistent quantum field theory is obtained in spontaneous compactified Minkowski space M 4 xS 7 ,is where M 4 is Minkowski space-time, and S 7 is seven-dimensional sphere
Fate of the Hoop Conjecture in Quantum Gravity.
Anzà, Fabio; Chirco, Goffredo
2017-12-08
We consider a closed region R of 3D quantum space described via SU(2) spin networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary ∂R and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interpret such phenomenon as a pregeometric analogue of Thorne's "hoop conjecture," at the core of the formation of a horizon in general relativity.
Higgs inflation and quantum gravity: an exact renormalisation group approach
International Nuclear Information System (INIS)
Saltas, Ippocratis D.
2016-01-01
We use the Wilsonian functional Renormalisation Group (RG) to study quantum corrections for the Higgs inflationary action including the effect of gravitons, and analyse the leading-order quantum gravitational corrections to the Higgs' quartic coupling, as well as its non-minimal coupling to gravity and Newton's constant, at the inflationary regime and beyond. We explain how within this framework the effect of Higgs and graviton loops can be sufficiently suppressed during inflation, and we also place a bound on the corresponding value of the infrared RG cut-off scale during inflation. Finally, we briefly discuss the potential embedding of the model within the scenario of Asymptotic Safety, while all main equations are explicitly presented
Cosmological perturbation theory and quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Brunetti, Romeo [Dipartimento di Matematica, Università di Trento,Via Sommarive 14, 38123 Povo TN (Italy); Fredenhagen, Klaus [II Institute für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Hack, Thomas-Paul [Institute für Theoretische Physik, Universität Leipzig,Brüderstr. 16, 04103 Leipzig (Germany); Pinamonti, Nicola [Dipartimento di Matematica, Università di Genova,Via Dodecaneso 35, 16146 Genova (Italy); INFN, Sezione di Genova,Via Dodecaneso 33, 16146 Genova (Italy); Rejzner, Katarzyna [Department of Mathematics, University of York,Heslington, York YO10 5DD (United Kingdom)
2016-08-04
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
New variables for classical and quantum gravity
Ashtekar, Abhay
1986-01-01
A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced. These variables simplify the constraints of general relativity considerably and enable one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory. The imbedding suggests new ways of attacking a number of problems in both classical and quantum gravity. Some illustrative applications are discussed.
Quantum gravity signals in neutrino oscillations
International Nuclear Information System (INIS)
Sprenger, M.; Nicolini, P.; Bleicher, M.
2011-01-01
We investigate the effect of a Quantum Gravity-induced minimal length on neutrino oscillations. The minimal length is implemented in a phenomenological framework, allowing us to make predictions independently of any fundamental approach. We obtain clear minimal length signatures and discuss their observability in current and future experiments. We present an overview over other scenarios in which the minimal length leaves its signature and show new results concerning minimal length thermodynamics. (author)
Bouncing cosmologies from quantum gravity condensates
Oriti, Daniele; Sindoni, Lorenzo; Wilson-Ewing, Edward
2017-02-01
We show how the large-scale cosmological dynamics can be obtained from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.
Superrenormalizable quantum gravity with complex ghosts
Energy Technology Data Exchange (ETDEWEB)
Modesto, Leonardo, E-mail: lmodesto@fudan.edu.cn [Department of Physics & Center for Field Theory and Particle Physics, Fudan University, 200433, Shanghai (China); Shapiro, Ilya L., E-mail: shapiro@fisica.ufjf.br [Departamento de Fisica – ICE, Universidade Federal de Juiz de Fora, 33036-900 Juiz de Fora, Minas Gerais (Brazil); Tomsk State Pedagogical University and Tomsk State University, 634041, Tomsk (Russian Federation)
2016-04-10
We suggest and briefly review a new sort of superrenormalizable models of higher derivative quantum gravity. The higher derivative terms in the action can be introduced in such a way that all the unphysical massive states have complex poles. According to the literature on Lee–Wick quantization, in this case the theory can be formulated as unitary, since all massive ghosts-like degrees of freedom are unstable.
Towards quantum gravity via quantum field theory. Problems and perspectives
Energy Technology Data Exchange (ETDEWEB)
Fredenhagen, Klaus [II. Institut fuer Theoretische Physik, Universitaet Hamburg (Germany)
2016-07-01
General Relativity is a classical field theory; the standard methods for constructing a corresponding quantum field theory, however, meet severe difficulties, in particular perturbative non-renormalizability and the problem of background independence. Nevertheless, modern approaches to quantum field theory have significantly lowered these obstacles. On the side of non-renormalizability, this is the concept of effective theories, together with indications for better non-perturbative features of the renormalization group flow. On the side of background independence the main progress comes from an improved understanding of quantum field theories on generic curved spacetimes. Combining these informations, a promising approach to quantum gravity is an expansion around a classical solution which then is a quantum field theory on a given background, augmented by an identity which expresses independence against infinitesimal shifts of the background. The arising theory is expected to describe small corrections to classical general relativity. Inflationary cosmology is expected to arise as a lowest order approximation.
A lattice approach to spinorial quantum gravity
Renteln, Paul; Smolin, Lee
1989-01-01
A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.
Entropic Phase Maps in Discrete Quantum Gravity
Directory of Open Access Journals (Sweden)
Benjamin F. Dribus
2017-06-01
Full Text Available Path summation offers a flexible general approach to quantum theory, including quantum gravity. In the latter setting, summation is performed over a space of evolutionary pathways in a history configuration space. Discrete causal histories called acyclic directed sets offer certain advantages over similar models appearing in the literature, such as causal sets. Path summation defined in terms of these histories enables derivation of discrete Schrödinger-type equations describing quantum spacetime dynamics for any suitable choice of algebraic quantities associated with each evolutionary pathway. These quantities, called phases, collectively define a phase map from the space of evolutionary pathways to a target object, such as the unit circle S 1 ⊂ C , or an analogue such as S 3 or S 7 . This paper explores the problem of identifying suitable phase maps for discrete quantum gravity, focusing on a class of S 1 -valued maps defined in terms of “structural increments” of histories, called terminal states. Invariants such as state automorphism groups determine multiplicities of states, and induce families of natural entropy functions. A phase map defined in terms of such a function is called an entropic phase map. The associated dynamical law may be viewed as an abstract combination of Schrödinger’s equation and the second law of thermodynamics.
Three-dimensional simplicial quantum gravity and generalized matrix models
International Nuclear Information System (INIS)
Ambjoern, J.; Durhuus, B.; Jonsson, T.
1990-11-01
We consider a discrete model of Euclidean quantum gravity in three dimensions based on a summation over random simplicial manifolds. We derive some elementary properties of the model and discuss possible 'matrix' models for 3d gravity. (orig.)
Nonsingular cosmology from evolutionary quantum gravity
Cianfrani, Francesco; Montani, Giovanni; Pittorino, Fabrizio
2014-11-01
We provide a cosmological implementation of the evolutionary quantum gravity, describing an isotropic Universe, in the presence of a negative cosmological constant and a massive (preinflationary) scalar field. We demonstrate that the considered Universe has a nonsingular quantum behavior, associated to a primordial bounce, whose ground state has a high occupation number. Furthermore, in such a vacuum state, the super-Hamiltonian eigenvalue is negative, corresponding to a positive emerging dust energy density. The regularization of the model is performed via a polymer quantum approach to the Universe scale factor and the proper classical limit is then recovered, in agreement with a preinflationary state of the Universe. Since the dust energy density is redshifted by the Universe de Sitter phase and the cosmological constant does not enter the ground state eigenvalue, we get a late-time cosmology, compatible with the present observations, endowed with a turning point in the far future.
Consistent probabilities in loop quantum cosmology
International Nuclear Information System (INIS)
Craig, David A; Singh, Parampreet
2013-01-01
A fundamental issue for any quantum cosmological theory is to specify how probabilities can be assigned to various quantum events or sequences of events such as the occurrence of singularities or bounces. In previous work, we have demonstrated how this issue can be successfully addressed within the consistent histories approach to quantum theory for Wheeler–DeWitt-quantized cosmological models. In this work, we generalize that analysis to the exactly solvable loop quantization of a spatially flat, homogeneous and isotropic cosmology sourced with a massless, minimally coupled scalar field known as sLQC. We provide an explicit, rigorous and complete decoherent-histories formulation for this model and compute the probabilities for the occurrence of a quantum bounce versus a singularity. Using the scalar field as an emergent internal time, we show for generic states that the probability for a singularity to occur in this model is zero, and that of a bounce is unity, complementing earlier studies of the expectation values of the volume and matter density in this theory. We also show from the consistent histories point of view that all states in this model, whether quantum or classical, achieve arbitrarily large volume in the limit of infinite ‘past’ or ‘future’ scalar ‘time’, in the sense that the wave function evaluated at any arbitrary fixed value of the volume vanishes in that limit. Finally, we briefly discuss certain misconceptions concerning the utility of the consistent histories approach in these models. (paper)
Inhomogenous loop quantum cosmology with matter
International Nuclear Information System (INIS)
Martín-de Bias, D; Mena Marugán, G A; Martín-Benito, M
2012-01-01
The linearly polarized Gowdy T 3 model with a massless scalar field with the same symmetries as the metric is quantized by applying a hybrid approach. The homogeneous geometry degrees of freedom are loop quantized, fact which leads to the resolution of the cosmological singularity, while a Fock quantization is employed for both matter and gravitational inhomogeneities. Owing to the inclusion of the massless scalar field this system allows us to modelize flat Friedmann-Robertson-Walker cosmologies filled with inhomogeneities propagating in one direction. It provides a perfect scenario to study the quantum back-reaction between the inhomogeneities and the polymeric homogeneous and isotropic background.
Husain, Viqar
2012-03-01
Research on quantum gravity from a non-perturbative 'quantization of geometry' perspective has been the focus of much research in the past two decades, due to the Ashtekar-Barbero Hamiltonian formulation of general relativity. This approach provides an SU(2) gauge field as the canonical configuration variable; the analogy with Yang-Mills theory at the kinematical level opened up some research space to reformulate the old Wheeler-DeWitt program into what is now known as loop quantum gravity (LQG). The author is known for his work in the LQG approach to cosmology, which was the first application of this formalism that provided the possibility of exploring physical questions. Therefore the flavour of the book is naturally informed by this history. The book is based on a set of graduate-level lectures designed to impart a working knowledge of the canonical approach to gravitation. It is more of a textbook than a treatise, unlike three other recent books in this area by Kiefer [1], Rovelli [2] and Thiemann [3]. The style and choice of topics of these authors are quite different; Kiefer's book provides a broad overview of the path integral and canonical quantization methods from a historical perspective, whereas Rovelli's book focuses on philosophical and formalistic aspects of the problems of time and observables, and gives a development of spin-foam ideas. Thiemann's is much more a mathematical physics book, focusing entirely on the theory of representing constraint operators on a Hilbert space and charting a mathematical trajectory toward a physical Hilbert space for quantum gravity. The significant difference from these books is that Bojowald covers mainly classical topics until the very last chapter, which contains the only discussion of quantization. In its coverage of classical gravity, the book has some content overlap with Poisson's book [4], and with Ryan and Shepley's older work on relativistic cosmology [5]; for instance the contents of chapter five of the
Quantum gravity at a Lifshitz point
International Nuclear Information System (INIS)
Horava, Petr
2009-01-01
We present a candidate quantum field theory of gravity with dynamical critical exponent equal to z=3 in the UV. (As in condensed-matter systems, z measures the degree of anisotropy between space and time.) This theory, which at short distances describes interacting nonrelativistic gravitons, is power-counting renormalizable in 3+1 dimensions. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory flows naturally to the relativistic value z=1, and could therefore serve as a possible candidate for a UV completion of Einstein's general relativity or an infrared modification thereof. The effective speed of light, the Newton constant and the cosmological constant all emerge from relevant deformations of the deeply nonrelativistic z=3 theory at short distances.
Palatini actions and quantum gravity phenomenology
International Nuclear Information System (INIS)
Olmo, Gonzalo J.
2011-01-01
We show that an invariant an universal length scale can be consistently introduced in a generally covariant theory through the gravitational sector using the Palatini approach. The resulting theory is able to capture different aspects of quantum gravity phenomenology in a single framework. In particular, it is found that in this theory field excitations propagating with different energy-densities perceive different background metrics, which is a fundamental characteristic of the DSR and Rainbow Gravity approaches. We illustrate these properties with a particular gravitational model and explicitly show how the soccer ball problem is avoided in this framework. The isotropic and anisotropic cosmologies of this model also avoid the big bang singularity by means of a big bounce
Palatini actions and quantum gravity phenomenology
Energy Technology Data Exchange (ETDEWEB)
Olmo, Gonzalo J., E-mail: gonzalo.olmo@csic.es [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia - CSIC, Facultad de Física, Universidad de Valencia, Burjassot-46100, Valencia (Spain)
2011-10-01
We show that an invariant an universal length scale can be consistently introduced in a generally covariant theory through the gravitational sector using the Palatini approach. The resulting theory is able to capture different aspects of quantum gravity phenomenology in a single framework. In particular, it is found that in this theory field excitations propagating with different energy-densities perceive different background metrics, which is a fundamental characteristic of the DSR and Rainbow Gravity approaches. We illustrate these properties with a particular gravitational model and explicitly show how the soccer ball problem is avoided in this framework. The isotropic and anisotropic cosmologies of this model also avoid the big bang singularity by means of a big bounce.
An alternative path integral for quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Krishnan, Chethan; Kumar, K.V. Pavan; Raju, Avinash [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)
2016-10-10
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This “Neumann ensemble” perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
Covariant effective action for loop quantum cosmology from order reduction
International Nuclear Information System (INIS)
Sotiriou, Thomas P.
2009-01-01
Loop quantum cosmology (LQC) seems to be predicting modified effective Friedmann equations without extra degrees of freedom. A puzzle arises if one decides to seek for a covariant effective action which would lead to the given Friedmann equation: The Einstein-Hilbert action is the only action that leads to second order field equations and, hence, there exists no covariant action which, under metric variation, leads to a modified Friedmann equation without extra degrees of freedom. It is shown that, at least for isotropic models in LQC, this issue is naturally resolved and a covariant effective action can be found if one considers higher order theories of gravity but faithfully follows effective field theory techniques. However, our analysis also raises doubts on whether a covariant description without background structures can be found for anisotropic models.
Puzzles in quantum gravity : what can black hole microstates teach us about quantum gravity?
El-Showk, S.
2009-01-01
In this thesis we review two independent lines of research directed towards helping us construct a theory of Quantum Gravity. While, in string/M-theory, we already enjoy a potential theory of this type there remain many unanswered foundational questions and missing precepts. By probing the
Universe before Planck time: A quantum gravity model
International Nuclear Information System (INIS)
Padmanabhan, T.
1983-01-01
A model for quantum gravity can be constructed by treating the conformal degree of freedom of spacetime as a quantum variable. An isotropic, homogeneous cosmological solution in this quantum gravity model is presented. The spacetime is nonsingular for all the three possible values of three-space curvature, and agrees with the classical solution for time scales larger than the Planck time scale. A possibility of quantum fluctuations creating the matter in the universe is suggested
An Einstein equation for discrete quantum gravity
Gudder, Stan
2012-01-01
The basic framework for this article is the causal set approach to discrete quantum gravity (DQG). Let $Q_n$ be the collection of causal sets with cardinality not greater than $n$ and let $K_n$ be the standard Hilbert space of complex-valued functions on $Q_n$. The formalism of DQG presents us with a decoherence matrix $D_n(x,y)$, $x,y\\in Q_n$. There is a growth order in $Q_n$ and a path in $Q_n$ is a maximal chain relative to this order. We denote the set of paths in $Q_n$ by $\\Omega_n$. For...
Hypercuboidal renormalization in spin foam quantum gravity
Bahr, Benjamin; Steinhaus, Sebastian
2017-06-01
In this article, we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion paper, in which the existence of a fixed point in the truncated renormalization group flow for the model was reported. Here, we repeat the analysis with various modifications and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.
Quantum Gravity and Cosmology: an intimate interplay
Sakellariadou, Mairi
2017-08-01
I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological rôle of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics.
Exact RG flow equations and quantum gravity
de Alwis, S. P.
2018-03-01
We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg's asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.
Horizon Entropy from Quantum Gravity Condensates.
Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo
2016-05-27
We construct condensate states encoding the continuum spherically symmetric quantum geometry of a horizon in full quantum gravity, i.e., without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits a holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein-Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one.
Liouville quantum gravity on complex tori
Energy Technology Data Exchange (ETDEWEB)
David, François [Institut de Physique Théorique, CNRS, URA 2306, CEA, IPhT, Gif-sur-Yvette (France); Rhodes, Rémi [Université Paris-Est Marne la Vallée, LAMA, Champs sur Marne (France); Vargas, Vincent [ENS Paris, DMA, 45 rue d’Ulm, 75005 Paris (France)
2016-02-15
In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov [Phys. Lett. B 103, 207 (1981)]. Our approach follows the construction carried out by the authors together with Kupiainen in the case of the Riemann sphere [“Liouville quantum gravity on the Riemann sphere,” e-print arXiv:1410.7318]. The difference is here that the moduli space for complex tori is non-trivial. Modular properties of LQFT are thus investigated. This allows us to integrate the LQFT on complex tori over the moduli space, to compute the law of the random Liouville modulus, therefore recovering (and extending) formulae obtained by physicists, and make conjectures about the relationship with random planar maps of genus one, eventually weighted by a conformal field theory and conformally embedded onto the torus.
Half-integral spin from quantum gravity
International Nuclear Information System (INIS)
Friedman, J.L.
1982-01-01
For a certain class of three-manifolds, the angular momentum of an asymptotically flat quantum gravitational field can have half-integral values. In the absence of a full theory of quantum gravity, this result relies on a set of apparently natural assumptions governing the kinematics of such a theory. A key feature is that state vectors are in general invariant only under asymptotically trivial diffeomorphisms that can be continuously deformed to the identity. Angular momentum is associated with diffeomorphisms that look asymptotically like rotations; and the question of whether half-integral values occur depends on whether the diffeomorphism associated with a 2π rotation is itself deformable to the identity. (author)
On quantum gravity and the many-worlds interpretation of quantum mechanics
International Nuclear Information System (INIS)
Smolin, L.
1984-01-01
The paper examines the interpretation of quantum mechanics and the quantum theory of gravity. Foundational problems in quantum gravity; the many-worlds interpretation of quantum mechanics; the role of observation in the many-worlds and in the minimal relative state interpretations; and advantages of the many-worlds interpretation; are all discussed. (U.K.)
Energy Technology Data Exchange (ETDEWEB)
El-Menoufi, Basem Kamal [Department of Physics, University of Massachusetts,Amherst, MA 01003 (United States)
2016-05-05
In the context of effective field theory, we consider quantum gravity with minimally coupled massless particles. Fixing the background geometry to be of the Kerr-Schild type, we fully determine the one-loop effective action of the theory whose finite non-local part is induced by the long-distance portion of quantum loops. This is accomplished using the non-local expansion of the heat kernel in addition to a non-linear completion technique through which the effective action is expanded in gravitational curvatures. Via Euclidean methods, we identify a logarithmic correction to the Bekenstein-Hawking entropy of Schwarzschild black hole. Using dimensional transmutation the result is shown to exhibit an interesting interplay between the UV and IR properties of quantum gravity.
Algorithmic Complexity in Cosmology and Quantum Gravity
Directory of Open Access Journals (Sweden)
D. Singleton
2002-01-01
Full Text Available Abstract: In this article we use the idea of algorithmic complexity (AC to study various cosmological scenarios, and as a means of quantizing the ravitational interaction. We look at 5D and 7D cosmological models where the Universe begins as a higher dimensional Planck size spacetime which fluctuates between Euclidean and Lorentzian signatures. These fluctuations are overned by the AC of the two different signatures. At some point a transition to a 4D Lorentzian signature Universe occurs, with the extra dimensions becoming "frozen" or non-dynamical. We also apply the idea of algorithmic complexity to study composite wormholes, the entropy of black holes, and the path integral for quantum gravity. Some of the physical consequences of the idea presented here are:the birth of the Universe with a fluctuating metric signature; the transition from a fluctuating metric signature to Lorentzian one; "frozen" extra dimensions as a consequence of this transition; quantum handles in the spacetime foam as regions with multidimensional gravity.
Coherent semiclassical states for loop quantum cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Montoya, Edison
2011-01-01
The spatially flat Friedmann-Robertson-Walker cosmological model with a massless scalar field in loop quantum cosmology admits a description in terms of a completely solvable model. This has been used to prove that: (i) the quantum bounce that replaces the big bang singularity is generic; (ii) there is an upper bound on the energy density for all states, and (iii) semiclassical states at late times had to be semiclassical before the bounce. Here we consider a family of exact solutions to the theory, corresponding to generalized coherent Gaussian and squeezed states. We analyze the behavior of basic physical observables and impose restrictions on the states based on physical considerations. These turn out to be enough to select, from all the generalized coherent states, those that behave semiclassical at late times. We study then the properties of such states near the bounce where the most 'quantum behavior' is expected. As it turns out, the states remain sharply peaked and semiclassical at the bounce and the dynamics is very well approximated by the ''effective theory'' throughout the time evolution. We compare the semiclassicality properties of squeezed states to those of the Gaussian semiclassical states and conclude that the Gaussians are better behaved. In particular, the asymmetry in the relative fluctuations before and after the bounce are negligible, thus ruling out claims of so-called 'cosmic forgetfulness'.
Quantum gravity from descriptive set theory
International Nuclear Information System (INIS)
El Naschie, M.S.
2004-01-01
We start from Hilbert's criticism of the axioms of classical geometry and the possibility of abandoning the Archimedean axiom. Subsequently we proceed to the physical possibility of a fundamental limitation on the smallest length connected to certain singular points in spacetime and below which measurements become meaningless, Finally we arrive at the conclusion that maximising the Hawking-Bekenstein informational content of spacetime makes the existence of a transfinite geometry for physical 'spacetime' not only plausible but probably inevitable. The main part of the paper is then concerned with a proposal for a mathematical description of a transfinite, non-Archimedean geometry using descriptive set theory. Nevertheless, and despite all abstract mathematics, we remain quite close to similar lines of investigation initiated by physicists like A. Wheeler, D. Finkelstein and G. 'tHooft. In particular we introduce a logarithmic gauge transformation linking classical gravity with the electro weak via a version of informational entropy. That way we may claim to have accomplished an important step towards a general theory of quantum gravity using ε (∞) and complexity theory and finding that α G =(2) α-bar ew -1 congruent with (1.7)(10) 38 where α G is the dimensionless Newton gravity constant, and α ew ≅128 is the fine structure constant at the electro weak scale
Spin foam models for quantum gravity
International Nuclear Information System (INIS)
Perez, Alejandro
2003-01-01
In this topical review, we review the present status of the spin foam formulation of non-perturbative (background-independent) quantum gravity. The topical review is divided into two parts. In the first part, we present a general introduction to the main ideas emphasizing their motivation from various perspectives. Riemannian three-dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for four-dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four dimensions (gauge invariance, discretization independence, etc). In the second part, we concentrate on the definition of the Barrett-Crane model. We present the main results obtained in this framework from a critical perspective. Finally, we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the Barrett-Crane model in this framework and review the finiteness results obtained for both its Riemannian and its Lorentzian variants. (topical review)
The relation between Euclidean and Lorentzian 2D quantum gravity
Ambjørn, J.; Correia, J.; Kristjansen, C.; Loll, R.
1999-01-01
Starting from 2D Euclidean quantum gravity, we show that one recovers 2D Lorentzian quantum gravity by removing all baby universes. Using a peeling procedure to decompose the discrete, triangulated geometries along a one-dimensional path, we explicitly associate with each Euclidean space-time a
Euclidean and Lorentzian Quantum Gravity – Lessons from Two Dimensions
Ambjørn, J.; Loll, R.; Nielsen, J. L.; Rolf, J.
1998-01-01
No theory of four-dimensional quantum gravity exists as yet. In this situation the two-dimensional theory, which can be analyzed by conventional field-theoretical methods, can serve as a toy model for studying some aspects of quantum gravity. It represents one of the rare settings in a
The contributions of Bryce DeWitt to quantum gravity
International Nuclear Information System (INIS)
Isham, C.J.
1984-01-01
The paper reviews the work of Bryce DeWitt in the field of Quantum Gravity. Covariant commutators; R 2 lagrangians; DeWitt and Schwinger; gravity as a regulator; the full background field method; and the canonical quantization of gravity; are all discussed. (U.K.)
Gauges and functional measures in quantum gravity II: higher-derivative gravity
Energy Technology Data Exchange (ETDEWEB)
Ohta, N. [Kindai University, Department of Physics, Higashi-Osaka, Osaka (Japan); Percacci, R. [International School for Advanced Studies, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Pereira, A.D. [UERJ-Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil)
2017-09-15
We compute the one-loop divergences in a higher-derivative theory of gravity including Ricci tensor squared and Ricci scalar squared terms, in addition to the Hilbert and cosmological terms, on an (generally off-shell) Einstein background. We work with a two-parameter family of parametrizations of the graviton field, and a two-parameter family of gauges. We find that there are some choices of gauge or parametrization that reduce the dependence on the remaining parameters. The results are invariant under a recently discovered ''duality'' that involves the replacement of the densitized metric by a densitized inverse metric as the fundamental quantum variable. (orig.)
Evaporation Spectrum of Black Holes from a Local Quantum Gravity Perspective.
Barrau, Aurélien
2016-12-30
We revisit the hypothesis of a possible line structure in the Hawking evaporation spectrum of black holes. Because of nonperturbative quantum gravity effects, this would take place arbitrarily far away from the Planck mass. We show, based on a speculative but consistent hypothesis, that this naive prediction might in fact hold in the specific context of loop quantum gravity. A small departure from the ideal case is expected for some low-spin transitions and could allow us to distinguish several quantum gravity models. We also show that the effect is not washed out by the dynamics of the process, by the existence of a mass spectrum up to a given width, or by the secondary component induced by the decay of neutral pions emitted during the time-integrated evaporation.
Quantum gravity in more than four dimensions
International Nuclear Information System (INIS)
Vaz, C.
1987-01-01
Ever since its inception, Einstein's general relativity has been considered a most remarkable theory. It is generally believed today, that the classical theory is well understood. Nevertheless, in the pursuit of a deeper understanding of physics in terms of a grand unification of forces, one would like to quantize the theory, thus bringing it under the known forces of nature. The author will address the possibility that space-time is of dimension greater that four. In the pursuit of Einstein's dream of a unification of physical interactions, many interesting ideas have been developed. Beginning with Weyl and Kaluza, we have progressed to strings and superstrings. The thing that is common to all these theories is the requirement of a space-time of more than four dimensions. While Kaluza's theory implicitly assumes that Einstein's gravity is classically correct in any number of dimensions, superstring phenomenology may suggest otherwise. Generalizations to Einstein's gravity are indicated, and the gravitational Casimir energy is explicitly approximate on a background configuration M 4 x S 6 , on a ten dimensional space-time. Weyl invariance is particularly interesting to the quantum gravitationalist. One finds that energy momentum tensor of the Weyl invariant quantum field picks up an anomalous trace, which is related to particle production by the curved background. He therefore computes the conformal anomaly for a conformally coupled scalar field and considers some of its consequences. He then suggest that the conformal anomaly, when combined with the perfect fluid hypothesis, can be used to determine the complete energy momentum tensor of the quantum field in certain backgrounds
Torsion as a dynamic degree of freedom of quantum gravity
International Nuclear Information System (INIS)
Kim, Sang-Woo; Pak, D G
2008-01-01
The gauge approach to gravity based on the local Lorentz group with a general independent affine connection A μcd is developed. We consider SO(1, 3) gauge theory with a Lagrangian quadratic in curvature as a simple model of quantum gravity. The torsion is proposed to represent a dynamic degree of freedom of quantum gravity at scales above the Planckian energy. The Einstein-Hilbert theory is induced as an effective theory due to quantum corrections of torsion via generating a stable gravito-magnetic condensate. We conjecture that torsion possesses an intrinsic quantum nature and can be confined
Loop quantum cosmology and spin foams
International Nuclear Information System (INIS)
Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam
2009-01-01
Loop quantum cosmology (LQC) is used to provide concrete evidence in support of the general paradigm underlying spin foam models (SFMs). Specifically, it is shown that: (i) the physical inner product in the timeless framework equals the transition amplitude in the deparameterized theory; (ii) this quantity admits a vertex expansion a la SFMs in which the M-th term refers just to M volume transitions, without any reference to the time at which the transition takes place; (iii) the exact physical inner product is obtained by summing over just the discrete geometries; no 'continuum limit' is involved; and, (iv) the vertex expansion can be interpreted as a perturbative expansion in the spirit of group field theory. This sum over histories reformulation of LQC also addresses certain other issues which are briefly summarized.
The Structural Foundations of Quantum Gravity
International Nuclear Information System (INIS)
Rovelli, Carlo
2007-01-01
The core of the collection of papers that form the book originates from a workshop on 'Structural Aspects of Quantum Gravity' held in Milwaukee, WI, in 2002. But the collection also includes contributions from philosophers and scientists who did not attend the meeting. The book is presented with a structuralist agenda: to emphasize the idea that 'relational structures are of equal or more fundamental ontological status than objects'. The goal of the editors is, as they put it, to 'suggest' a possible 'interpretative and ontological perspective from which to view quantum gravity physics'. Attention to structure rather than objects is a long-standing tradition. It played a major role in anthropology and linguistics, from which it fertilized numerous other disciplines. In the recent philosophy of science, when criticism of the dominant positivism of the beginning of the century has begun to pile up, several thinkers have steered towards more realist positions. The conceptual problems of quantum gravity are illustrated and discussed in detail throughout the book, often from different perspectives, and sometimes with discordant conclusions. At times, the book reads almost as a dialogue, where different thinkers present different sides of the issue. Perhaps it is our full conceptualization of reality that evolves, not just its ontology: our knowledge of the world's structures (and equations) persists and changes historically as much as our knowledge of the world's objects. Efforts to find a fixed ground on which to anchor our beliefs often fail; I think the scientific picture of the world is credible because it captures the best that we know today, not because it captures something definitive. Still, I find the ideas underlying the structural proposal challenging and very intriguing. Notions such as object, entity or substance keep playing a fundamental role in physics, but continue also to show their limits: a physicist often thinks that the prototypical 'object' is
The matter-ekpyrotic bounce scenario in Loop Quantum Cosmology
Energy Technology Data Exchange (ETDEWEB)
Haro, Jaume; Amorós, Jaume; Saló, Llibert Aresté, E-mail: jaime.haro@upc.edu, E-mail: jaume.amoros@upc.edu, E-mail: llibert.areste@estudiant.upc.edu [Departament de Matemàtica Aplicada, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona (Spain)
2017-09-01
We will perform a detailed study of the matter-ekpyrotic bouncing scenario in Loop Quantum Cosmology using the methods of the dynamical systems theory. We will show that when the background is driven by a single scalar field, at very late times, in the contracting phase, all orbits depict a matter dominated Universe, which evolves to an ekpyrotic phase. After the bounce the Universe enters in the expanding phase, where the orbits leave the ekpyrotic regime going to a kination (also named deflationary) regime. Moreover, this scenario supports the production of heavy massive particles conformally coupled with gravity, which reheats the universe at temperatures compatible with the nucleosynthesis bounds and also the production of massless particles non-conformally coupled with gravity leading to very high reheating temperatures but ensuring the nucleosynthesis success. Dealing with cosmological perturbations, these background dynamics produce a nearly scale invariant power spectrum for the modes that leave the Hubble radius, in the contracting phase, when the Universe is quasi-matter dominated, whose spectral index and corresponding running is compatible with the recent experimental data obtained by PLANCK's team.
The matter-ekpyrotic bounce scenario in Loop Quantum Cosmology
Haro, Jaume; Amorós, Jaume; Aresté Saló, Llibert
2017-09-01
We will perform a detailed study of the matter-ekpyrotic bouncing scenario in Loop Quantum Cosmology using the methods of the dynamical systems theory. We will show that when the background is driven by a single scalar field, at very late times, in the contracting phase, all orbits depict a matter dominated Universe, which evolves to an ekpyrotic phase. After the bounce the Universe enters in the expanding phase, where the orbits leave the ekpyrotic regime going to a kination (also named deflationary) regime. Moreover, this scenario supports the production of heavy massive particles conformally coupled with gravity, which reheats the universe at temperatures compatible with the nucleosynthesis bounds and also the production of massless particles non-conformally coupled with gravity leading to very high reheating temperatures but ensuring the nucleosynthesis success. Dealing with cosmological perturbations, these background dynamics produce a nearly scale invariant power spectrum for the modes that leave the Hubble radius, in the contracting phase, when the Universe is quasi-matter dominated, whose spectral index and corresponding running is compatible with the recent experimental data obtained by PLANCK's team.
Loop space representation of quantum general relativity and the group of loops
International Nuclear Information System (INIS)
Gambini, R.
1991-01-01
The action of the constraints of quantum general relativity on a general state in the loop representation is coded in terms of loop derivatives. These differential operators are related to the infinitesimal generators of the group of loops and generalize the area derivative first considered by Mandelstam. A new sector of solutions of the physical states space of nonperturbative quantum general relativity is found. (orig.)
Unimodular gravity and the lepton anomalous magnetic moment at one-loop
Energy Technology Data Exchange (ETDEWEB)
Martín, Carmelo P., E-mail: carmelop@fis.ucm.es [Departamento de Física Teórica I, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040 Madrid (Spain)
2017-07-01
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.
(2+1)-dimensional quantum gravity
International Nuclear Information System (INIS)
Hosoya, Akio; Nakao, Ken-ichi.
1989-05-01
The (2+1)-dimensional pure Einstein gravity is studied in the canonical ADM formalism, assuming that the spatial surface is closed and compact. Owing to the constraints, the dynamical variables are reduced to the moduli parameters of the 2-surface. Upon quantization, the system becomes a quantum mechanics of moduli parameters in a curved space endowed with the Weil-Petersson metric. In the case of torus in particular, the superspace, on which the wave function of universe is defined, turns out to be the fundamental region is the moduli space. The solution of the Wheeler-DeWitt equation is explicitly given as the Maass form which is perfectly regular in the superspace. (author)
Chiral vacuum fluctuations in quantum gravity.
Magueijo, João; Benincasa, Dionigi M T
2011-03-25
We examine tensor perturbations around a de Sitter background within the framework of Ashtekar's variables and its cousins parameterized by the Immirzi parameter γ. At the classical level we recover standard cosmological perturbation theory, with illuminating insights. Quantization leads to real novelties. In the low energy limit we find a second quantized theory of gravitons which displays different vacuum fluctuations for right and left gravitons. Nonetheless right and left gravitons have the same (positive) energies, resolving a number of paradoxes suggested in the literature. The right-left asymmetry of the vacuum fluctuations depends on γ and the ordering of the Hamiltonian constraint, and it would leave a distinctive imprint in the polarization of the cosmic microwave background, thus opening quantum gravity to observational test.
String theory and quantum gravity '92
International Nuclear Information System (INIS)
Harvey, J.; Iengo, R.; Narain, K.S.; Randjbar Daemi, S.; Verlinde, H.
1993-01-01
These proceedings of the 1992 Trieste Spring School and Workshop on String Theory and Quantum Gravity contains introductions and overviews of recent work on the use of two-dimensional string inspired models in the study of black holes, a lecture on gravitational scattering at planckian energies, another on the physical properties of higher-dimensional black holes and black strings in string theory, a discussion on N=2 superconformal field theories, a lecture about the application of matrix model techniques to the study of string theory in two dimensions, and an overview of the current status and developments in string field theory. Connections with models in statistical mechanics are also discussed. These proceedings contain seven lectures and ten contributions. Refs and figs
Discrete Hamiltonian evolution and quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization
More on Weinberg's no-go theorem in quantum gravity
Nagahama, Munehiro; Oda, Ichiro
2018-05-01
We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.
How far are we from the quantum theory of gravity?
International Nuclear Information System (INIS)
Woodard, R P
2009-01-01
I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is unavoidable, why quantum field theories have divergences, why the divergences of quantum general relativity are worse than those of the other forces, what physicists think this means and what they might do with a consistent theory of quantum gravity if they had one. Finally, I discuss the quantum gravitational data that have recently become available from cosmology.
Finite field-dependent symmetries in perturbative quantum gravity
International Nuclear Information System (INIS)
Upadhyay, Sudhaker
2014-01-01
In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also
Quantum gravity and Standard-Model-like fermions
International Nuclear Information System (INIS)
Eichhorn, Astrid; Lippoldt, Stefan
2017-01-01
We discover that chiral symmetry does not act as an infrared attractor of the renormalization group flow under the impact of quantum gravity fluctuations. Thus, observationally viable quantum gravity models must respect chiral symmetry. In our truncation, asymptotically safe gravity does, as a chiral fixed point exists. A second non-chiral fixed point with massive fermions provides a template for models with dark matter. This fixed point disappears for more than 10 fermions, suggesting that an asymptotically safe ultraviolet completion for the standard model plus gravity enforces chiral symmetry.
Fixed points of quantum gravity in extra dimensions
International Nuclear Information System (INIS)
Fischer, Peter; Litim, Daniel F.
2006-01-01
We study quantum gravity in more than four dimensions with renormalisation group methods. We find a non-trivial ultraviolet fixed point in the Einstein-Hilbert action. The fixed point connects with the perturbative infrared domain through finite renormalisation group trajectories. We show that our results for fixed points and related scaling exponents are stable. If this picture persists at higher order, quantum gravity in the metric field is asymptotically safe. We discuss signatures of the gravitational fixed point in models with low scale quantum gravity and compact extra dimensions
Loop quantum cosmology with complex Ashtekar variables
International Nuclear Information System (INIS)
Achour, Jibril Ben; Grain, Julien; Noui, Karim
2015-01-01
We construct and study loop quantum cosmology (LQC) when the Barbero–Immirzi parameter takes the complex value γ=±i. We refer to this new approach to quantum cosmology as complex LQC. This formulation is obtained via an analytic continuation of the Hamiltonian constraint (with no inverse volume corrections) from real γ to γ=±i, in the simple case of a flat FLRW Universe coupled to a massless scalar field with no cosmological constant. For this, we first compute the non-local curvature operator (defined by the trace of the holonomy of the connection around a fundamental plaquette) evaluated in an arbitrary spin j representation, and find a new close formula for its expression. This allows us to define explicitly a one parameter family of regularizations of the Hamiltonian constraint in LQC, parametrized by the spin j. It is immediate to see that any spin j regularization leads to a bouncing scenario. Then, motivated in particular by previous results on black hole thermodynamics, we perform the analytic continuation of the Hamiltonian constraint to values of the Barbero–Immirzi parameter given by γ=±i and to spins j=(1/2)(−1+is) where s is real. Even if the area spectrum then becomes continuous, we show that the complex LQC defined in this way does also replace the initial big-bang singularity by a big-bounce. In addition to this, the maximal density and the minimal volume of the Universe are obviously independent of γ. Furthermore, the dynamics before and after the bounce is not symmetrical anymore, which makes a clear distinction between these two phases of the evolution of the Universe. (paper)
Emergence of a classical Universe from quantum gravity and cosmology.
Kiefer, Claus
2012-09-28
I describe how we can understand the classical appearance of our world from a universal quantum theory. The essential ingredient is the process of decoherence. I start with a general discussion in ordinary quantum theory and then turn to quantum gravity and quantum cosmology. There is a whole hierarchy of classicality from the global gravitational field to the fluctuations in the cosmic microwave background, which serve as the seeds for the structure in the Universe.
C*-algebras of holonomy-diffeomorphisms and quantum gravity: I
International Nuclear Information System (INIS)
Aastrup, Johannes; Grimstrup, Jesper Møller
2013-01-01
A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a quantized Dirac-type operator, the two capturing the kinematics of quantum gravity formulated in terms of Ashtekar variables. We prove that the separable part of the spectrum of the algebra is contained in the space of measurable connections modulo gauge transformations and we give limitations to the non-separable part. The construction of the Dirac-type operator—and thus the application of noncommutative geometry—is motivated by the requirement of diffeomorphism invariance. We conjecture that a semi-finite spectral triple, which is invariant under volume-preserving diffeomorphisms, arises from a GNS construction of a semi-classical state. Key elements of quantum field theory emerge from the construction in a semi-classical limit, as does an almost commutative algebra. Finally, we note that the spectrum of loop quantum gravity emerges from a discretization of our construction. Certain convergence issues are left unresolved. This paper is the first of two where the second paper [1] is concerned with mathematical details and proofs concerning the spectrum of the holonomy-diffeomorphism algebra. (paper)
Dynamics and entanglement in spherically symmetric quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Terno, Daniel R.
2010-01-01
The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the Hamiltonian operator, and of semiclassical states peaked on constraint-free data. Such states provide explicit examples of physical states. We also show that matter-gravity entanglement is an inherent feature of physical states, whether or not there is a black hole.
Classical limit of quantum gravity in an accelerating universe
International Nuclear Information System (INIS)
Schuller, Frederic P.; Wohlfarth, Mattias N.R.
2005-01-01
A one-parameter deformation of Einstein-Hilbert gravity with an inverse Riemann curvature term is derived as the classical limit of quantum gravity compatible with an accelerating universe. This result is based on the investigation of semi-classical theories with sectional curvature bounds which are shown not to admit static spherically symmetric black holes if otherwise of phenomenological interest. We discuss the impact on the canonical quantization of gravity, and observe that worldsheet string theory is not affected
String theory as a quantum theory of gravity
International Nuclear Information System (INIS)
Horowitz, G.T.
1990-01-01
First, the connection between string theory and gravity is discussed - at first sight the theory of strings seem to have nothing to do with gravity but an intimate connection is shown. Then the quantum perturbation expansion is discussed. Thirdly, string theory is considered as a classical theory of gravity and finally recent speculation about a phase of string theory which is independent of a spacetime metric is discussed. (author)
Quantum gravity from simplices: analytical investigations of causal dynamical triangulations
Benedetti, D.
2007-01-01
A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Although these models can be solved exactly in a variety of ways in the case of pure gravity in (1+1) dimensions,it is difficult to extend any of the
Matter coupled to quantum gravity in group field theory
International Nuclear Information System (INIS)
Ryan, James
2006-01-01
We present an account of a new model incorporating 3d Riemannian quantum gravity and matter at the group field theory level. We outline how the Feynman diagram amplitudes of this model are spin foam amplitudes for gravity coupled to matter fields and discuss some features of the model. To conclude, we describe some related future work
New formulation of Horava-Lifshitz quantum gravity as a master constraint theory
Energy Technology Data Exchange (ETDEWEB)
Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw [Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan (China); Yang Jinsong, E-mail: Yangksong@gmail.com [Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan (China); Yu, Hoi-Lai, E-mail: hlyu@phys.sinica.edu.tw [Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan (China)
2011-07-04
Both projectable and non-projectable versions of Horava-Lifshitz gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian constraint, thus allowing for an extra scalar mode which can be problematic. A new formulation of non-projectable Horava-Lifshitz gravity, naturally realized as a representation of the master constraint algebra studied by loop quantum gravity researchers, is presented. This yields a consistent canonical theory with first class constraints. It captures the essence of Horava-Lifshitz gravity in retaining only spatial diffeomorphisms (instead of full space-time covariance) as the physically relevant non-trivial gauge symmetry; at the same time the local Hamiltonian constraint needed to eliminate the extra mode is equivalently enforced by the master constraint.
Universal features of quantum bounce in loop quantum cosmology
Directory of Open Access Journals (Sweden)
Tao Zhu
2017-10-01
Full Text Available In this Letter, we study analytically the evolutions of the flat Friedmann–Lemaitre–Robertson–Walker (FLRW universe and its linear perturbations in the framework of the dressed metric approach in loop quantum cosmology (LQC. Assuming that the evolution of the background is dominated by the kinetic energy of the inflaton at the quantum bounce, we find that both evolutions of the background and its perturbations are independent of the inflationary potentials during the pre-inflationary phase. During this period the effective potentials of the perturbations can be well approximated by a Pöschl–Teller (PT potential, from which we find analytically the mode functions and then calculate the corresponding Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary model with a single scalar field. Imposing the Bunch–Davies (BD vacuum in the contracting phase prior to the bounce when the modes are all inside the Hubble horizon, we show that particles are generically created due to the pre-inflation dynamics. Matching them to those obtained in the slow-roll inflationary phase, we investigate the effects of the pre-inflation dynamics on the scalar and tensor power spectra and find features that can be tested by current and forthcoming observations. In particular, to be consistent with the Planck 2015 data, we find that the universe must have expanded at least 141 e-folds since the bounce.
Lattice quantum gravity and asymptotic safety
Laiho, J.; Bassler, S.; Coumbe, D.; Du, D.; Neelakanta, J. T.
2017-09-01
We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we argue that the target symmetry is the general coordinate invariance of the theory. After introducing and fine-tuning a nontrivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3 /2 , a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue that the number of relevant couplings in the continuum theory is one, once symmetry breaking by the lattice regulator is accounted for. Such a theory is maximally predictive, with no adjustable parameters. The cosmological constant in Planck units is the only relevant parameter, which serves to set the lattice scale. The cosmological constant in Planck units is of order 1 in the ultraviolet and undergoes renormalization group running to small values in the infrared. If these findings hold up under further scrutiny, the lattice may provide a nonperturbative definition of a renormalizable quantum field theory of general relativity with no adjustable parameters and a cosmological constant that is naturally small in the infrared.
Gauge dependence and new kind of two-dimensional gravity theory with trivial quantum corrections
International Nuclear Information System (INIS)
Banin, A.T.; Shapiro, I.L.
1993-12-01
We search for the new kinds of classical potentials in two-dimensional induced gravity, which provide the triviality of the one-loop quantum corrections. First of all the gauge dependence of the effective potential is studied. The unique effective potential, introduced by Vilkovisly in 1984 is found to manifest the gauge dependence due to some unusual properties of the theory under consideration. Then we take the gauge of harmonical type, which provides the one-loop finiteness off shell, and then the solution for the required classical potential is found. (author). 35 refs
One-loop effective action for non-local modified Gauss-Bonnet gravity in de Sitter space
Energy Technology Data Exchange (ETDEWEB)
Cognola, Guido; Zerbini, Sergio [Universita di Trento (Italy); Istituto Nazionale di Fisica Nucleare Gruppo Collegato di Trento, Dipartimento di Fisica, Trento (Italy); Elizalde, Emilio [Consejo Superior de Investigaciones Cientificas (ICE/CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC), Facultat Ciencies, Bellaterra (Barcelona) (Spain); Nojiri, Shin' ichi [Nagoya University, Department of Physics, Nagoya (Japan); Odintsov, Sergei D. [Consejo Superior de Investigaciones Cientificas (ICE/CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC), Facultat Ciencies, Bellaterra (Barcelona) (Spain); ICREA, Barcelona (Spain); TSPU, Center of Theor. Phys., Tomsk (Russian Federation)
2009-12-15
We discuss the classical and quantum properties of non-local modified Gauss-Bonnet gravity in de Sitter space, using its equivalent representation via string-inspired local scalar-Gauss-Bonnet gravity with a scalar potential. A classical, multiple de Sitter universe solution is found where one of the de Sitter phases corresponds to the primordial inflationary epoch, while the other de Sitter space solution - the one with the smallest Hubble rate - describes the late-time acceleration of our universe. A Chameleon scenario for the theory under investigation is developed, and it is successfully used to show that the theory complies with gravitational tests. An explicit expression for the one-loop effective action for this non-local modified Gauss-Bonnet gravity in the de Sitter space is obtained. It is argued that this effective action might be an important step towards the solution of the cosmological constant problem. (orig.)
Towards loop quantum supergravity (LQSG): I. Rarita–Schwinger sector
International Nuclear Information System (INIS)
Bodendorfer, N; Thiemann, T; Thurn, A
2013-01-01
In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is Poisson-commuting, which implies that loop quantum gravity quantization methods apply. We also provided the coupling to standard matter. In this paper, we extend our methods to derive a connection formulation of a large class of Lorentzian signature supergravity theories, in particular 11 D SUGRA and 4 D, N = 8 SUGRA, which was in fact the motivation to consider higher dimensions. Starting from a Hamiltonian formulation in the time gauge which yields a Spin(D) theory, a major challenge is to extend the internal gauge group to Spin(D + 1) in the presence of the Rarita–Schwinger field. This is non-trivial because SUSY typically requires the Rarita–Schwinger field to be a Majorana fermion for the Lorentzian Clifford algebra and Majorana representations of the Clifford algebra are not available in the same spacetime dimension for both Lorentzian and Euclidean signatures. We resolve the arising tension and provide a background-independent representation of the non-trivial Dirac antibracket *-algebra for the Majorana field which significantly differs from the analogous construction for Dirac fields already available in the literature. (paper)
Further results on geometric operators in quantum gravity
Loll, R.
1996-01-01
We investigate some properties of geometric operators in canonical quantum gravity in the connection approach `a la Ashtekar, which are associated with volume, area and length of spatial regions. We motivate the construction of analogous discretized lattice quantities, compute various quantum
The Spin-Foam Approach to Quantum Gravity.
Perez, Alejandro
2013-01-01
This article reviews the present status of the spin-foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently-introduced new models for four-dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self-contained treatment of 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.
The Spin-Foam Approach to Quantum Gravity
Directory of Open Access Journals (Sweden)
Alejandro Perez
2013-02-01
Full Text Available This article reviews the present status of the spin-foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently-introduced new models for four-dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self contained treatment of 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.
Algebraic quantum field theory, perturbation theory, and the loop expansion
International Nuclear Information System (INIS)
Duetsch, M.; Fredenhagen, K.
2001-01-01
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A (n) of observables ''up to n loops'', where A (0) is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions. (orig.)
Quantum chromodynamics as dynamics of loops
International Nuclear Information System (INIS)
Makeenko, Yu.M.; Migdal, A.A.
1981-01-01
QCD is entirely reformulated in terms of white composite fields - the traces of the loop products. The 1/N expansion turns out to be the WKB (Hartree-Fock) approximation for these fields. The 'classical' equation describing the N = infinite case is reduced tp a bootstrap form. New, manifestly gauge-invariant perturbation theory in the loop space, reproducing asymptotic freedom, is developed by iterations of this equation. The area law appears to be a self-consistent solution at large loops. (orig.)
Induced gravity in quantum theory in a curved space
International Nuclear Information System (INIS)
Etim, E.
1983-01-01
The reason for interest in the unorthodox view of first order (about R(x)) gravity as a matter-induced quantum effect is really to find an argument not to quantise it. According to this view quantum gravity should be constructed with an action which is, at least, quadratic in the scalar curvature R(x). Such a theory will not contain a dimensional parameter, like Newton's constant, and would probably be renormalisable. This lecture is intended to acquaint the non-expert with the phenomenon of induction of the scalar curvature term in the matter Lagrangian in a curved space in both relativistic and non-relativistic quantum theories
Non-singular bounce scenarios in loop quantum cosmology and the effective field description
International Nuclear Information System (INIS)
Cai, Yi-Fu; Wilson-Ewing, Edward
2014-01-01
A non-singular bouncing cosmology is generically obtained in loop quantum cosmology due to non-perturbative quantum gravity effects. A similar picture can be achieved in standard general relativity in the presence of a scalar field with a non-standard kinetic term such that at high energy densities the field evolves into a ghost condensate and causes a non-singular bounce. During the bouncing phase, the perturbations can be stabilized by introducing a Horndeski operator. Taking the matter content to be a dust field and an ekpyrotic scalar field, we compare the dynamics in loop quantum cosmology and in a non-singular bouncing effective field model with a non-standard kinetic term at both the background and perturbative levels. We find that these two settings share many important properties, including the result that they both generate scale-invariant scalar perturbations. This shows that some quantum gravity effects of the very early universe may be mimicked by effective field models
Beyond the Standard Model with noncommutative geometry, strolling towards quantum gravity
International Nuclear Information System (INIS)
Martinetti, Pierre
2015-01-01
Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics: from models of quantum spacetime(with or without breaking of Lorentz symmetry) to loop gravity and string theory, from early considerations on UV-divergenciesin quantum field theory to recent models of gauge theories on noncommutatives pacetime, from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. We list several of these applications, emphasizing also the original point of view brought by noncommutative geometry on the nature of time. This text serves as an introduction to the volume of proceedings of the parallel session “Noncommutative geometry and quantum gravity”, as a part of the conference “Conceptual and technical challenges in quantum gravity” organized at the University of Rome La Sapienza sin September 2014. (paper)
Geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Singh, Parampreet
2009-01-01
We reexamine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so-called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.
Gravity waves from quantum stress tensor fluctuations in inflation
International Nuclear Information System (INIS)
Wu, Chun-Hsien; Hsiang, Jen-Tsung; Ford, L. H.; Ng, Kin-Wang
2011-01-01
We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a nonscale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both in the CMB radiation and in gravity wave detectors, and could offer a probe of trans-Planckian physics. The fact that they have not yet been observed might be used to constrain the duration and energy scale of inflation. However, this conclusion is contingent upon including the contribution of modes which were trans-Planckian at the beginning of inflation.
Gravity waves from quantum stress tensor fluctuations in inflation
Wu, Chun-Hsien; Hsiang, Jen-Tsung; Ford, L. H.; Ng, Kin-Wang
2011-11-01
We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a nonscale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both in the CMB radiation and in gravity wave detectors, and could offer a probe of trans-Planckian physics. The fact that they have not yet been observed might be used to constrain the duration and energy scale of inflation. However, this conclusion is contingent upon including the contribution of modes which were trans-Planckian at the beginning of inflation.
On the Convergence in Effective Loop Quantum Cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose Antonio
2010-01-01
In Loop Quantum Cosmology (LQC) there is a discreteness parameter λ, that has been heuristically associated to a fundamental granularity of quantum geometry. It is also possible to consider λ as a regulator in the same spirit as that used in lattice field theory, where it specifies a regular lattice in the real line. A particular quantization of the k = 0 FLRW loop cosmological model yields a completely solvable model, known as solvable loop quantum cosmology(sLQC). In this contribution, we consider effective classical theories motivated by sLQC and study their λ-dependence, with a special interest on the limit λ→0 and the role of the evolution parameter in the convergence of such limit.
Unruly topologies in two-dimensional quantum gravity
International Nuclear Information System (INIS)
Hartle, J.B.
1985-01-01
A sum over histories formulation of quantum geometry could involve sums over different topologies as well as sums over different metrics. In classical gravity a geometry is a manifold with a metric, but it is difficult to implement a sum over manifolds in quantum gravity. In this difficulty, motivation is found for including in the sum over histories, geometries defined on more general objects than manifolds-unruly topologies. In simplicial two-dimensional quantum gravity a class of simplicial complexes is found to which the gravitational action can be extended, for which sums over the class are straightforwardly defined, and for which a manifold dominates the sum in the classical limit. The situation in higher dimensions is discussed. (author)
Closed-Loop and Robust Control of Quantum Systems
Directory of Open Access Journals (Sweden)
Chunlin Chen
2013-01-01
Full Text Available For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA, and reinforcement learning (RL methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control as H∞ control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention.
Closed-loop and robust control of quantum systems.
Chen, Chunlin; Wang, Lin-Cheng; Wang, Yuanlong
2013-01-01
For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control) have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA), and reinforcement learning (RL) methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control as H(∞) control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention.
Regularization of quantum gravity in the matrix model approach
International Nuclear Information System (INIS)
Ueda, Haruhiko
1991-02-01
We study divergence problem of the partition function in the matrix model approach for two-dimensional quantum gravity. We propose a new model V(φ) = 1/2Trφ 2 + g 4 /NTrφ 4 + g'/N 4 Tr(φ 4 ) 2 and show that in the sphere case it has no divergence problem and the critical exponent is of pure gravity. (author)
Discrete Approaches to Quantum Gravity in Four Dimensions
Directory of Open Access Journals (Sweden)
Loll Renate
1998-01-01
Full Text Available The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation; quantum Regge calculus; and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.
Quantum-Gravity Phenomenology of soft ultraviolet/infrared mixing
International Nuclear Information System (INIS)
Amelino-Camelia, Giovanni; Loret, Niccolo; Mercati, Flavio
2010-01-01
We reexamine the motivation for ultraviolet/infrared mixing in quantum gravity and some of the quantum-spacetime formalizations where it has been found. We then focus on cases in which the infrared manifestations of the mixing are relatively soft, arguing that they can motivate a particularly appealing phenomenology. Among the possible implications for the large-distance behavior of gravity one intriguingly finds a correction with logarithmic dependence on distance. And one can explain in terms of soft ultraviolet/infrared mixing a four-standard-deviation discrepancy that was recently established in the context of studies of cold neutrons.
Quantum Gravity, Dynamical Triangulation and Higer Derivative Regularization
DEFF Research Database (Denmark)
Ambjorn, J.; Jurkiewicz, J.; Kristjansen, C. F.
1992-01-01
We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the bare coupling constants is studied in the search for a sens......We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the bare coupling constants is studied in the search...
Quantum gravity removes classical singularities and shortens the life of black holes
International Nuclear Information System (INIS)
Frolov, V.P.; Vilkovisky, G.A.
1979-07-01
The problem of the gravitational collapse is considered in the framework of the quantum gravity effective action. It is shown that quantum gravity removes classical singularity and possibly shortens the lifetime of the black hole. (author)
Quantum-gravity fluctuations and the black-hole temperature
Energy Technology Data Exchange (ETDEWEB)
Hod, Shahar [The Ruppin Academic Center, Emeq Hefer (Israel); The Hadassah Institute, Jerusalem (Israel)
2015-05-15
Bekenstein has put forward the idea that, in a quantum theory of gravity, a black hole should have a discrete energy spectrum with concomitant discrete line emission. The quantized black-hole radiation spectrum is expected to be very different from Hawking's semi-classical prediction of a thermal black-hole radiation spectrum. One naturally wonders: Is it possible to reconcile the discrete quantum spectrum suggested by Bekenstein with the continuous semi-classical spectrum suggested by Hawking? In order to address this fundamental question, in this essay we shall consider the zero-point quantum-gravity fluctuations of the black-hole spacetime. In a quantum theory of gravity, these spacetime fluctuations are closely related to the characteristic gravitational resonances of the corresponding black-hole spacetime. Assuming that the energy of the black-hole radiation stems from these zero-point quantum-gravity fluctuations of the black-hole spacetime, we derive the effective temperature of the quantized black-hole radiation spectrum. Remarkably, it is shown that this characteristic temperature of the discrete (quantized) black-hole radiation agrees with the well-known Hawking temperature of the continuous (semi-classical) black-hole spectrum. (orig.)
Quantum-gravity fluctuations and the black-hole temperature
International Nuclear Information System (INIS)
Hod, Shahar
2015-01-01
Bekenstein has put forward the idea that, in a quantum theory of gravity, a black hole should have a discrete energy spectrum with concomitant discrete line emission. The quantized black-hole radiation spectrum is expected to be very different from Hawking's semi-classical prediction of a thermal black-hole radiation spectrum. One naturally wonders: Is it possible to reconcile the discrete quantum spectrum suggested by Bekenstein with the continuous semi-classical spectrum suggested by Hawking? In order to address this fundamental question, in this essay we shall consider the zero-point quantum-gravity fluctuations of the black-hole spacetime. In a quantum theory of gravity, these spacetime fluctuations are closely related to the characteristic gravitational resonances of the corresponding black-hole spacetime. Assuming that the energy of the black-hole radiation stems from these zero-point quantum-gravity fluctuations of the black-hole spacetime, we derive the effective temperature of the quantized black-hole radiation spectrum. Remarkably, it is shown that this characteristic temperature of the discrete (quantized) black-hole radiation agrees with the well-known Hawking temperature of the continuous (semi-classical) black-hole spectrum. (orig.)
How many 'times' do we have in quantum gravity?
International Nuclear Information System (INIS)
Hosoya, Akio; Soda, Jiro.
1990-07-01
Apparently, there are infinite number of time-like variables in the Wheeler-DeWitt equation in quantum gravity. This gives rise to an obvious conceptual difficulty and further becomes an obstacle if one wants to canonically third quantize the universe. In this paper, adopting York's gauge in the path-integral approach, we formulate quantum geometrodynamics so that it contains only a single time-like variable corresponding to the total volume of the universe. (author)
Spacetime structure of an evaporating black hole in quantum gravity
International Nuclear Information System (INIS)
Bonanno, A.; Reuter, M.
2006-01-01
The impact of the leading quantum gravity effects on the dynamics of the Hawking evaporation process of a black hole is investigated. Its spacetime structure is described by a renormalization group improved Vaidya metric. Its event horizon, apparent horizon, and timelike limit surface are obtained by taking the scale dependence of Newton's constant into account. The emergence of a quantum ergosphere is discussed. The final state of the evaporation process is a cold, Planck size remnant
Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries
International Nuclear Information System (INIS)
Bombelli, L.; Corichi, A.; Winkler, O.
2005-01-01
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at ''quantum scales'' and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a ''semiclassical'' state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity. (Abstract Copyright [2005], Wiley Periodicals, Inc.)
q-deformation and semidualization in 3D quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Majid, S [School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Rd, London E1 4NS (United Kingdom); Schroers, B J [Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)], E-mail: s.majid@qmul.ac.uk, E-mail: bernd@ma.hw.ac.uk
2009-10-23
We explore in detail the role in euclidean 3D quantum gravity of quantum Born reciprocity or 'semidualization'. The latter is an algebraic operation defined using quantum group methods that interchanges position and momentum. Using this we are able to clarify the structural relationships between the effective noncommutative geometries that have been discussed in the context of 3D gravity. We show that the spin model based on D(U(su{sub 2})) for quantum gravity without cosmological constant is the semidual of a quantum particle on a 3-sphere, while the bicrossproduct (DSR) model is the semidual of a quantum particle on hyperbolic space. We show further how the different models are all specific limits of q-deformed models with q=e{sup -{Dirac_h}}{sup {radical}}{sup (-{lambda})/m{sub p}}, where m{sub p} is the Planck mass and {lambda} is the cosmological constant, and argue that semidualization interchanges m{sub p} {r_reversible} l{sub c}, where l{sub c} is the cosmological length scale l{sub c}=1/{radical}(|{lambda}|). We investigate the physics of semidualization by studying representation theory. In both the spin model and its semidual we show that irreducible representations have a physical picture as solutions of a respectively noncommutative/curved wave equation. We explain, moreover, that the q-deformed model, at a certain algebraic level, is self-dual under semidualization.
Quantum gravity and the large scale anomaly
Energy Technology Data Exchange (ETDEWEB)
Kamenshchik, Alexander Y.; Tronconi, Alessandro; Venturi, Giovanni, E-mail: Alexander.Kamenshchik@bo.infn.it, E-mail: Alessandro.Tronconi@bo.infn.it, E-mail: Giovanni.Venturi@bo.infn.it [Dipartimento di Fisica e Astronomia and INFN, Via Irnerio 46,40126 Bologna (Italy)
2015-04-01
The spectrum of primordial perturbations obtained by calculating the quantum gravitational corrections to the dynamics of scalar perturbations is compared with Planck 2013 and BICEP2/Keck Array public data. The quantum gravitational effects are calculated in the context of a Wheeler-De Witt approach and have quite distinctive features. We constrain the free parameters of the theory by comparison with observations.
Inflationary universe from higher derivative quantum gravity coupled with scalar electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Myrzakulov, R. [Department of General & Theoretical Physics and Eurasian Center for Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Odintsov, S.D. [Consejo Superior de Investigaciones Científicas, ICE/CSIC-IEEC, Campus UAB, Facultat de Ciències, Torre C5-Parell-2a pl, E-08193 Bellaterra, Barcelona (Spain); Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n 08193 Cerdanyola del Valles, Barcelona (Spain); Tomsk State Pedagogical University, 634050 Tomsk (Russian Federation); Tomsk State University of Control Systems and Radioelectronics (TUSUR) 634050 Tomsk (Russian Federation); Sebastiani, L., E-mail: lorenzo.sebastiani@unitn.it [Department of General & Theoretical Physics and Eurasian Center for Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan)
2016-06-15
We study inflation for a quantum scalar electrodynamics model in curved space–time and for higher-derivative quantum gravity (QG) coupled with scalar electrodynamics. The corresponding renormalization-group (RG) improved potential is evaluated for both theories in Jordan frame where non-minimal scalar-gravitational coupling sector is explicitly kept. The role of one-loop quantum corrections is investigated by showing how these corrections enter in the expressions for the slow-roll parameters, the spectral index and the tensor-to-scalar ratio and how they influence the bound of the Hubble parameter at the beginning of the primordial acceleration. We demonstrate that the viable inflation maybe successfully realized, so that it turns out to be consistent with last Planck and BICEP2/Keck Array data.
Distance between Quantum States and Gauge-Gravity Duality.
Miyaji, Masamichi; Numasawa, Tokiro; Shiba, Noburo; Takayanagi, Tadashi; Watanabe, Kento
2015-12-31
We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an anti-de Sitter spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.
Nonperturbative sum over topologies in 2-D Lorentzian quantum gravity
Loll, R.; Westra, W.; Zohren, S.
The recent progress in the Causal Dynamical Triangulations (CDT) approach to quantum gravity indicates that gravitation is nonperturbatively renormalizable. We review some of the latest results in 1+1 and 3+1 dimensions with special emphasis on the 1+1 model. In particular we discuss a
Quantum gravity effect in torsion driven inflation and CP violation
Energy Technology Data Exchange (ETDEWEB)
Choudhury, Sayantan [Department of Theoretical Physics, Tata Institute of Fundamental Research,Colaba, 1, Homi Bhabha Road, Mumbai 400005 (India); Pal, Barun Kumar [Inter-University Centre for Astronomy and Astrophysics,Ganeshkhind, Pune 411007 (India); Netaji Nagar College for Women,Regent Estate, Kolkata 700092 (India); Basu, Banasri; Bandyopadhyay, Pratul [Physics and Applied Mathematics Unit, Indian Statistical Institute,203 B.T. Road, Kolkata 700 108 (India)
2015-10-28
We have derived an effective potential for inflationary scenario from torsion and quantum gravity correction in terms of the scalar field hidden in torsion. A strict bound on the CP violating θ parameter, O(10{sup −10})<θ
Computer simulations of 3d Lorentzian quantum gravity
Ambjørn, J.; Jurkiewicz, J.; Loll, R.
2000-01-01
We investigate the phase diagram of non-perturbative three-dimensional Lorentzian quantum gravity with the help of Monte Carlo simulations. The system has a first-order phase transition at a critical value kc 0 of the bare inverse gravitational coupling constant k0. For k0 > kc0 the system
Quantum gravity effect in torsion driven inflation and CP violation
International Nuclear Information System (INIS)
Choudhury, Sayantan; Pal, Barun Kumar; Basu, Banasri; Bandyopadhyay, Pratul
2015-01-01
We have derived an effective potential for inflationary scenario from torsion and quantum gravity correction in terms of the scalar field hidden in torsion. A strict bound on the CP violating θ parameter, O(10"−"1"0)<θ< O(10"−"9) has been obtained, using Planck+WMAP9 best fit cosmological parameters.
Physical states in Quantum Einstein-Cartan Gravity
Cianfrani, Francesco
2016-01-01
The definition of physical states is the main technical issue of canonical approaches towards Quantum Gravity. In this work, we outline how those states can be found in Einstein-Cartan theory via a continuum limit and they are given by finite dimensional representations of the Lorentz group.
Effective state metamorphosis in semi-classical loop quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Singh, Parampreet [Institute for Gravitational Physics and Geometry, Pennsylvania State University, University Park, PA 16802 (United States)
2005-10-21
Modification to the behaviour of geometrical density at short scales is a key result of loop quantum cosmology, responsible for an interesting phenomenology in the very early universe. We demonstrate the way matter with arbitrary scale factor dependence in Hamiltonian incorporates this change in its effective dynamics in the loop-modified phase. For generic matter, the equation of state starts varying near a critical scale factor, becomes negative below it and violates the strong energy condition. This opens a new avenue to generalize various phenomenological applications in loop quantum cosmology. We show that different ways to define energy density may yield radically different results, especially for the case corresponding to classical dust. We also discuss implications for frequency dispersion induced by modification to geometric density at small scales.
Progress towards a space-borne quantum gravity gradiometer
Yu, Nan; Kohel, James M.; Ramerez-Serrano, Jaime; Kellogg, James R.; Lim, Lawrence; Maleki, Lute
2004-01-01
Quantum interferometer gravity gradiometer for 3D mapping is a project for developing the technology of atom interferometer-based gravity sensor in space. The atom interferometer utilizes atomic particles as free fall test masses to measure inertial forces with unprecedented sensitivity and precision. It also allows measurements of the gravity gradient tensor components for 3D mapping of subsurface mass distribution. The overall approach is based on recent advances of laser cooling and manipulation of atoms in atomic and optical physics. Atom interferometers have been demonstrated in research laboratories for gravity and gravity gradient measurements. In this approach, atoms are first laser cooled to micro-kelvin temperatures. Then they are allowed to freefall in vacuum as true drag-free test masses. During the free fall, a sequence of laser pulses is used to split and recombine the atom waves to realize the interferometric measurements. We have demonstrated atom interferometer operation in the Phase I period, and we are implementing the second generation for a complete gradiometer demonstration unit in the laboratory. Along with this development, we are developing technologies at component levels that will be more suited for realization of a space instrument. We will present an update of these developments and discuss the future directions of the quantum gravity gradiometer project.
Schramm-Loewner evolution and Liouville quantum gravity.
Duplantier, Bertrand; Sheffield, Scott
2011-09-23
We show that when two boundary arcs of a Liouville quantum gravity random surface are conformally welded to each other (in a boundary length-preserving way) the resulting interface is a random curve called the Schramm-Loewner evolution. We also develop a theory of quantum fractal measures (consistent with the Knizhnik-Polyakov-Zamolochikov relation) and analyze their evolution under conformal welding maps related to Schramm-Loewner evolution. As an application, we construct quantum length and boundary intersection measures on the Schramm-Loewner evolution curve itself.
Dynamical study of DBI-essence in loop quantum cosmology and brane world
Energy Technology Data Exchange (ETDEWEB)
Bhadra, Jhumpa; Debnath, Ujjal [Bengal Engineering and Science University, Department of Mathematics, Howrah (India)
2012-08-15
We have studied homogeneous isotropic FRW model having dynamical dark energy DBI-essence with scalar field. Existence of cosmological scaling solutions restricts the Lagrangian of the scalar field {phi}. Choosing p=Xg(Xe{sup {lambda}{phi}}), where X=-g {sup {mu}{nu}}{partial_derivative}{sub {mu}}{phi}{partial_derivative}{sub {nu}}{phi}/2 with g any function of Xe{sup {lambda}{phi}} and defining some suitable transformations, we have constructed the dynamical system in different models of gravity: (i) Loop Quantum Cosmology (LQC), (ii) DGP brane world and (iii) RS II brane world. We have investigated stability of this dynamical system around the critical point for three gravity models and investigated the scalar-field dominated attractor solution in support of accelerated universe. The roles of the physical parameters have also been shown graphically during the accelerating phase of the universe. (orig.)
Dynamical study of DBI-essence in loop quantum cosmology and brane world
International Nuclear Information System (INIS)
Bhadra, Jhumpa; Debnath, Ujjal
2012-01-01
We have studied homogeneous isotropic FRW model having dynamical dark energy DBI-essence with scalar field. Existence of cosmological scaling solutions restricts the Lagrangian of the scalar field φ. Choosing p=Xg(Xe λφ ), where X=-g μν ∂ μ φ∂ ν φ/2 with g any function of Xe λφ and defining some suitable transformations, we have constructed the dynamical system in different models of gravity: (i) Loop Quantum Cosmology (LQC), (ii) DGP brane world and (iii) RS II brane world. We have investigated stability of this dynamical system around the critical point for three gravity models and investigated the scalar-field dominated attractor solution in support of accelerated universe. The roles of the physical parameters have also been shown graphically during the accelerating phase of the universe. (orig.)
Relating covariant and canonical approaches to triangulated models of quantum gravity
International Nuclear Information System (INIS)
Arnsdorf, Matthias
2002-01-01
In this paper we explore the relation between covariant and canonical approaches to quantum gravity and BF theory. We will focus on the dynamical triangulation and spin-foam models, which have in common that they can be defined in terms of sums over spacetime triangulations. Our aim is to show how we can recover these covariant models from a canonical framework by providing two regularizations of the projector onto the kernel of the Hamiltonian constraint. This link is important for the understanding of the dynamics of quantum gravity. In particular, we will see how in the simplest dynamical triangulation model we can recover the Hamiltonian constraint via our definition of the projector. Our discussion of spin-foam models will show how the elementary spin-network moves in loop quantum gravity, which were originally assumed to describe the Hamiltonian constraint action, are in fact related to the time-evolution generated by the constraint. We also show that the Immirzi parameter is important for the understanding of a continuum limit of the theory
Fidelity for kicked atoms with gravity near a quantum resonance.
Dubertrand, Rémy; Guarneri, Italo; Wimberger, Sandro
2012-03-01
Kicked atoms under a constant Stark or gravity field are investigated for experimental setups with cold and ultracold atoms. The parametric stability of the quantum dynamics is studied using the fidelity. In the case of a quantum resonance, it is shown that the behavior of the fidelity depends on arithmetic properties of the gravity parameter. Close to a quantum resonance, the long-time asymptotics of the fidelity is studied by means of a pseudoclassical approximation introduced by Fishman et al. [J. Stat. Phys. 110, 911 (2003)]. The long-time decay of fidelity arises from the tunneling out of pseudoclassical stable islands, and a simple ansatz is proposed which satisfactorily reproduces the main features observed in numerical simulations.
Quantum gravity effects in Myers-Perry space-times
International Nuclear Information System (INIS)
Litim, Daniel F.; Nikolakopoulos, Konstantinos
2014-01-01
We study quantum gravity effects for Myers-Perry black holes assuming that the leading contributions arise from the renormalization group evolution of Newton’s coupling. Provided that gravity weakens following the asymptotic safety conjecture, we find that quantum effects lift a degeneracy of higher-dimensional black holes, and dominate over kinematical ones induced by rotation, particularly for small black hole mass, large angular momentum, and higher space-time dimensionality. Quantum-corrected space-times display inner and outer horizons, and show the existence of a black hole of smallest mass in any dimension. Ultra-spinning solutions no longer persist. Thermodynamic properties including temperature, specific heat, the Komar integrals, and aspects of black hole mechanics are studied as well. Observing a softening of the ring singularity, we also discuss the validity of classical energy conditions
Motion and gravity effects in the precision of quantum clocks.
Lindkvist, Joel; Sabín, Carlos; Johansson, Göran; Fuentes, Ivette
2015-05-19
We show that motion and gravity affect the precision of quantum clocks. We consider a localised quantum field as a fundamental model of a quantum clock moving in spacetime and show that its state is modified due to changes in acceleration. By computing the quantum Fisher information we determine how relativistic motion modifies the ultimate bound in the precision of the measurement of time. While in the absence of motion the squeezed vacuum is the ideal state for time estimation, we find that it is highly sensitive to the motion-induced degradation of the quantum Fisher information. We show that coherent states are generally more resilient to this degradation and that in the case of very low initial number of photons, the optimal precision can be even increased by motion. These results can be tested with current technology by using superconducting resonators with tunable boundary conditions.
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2013-07-19
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
Cosmological implications of modified gravity induced by quantum metric fluctuations
Energy Technology Data Exchange (ETDEWEB)
Liu, Xing [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, Yat Sen School, Guangzhou (China); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom); Liang, Shi-Dong [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, State Key Laboratory of Optoelectronic Material and Technology, Guangdong Province Key Laboratory of Display Material and Technology, School of Physics, Guangzhou (China)
2016-08-15
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors. (orig.)
Fröb, Markus B.
2018-02-01
We study a proposal for gauge-invariant correlation functions in perturbative quantum gravity, which are obtained by fixing the geodesic distance between points in the fluctuating geometry. These correlation functions are non-local and strongly divergent, and we show how to renormalise them by performing a ‘wave function renormalisation’ of the geodesic embedding coordinates. The result is finite and gauge-independent, but displays unusual features such as double logarithms at one-loop order.
Noncommutative gravity and quantum field theory on noncummutative curved spacetimes
Energy Technology Data Exchange (ETDEWEB)
Schenkel, Alexander
2011-10-24
The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the
Noncommutative gravity and quantum field theory on noncummutative curved spacetimes
International Nuclear Information System (INIS)
Schenkel, Alexander
2011-01-01
The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the noncommutative
Quantum Gravity, Information Theory and the CMB
Kempf, Achim
2018-04-01
We review connections between the metric of spacetime and the quantum fluctuations of fields. We start with the finding that the spacetime metric can be expressed entirely in terms of the 2-point correlator of the fluctuations of quantum fields. We then discuss the open question whether the knowledge of only the spectra of the quantum fluctuations of fields also suffices to determine the spacetime metric. This question is of interest because spectra are geometric invariants and their quantization would, therefore, have the benefit of not requiring the modding out of diffeomorphisms. Further, we discuss the fact that spacetime at the Planck scale need not necessarily be either discrete or continuous. Instead, results from information theory show that spacetime may be simultaneously discrete and continuous in the same way that information can. Finally, we review the recent finding that a covariant natural ultraviolet cutoff at the Planck scale implies a signature in the cosmic microwave background (CMB) that may become observable.
Quantum gravity vacuum and invariants of embedded spin networks
International Nuclear Information System (INIS)
Mikovic, A
2003-01-01
We show that the path integral for the three-dimensional SU(2) BF theory with a Wilson loop or a spin network function inserted can be understood as the Rovelli-Smolin loop transform of a wavefunction in the Ashtekar connection representation, where the wavefunction satisfies the constraints of quantum general relativity with zero cosmological constant. This wavefunction is given as a product of the delta functions of the SU(2) field strength and therefore it can be naturally associated with a flat connection spacetime. The loop transform can be defined rigorously via the quantum SU(2) group, as a spin foam state sum model, so that one obtains invariants of spin networks embedded in a three-manifold. These invariants define a flat connection vacuum state in the q-deformed spin network basis. We then propose a modification of this construction in order to obtain a vacuum state corresponding to the flat metric spacetime
Signature change events: a challenge for quantum gravity?
International Nuclear Information System (INIS)
White, Angela; Weinfurtner, Silke; Visser, Matt
2010-01-01
Within the framework of either Euclidean (functional integral) quantum gravity or canonical general relativity the signature of the manifold is a priori unconstrained. Furthermore, recent developments in the emergent spacetime programme have led to a physically feasible implementation of (analogue) signature change events. This suggests that it is time to revisit the sometimes controversial topic of signature change in general relativity. Specifically, we shall focus on the behaviour of a quantum field defined on a manifold containing regions of different signature. We emphasize that regardless of the underlying classical theory, there are severe problems associated with any quantum field theory residing on a signature-changing background. (Such as the production of what is naively an infinite number of particles, with an infinite energy density.) We show how the problem of quantum fields exposed to finite regions of Euclidean-signature (Riemannian) geometry has similarities with the quantum barrier penetration problem. Finally we raise the question as to whether signature change transitions could be fully understood and dynamically generated within (modified) classical general relativity, or whether they require the knowledge of a theory of quantum gravity.
Emergent/quantum gravity: macro/micro structures of spacetime
International Nuclear Information System (INIS)
Hu, B L
2009-01-01
Emergent gravity views spacetime as an entity emergent from a more complete theory of interacting fundamental constituents valid at much finer resolution or higher energies, usually assumed to be above the Planck energy. In this view general relativity is an effective theory valid only at long wavelengths and low energies. We describe the tasks of emergent gravity from any ('top-down') candidate theory for the microscopic structure of spacetime (quantum gravity), namely, identifying the conditions and processes or mechanisms whereby the familiar macroscopic spacetime described by general relativity and matter content described by quantum field theory both emerge with high probability and reasonable robustness. We point out that this task may not be so easy as commonly conjured (as implied in the 'theory of everything') because there are emergent phenomena which cannot simply be deduced from a given micro-theory. Going in the opposite direction ('bottom-up') is the task of quantum gravity, i.e., finding a theory for the microscopic structure of spacetime, which, in this new view, cannot come from quantizing the metric or connection forms because they are the collective variables which are meaningful only for the macroscopic theory (valid below the Planck energy). This task looks very difficult or almost impossible because it entails reconstructing lost information. We point out that the situation may not be so hopeless if we ask the right questions and have the proper tools for what we want to look for. We suggest pathways to move 'up' (in energy) from the given macroscopic conditions of classical gravity and quantum field theory to the domain closer to the micro-macro interface where spacetime emerged and places to look for clues or tell-tale signs at low energy where one could infer indirectly some salient features of the micro-structure of spacetime.
Dynamical Symmetry Breaking in RN Quantum Gravity
Directory of Open Access Journals (Sweden)
A. T. Kotvytskiy
2011-01-01
Full Text Available We show that in the RN gravitation model, there is no dynamical symmetry breaking effect in the formalism of the Schwinger-Dyson equation (in flat background space-time. A general formula for the second variation of the gravitational action is obtained from the quantum corrections hμν (in arbitrary background metrics.
Quantum Gravity as a Dissipative Deterministic System
Hooft, G. 't
1999-01-01
It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion of time in GR is so different from the usual one in
Quantum gravity with matter and group field theory
International Nuclear Information System (INIS)
Krasnov, Kirill
2007-01-01
A generalization of the matrix model idea to quantum gravity in three and higher dimensions is known as group field theory (GFT). In this paper we study generalized GFT models that can be used to describe 3D quantum gravity coupled to point particles. The generalization considered is that of replacing the group leading to pure quantum gravity by the twisted product of the group with its dual-the so-called Drinfeld double of the group. The Drinfeld double is a quantum group in that it is an algebra that is both non-commutative and non-cocommutative, and special care is needed to define group field theory for it. We show how this is done, and study the resulting GFT models. Of special interest is a new topological model that is the 'Ponzano-Regge' model for the Drinfeld double. However, as we show, this model does not describe point particles. Motivated by the GFT considerations, we consider a more general class of models that are defined not using GFT, but the so-called chain mail techniques. A general model of this class does not produce 3-manifold invariants, but has an interpretation in terms of point particle Feynman diagrams
Quantum Gravity corrections and entropy at the Planck time
International Nuclear Information System (INIS)
Basilakos, Spyros; Vagenas, Elias C.; Das, Saurya
2010-01-01
We investigate the effects of Quantum Gravity on the Planck era of the universe. In particular, using different versions of the Generalized Uncertainty Principle and under specific conditions we find that the main Planck quantities such as the Planck time, length, mass and energy become larger by a factor of order 10−10 4 compared to those quantities which result from the Heisenberg Uncertainty Principle. However, we prove that the dimensionless entropy enclosed in the cosmological horizon at the Planck time remains unchanged. These results, though preliminary, indicate that we should anticipate modifications in the set-up of cosmology since changes in the Planck era will be inherited even to the late universe through the framework of Quantum Gravity (or Quantum Field Theory) which utilizes the Planck scale as a fundamental one. More importantly, these corrections will not affect the entropic content of the universe at the Planck time which is a crucial element for one of the basic principles of Quantum Gravity named Holographic Principle
Quantum mechanics vs. general covariance in gravity and string models
International Nuclear Information System (INIS)
Martinec, E.J.
1984-01-01
Quantization of simple low-dimensional systems embodying general covariance is studied. Functional methods are employed in the calculation of effective actions for fermionic strings and 1 + 1 dimensional gravity. The author finds that regularization breaks apparent symmetries of the theory, providing new dynamics for the string and non-trivial dynamics for 1 + 1 gravity. The author moves on to consider the quantization of some generally covariant systems with a finite number of physical degrees of freedom, assuming the existence of an invariant cutoff. The author finds that the wavefunction of the universe in these cases is given by the solution to simple quantum mechanics problems
Multi-loop correlators for rational theories of 2D gravity from the generalized Kontsevich models
DEFF Research Database (Denmark)
Kristjansen, C.
1994-01-01
functions of the susceptibilities and the eigenvalues of the external field. We furthermore use the moment technique to derive a closed expression for the genus zero multi-loop correlators for $(3,3m-1)$ and $(3,3m-2)$ rational matter fields coupled to gravity. We comment on the relation between the two-matrix...
Which Quantum Theory Must be Reconciled with Gravity? (And What Does it Mean for Black Holes?
Directory of Open Access Journals (Sweden)
Matthew J. Lake
2016-10-01
Full Text Available We consider the nature of quantum properties in non-relativistic quantum mechanics (QM and relativistic quantum field theories, and examine the connection between formal quantization schemes and intuitive notions of wave-particle duality. Based on the map between classical Poisson brackets and their associated commutators, such schemes give rise to quantum states obeying canonical dispersion relations, obtained by substituting the de Broglie relations into the relevant (classical energy-momentum relation. In canonical QM, this yields a dispersion relation involving ℏ but not c, whereas the canonical relativistic dispersion relation involves both. Extending this logic to the canonical quantization of the gravitational field gives rise to loop quantum gravity, and a map between classical variables containing G and c, and associated commutators involving ℏ. This naturally defines a “wave-gravity duality”, suggesting that a quantum wave packet describing self-gravitating matter obeys a dispersion relation involving G, c and ℏ. We propose an Ansatz for this relation, which is valid in the semi-Newtonian regime of both QM and general relativity. In this limit, space and time are absolute, but imposing v max = c allows us to recover the standard expressions for the Compton wavelength λ C and the Schwarzschild radius r S within the same ontological framework. The new dispersion relation is based on “extended” de Broglie relations, which remain valid for slow-moving bodies of any mass m. These reduce to canonical form for m ≪ m P , yielding λ C from the standard uncertainty principle, whereas, for m ≫ m P , we obtain r S as the natural radius of a self-gravitating quantum object. Thus, the extended de Broglie theory naturally gives rise to a unified description of black holes and fundamental particles in the semi-Newtonian regime.
Bending of light in quantum gravity.
Bjerrum-Bohr, N E J; Donoghue, John F; Holstein, Barry R; Planté, Ludovic; Vanhove, Pierre
2015-02-13
We consider the scattering of lightlike matter in the presence of a heavy scalar object (such as the Sun or a Schwarzschild black hole). By treating general relativity as an effective field theory we directly compute the nonanalytic components of the one-loop gravitational amplitude for the scattering of massless scalars or photons from an external massive scalar field. These results allow a semiclassical computation of the bending angle for light rays grazing the Sun, including long-range ℏ contributions. We discuss implications of this computation, in particular, the violation of some classical formulations of the equivalence principle.
Analog model for quantum gravity effects: phonons in random fluids.
Krein, G; Menezes, G; Svaiter, N F
2010-09-24
We describe an analog model for quantum gravity effects in condensed matter physics. The situation discussed is that of phonons propagating in a fluid with a random velocity wave equation. We consider that there are random fluctuations in the reciprocal of the bulk modulus of the system and study free phonons in the presence of Gaussian colored noise with zero mean. We show that, in this model, after performing the random averages over the noise function a free conventional scalar quantum field theory describing free phonons becomes a self-interacting model.
Discrete Quantum Gravity in the Regge Calculus Formalism
International Nuclear Information System (INIS)
Khatsymovsky, V.M.
2005-01-01
We discuss an approach to the discrete quantum gravity in the Regge calculus formalism that was developed in a number of our papers. The Regge calculus is general relativity for a subclass of general Riemannian manifolds called piecewise flat manifolds. The Regge calculus deals with a discrete set of variables, triangulation lengths, and contains continuous general relativity as a special limiting case where the lengths tend to zero. In our approach, the quantum length expectations are nonzero and of the order of the Plank scale, 10 -33 cm, implying a discrete spacetime structure on these scales
Quantum criticality in Einstein-Maxwell-dilaton gravity
International Nuclear Information System (INIS)
Wen, Wen-Yu
2012-01-01
We investigate the quantum Lifshitz criticality in a general background of Einstein-Maxwell-dilaton gravity. In particular, we demonstrate the existence of critical point with dynamic critical exponent z by tuning a nonminimal coupling to its critical value. We also study the effect of nonminimal coupling and exponent z to the Efimov states and holographic RG flow in the overcritical region. We have found that the nonminimal coupling increases the instability for a probe scalar to condensate and its back reaction is discussed. At last, we give a quantum mechanics treatment to a solvable system with z=2, and comment for generic z>2.
A gauge/gravity relation in the one-loop effective action
International Nuclear Information System (INIS)
Basar, Goekce; Dunne, Gerald V
2010-01-01
We identify an unusual new gauge/gravity relation: the one-loop effective action for a massive spinor in 2n-dimensional AdS space is expressed in terms of precisely the same function (a certain multiple gamma function) as the one-loop effective action for a massive charged scalar in 4n dimensions in a maximally symmetric background electromagnetic field (one for which the eigenvalues of F μν are maximally degenerate, corresponding in four dimensions to a self-dual field, equivalently to a field of definite helicity), subject to the identification F 2 ↔Λ, where Λ is the gravitational curvature. Since these effective actions generate the low energy limit of all one-loop multi-leg graviton or gauge amplitudes, this implies a nontrivial gauge/gravity relation at the non-perturbative level and at the amplitude level. (fast track communication)
Phenomenologically viable Lorentz-violating quantum gravity.
Sotiriou, Thomas P; Visser, Matt; Weinfurtner, Silke
2009-06-26
Horava's "Lifschitz point gravity" has many desirable features, but in its original incarnation one is forced to accept a nonzero cosmological constant of the wrong sign to be compatible with observation. We develop an extension of Horava's model that abandons "detailed balance" and regains parity invariance, and in 3+1 dimensions exhibit all five marginal (renormalizable) and four relevant (super-renormalizable) operators, as determined by power counting. We also consider the classical limit of this theory, evaluate the Hamiltonian and supermomentum constraints, and extract the classical equations of motion in a form similar to the Arnowitt-Deser-Misner formulation of general relativity. This puts the model in a framework amenable to developing detailed precision tests.
Quantum cosmology of classically constrained gravity
International Nuclear Information System (INIS)
Gabadadze, Gregory; Shang Yanwen
2006-01-01
In [G. Gabadadze, Y. Shang, hep-th/0506040] we discussed a classically constrained model of gravity. This theory contains known solutions of General Relativity (GR), and admits solutions that are absent in GR. Here we study cosmological implications of some of these new solutions. We show that a spatially-flat de Sitter universe can be created from 'nothing'. This universe has boundaries, and its total energy equals to zero. Although the probability to create such a universe is exponentially suppressed, it favors initial conditions suitable for inflation. Then we discuss a finite-energy solution with a nonzero cosmological constant and zero space-time curvature. There is no tunneling suppression to fluctuate into this state. We show that for a positive cosmological constant this state is unstable-it can rapidly transition to a de Sitter universe providing a new unsuppressed channel for inflation. For a negative cosmological constant the space-time flat solutions is stable.
First order formalism for quantum gravity
International Nuclear Information System (INIS)
Gleiser, M.; Holman, R.; Neto, N.P.
1987-05-01
We develop a first order formalism for the quantization of gravity. We take as canonical variables both the induced metric and the extrinsic curvature of the (d - 1) -dimensional hypersurfaces obtained by the foliation of the d - dimensional spacetime. After solving the constraint algebra we use the Dirac formalism to quantize the theory and obtain a new representation for the Wheeler-DeWitt equation, defined in the functional space of the extrinsic curvature. We also show how to obtain several different representations of the Wheeler-DeWitt equation by considering actions differing by a total divergence. In particular, the intrinsic and extrinsic time approaches appear in a natural way, as do equivalent representations obtained by functional Fourier transforms of appropriate variables. We conclude with some remarks about the construction of the Hilbert space within the first order formalism. 10 refs
Topics in Covariant Closed String Field Theory and Two-Dimensional Quantum Gravity
Saadi, Maha
1991-01-01
The closed string field theory based on the Witten vertex is found to be nonpolynomial in order to reproduce all tree amplitudes correctly. The interactions have a geometrical pattern of overlaps, which can be thought as the edges of a spherical polyhedron with face-perimeters equal to 2pi. At each vertex of the polyhedron there are three faces, thus all elementary interactions are cubic in the sense that at most three strings can coincide at a point. The quantum action is constructed by substracting counterterms which cancel the overcounting of moduli space, and by adding loop vertices in such a way no possible surfaces are missed. A counterterm that gives the correct one-string one-loop amplitude is formulated. The lowest order loop vertices are analyzed in the cases of genus one and two. Also, a one-loop two -string counterterm that restores BRST invariance to the respective scattering amplitude is constructed. An attempt to understand the formulation of two -dimensional pure gravity from the discrete representation of a two-dimensional surface is made. This is considered as a toy model of string theory. A well-defined mathematical model is used. Its continuum limit cannot be naively interpreted as pure gravity because each term of the sum over surfaces is not positive definite. The model, however, could be considered as an analytic continuation of the standard matrix model formulation of gravity. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).
An introduction to covariant quantum gravity and asymptotic safety
Percacci, Roberto
2017-01-01
This book covers recent developments in the covariant formulation of quantum gravity. Developed in the 1960s by Feynman and DeWitt, by the 1980s this approach seemed to lead nowhere due to perturbative non-renormalizability. The possibility of non-perturbative renormalizability or "asymptotic safety," originally suggested by Weinberg but largely ignored for two decades, was revived towards the end of the century by technical progress in the field of the renormalization group. It is now a very active field of research, providing an alternative to other approaches to quantum gravity. Written by one of the early contributors to this subject, this book provides a gentle introduction to the relevant ideas and calculational techniques. Several explicit calculations gradually bring the reader close to the current frontier of research. The main difficulties and present lines of development are also outlined.
Moment problems and the causal set approach to quantum gravity
International Nuclear Information System (INIS)
Ash, Avner; McDonald, Patrick
2003-01-01
We study a collection of discrete Markov chains related to the causal set approach to modeling discrete theories of quantum gravity. The transition probabilities of these chains satisfy a general covariance principle, a causality principle, and a renormalizability condition. The corresponding dynamics are completely determined by a sequence of non-negative real coupling constants. Using techniques related to the classical moment problem, we give a complete description of any such sequence of coupling constants. We prove a representation theorem: every discrete theory of quantum gravity arising from causal set dynamics satisfying covariance, causality, and renormalizability corresponds to a unique probability distribution function on the non-negative real numbers, with the coupling constants defining the theory given by the moments of the distribution
BRST and Anti-BRST Symmetries in Perturbative Quantum Gravity
Faizal, Mir
2011-02-01
In perturbative quantum gravity, the sum of the classical Lagrangian density, a gauge fixing term and a ghost term is invariant under two sets of supersymmetric transformations called the BRST and the anti-BRST transformations. In this paper we will analyse the BRST and the anti-BRST symmetries of perturbative quantum gravity in curved spacetime, in linear as well as non-linear gauges. We will show that even though the sum of ghost term and the gauge fixing term can always be expressed as a total BRST or a total anti-BRST variation, we can express it as a combination of both of them only in certain special gauges. We will also analyse the violation of nilpotency of the BRST and the anti-BRST transformations by introduction of a bare mass term, in the massive Curci-Ferrari gauge.
Central charge for AdS2 quantum gravity
International Nuclear Information System (INIS)
Hartman, Thomas; Strominger, Andrew
2009-01-01
Two-dimensional Maxwell-dilaton quantum gravity on AdS 2 with radius l and a constant electric field E is studied. In conformal gauge, this is equivalent to a CFT on a strip. In order to maintain consistent boundary conditions, the usual conformal diffeomorphisms must be accompanied by a certain U(1) gauge transformation. The resulting conformal transformations are generated by a twisted stress tensor, which has a central charge c = 3kE 2 l 4 /4 where k is the level of the U(1) current. This is an AdS 2 analog of the Brown-Henneaux formula c = 3l/2G for the central charge of quantum gravity on AdS 3 .
Ghost anomalous dimension in asymptotically safe quantum gravity
International Nuclear Information System (INIS)
Eichhorn, Astrid; Gies, Holger
2010-01-01
We compute the ghost anomalous dimension within the asymptotic-safety scenario for quantum gravity. For a class of covariant gauge fixings and using a functional renormalization group scheme, the anomalous dimension η c is negative, implying an improved UV behavior of ghost fluctuations. At the non-Gaussian UV fixed point, we observe a maximum value of η c ≅-0.78 for the Landau-deWitt gauge within the given scheme and truncation. Most importantly, the backreaction of the ghost flow onto the Einstein-Hilbert sector preserves the non-Gaussian fixed point with only mild modifications of the fixed-point values for the gravitational coupling and cosmological constant and the associated critical exponents; also their gauge dependence is slightly reduced. Our results provide further evidence for the asymptotic-safety scenario of quantum gravity.
Uniqueness of closure of the constraint algebra for quantum gravity
International Nuclear Information System (INIS)
Christodoulakis, T.; Korfiatis, E.
1989-08-01
We investigate the closure of the quantum algebra for the constraints of pure gravity considering a wide class of regularisation assumptions. We thus establish that the only regularisation assumption, within this class, that closes the algebra is the one introduced by one of the authors (T.C. with Jorge Zanelli) in earlier publications and that the closure is a result of both the regularisation and the introduction of a tensor distribution. (author). 15 refs
Uniqueness of closure of the constraint algebra for quantum gravity
International Nuclear Information System (INIS)
Christodoulakis, T.; Korfiatis, E.
1991-01-01
Considering a wide class of regularization assumptions, the closure of the quantum algebra is investigated for the constraints of pure gravity. It is thus established that the only regularization assumption, within this class, that closes the algebra is the one introduced by one of the authors (TC with J. Zanelli) in earlier publications and that the closure is a result of both the regularization and the introduction of a tensor distribution
Evidence for asymptotic safety from lattice quantum gravity.
Laiho, J; Coumbe, D
2011-10-14
We calculate the spectral dimension for nonperturbative quantum gravity defined via Euclidean dynamical triangulations. We find that it runs from a value of ∼3/2 at short distance to ∼4 at large distance scales, similar to results from causal dynamical triangulations. We argue that the short-distance value of 3/2 for the spectral dimension may resolve the tension between asymptotic safety and the holographic principle.
Metric dimensional reduction at singularities with implications to Quantum Gravity
International Nuclear Information System (INIS)
Stoica, Ovidiu Cristinel
2014-01-01
A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being just non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained
The propagator of quantum gravity in minisuperspace
International Nuclear Information System (INIS)
Louko, J.
1985-04-01
We study the quantum gravitational propagation amplitude between two spacelike three-surfaces in minisuperspaces where the supermomentum constraints are identically satisfied. We derive a well-defined path integral formula for the propagator and show that the propagator is an inverse of the canonical Hamiltonian operator. In an exactly solvable deSitter minisuperspace model the propagator is found to obey semi-classically correct boundary conditions. We discuss the implications for the full theory and suggest an approach to unravelling the physical meaning of the propagator. (orig.)
Entanglement of quantum clocks through gravity.
Castro Ruiz, Esteban; Giacomini, Flaminia; Brukner, Časlav
2017-03-21
In general relativity, the picture of space-time assigns an ideal clock to each world line. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of clocks along nearby world lines. However, if time is defined operationally, as a pointer position of a physical clock that obeys the principles of general relativity and quantum mechanics, such a picture is, at most, a convenient fiction. Specifically, we show that the general relativistic mass-energy equivalence implies gravitational interaction between the clocks, whereas the quantum mechanical superposition of energy eigenstates leads to a nonfixed metric background. Based only on the assumption that both principles hold in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well defined. However, the general relativistic notion of time is recovered in the classical limit of clocks.
Two-point functions in (loop) quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca; Oriti, Daniele [Max-Planck-Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany); Gielen, Steffen [Max-Planck-Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany); DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2011-07-01
We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions, with particular but non-exclusive reference to loop quantum cosmology (LQC). Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.
Two-point functions in (loop) quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca; Gielen, Steffen; Oriti, Daniele, E-mail: calcagni@aei.mpg.de, E-mail: gielen@aei.mpg.de, E-mail: doriti@aei.mpg.de [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany)
2011-06-21
The path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions is discussed, with particular but non-exclusive reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.
Two-point functions in (loop) quantum cosmology
International Nuclear Information System (INIS)
Calcagni, Gianluca; Gielen, Steffen; Oriti, Daniele
2011-01-01
The path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions is discussed, with particular but non-exclusive reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.
Quantum mechanics, gravity and modified quantization relations.
Calmet, Xavier
2015-08-06
In this paper, we investigate a possible energy scale dependence of the quantization rules and, in particular, from a phenomenological point of view, an energy scale dependence of an effective [Formula: see text] (reduced Planck's constant). We set a bound on the deviation of the value of [Formula: see text] at the muon scale from its usual value using measurements of the anomalous magnetic moment of the muon. Assuming that inflation has taken place, we can conclude that nature is described by a quantum theory at least up to an energy scale of about 10(16) GeV. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Gravity duals of half-BPS Wilson loops
International Nuclear Information System (INIS)
D'Hoker, Eric; Estes, John; Gutperle, Michael
2007-01-01
We explicitly construct the fully back-reacted half-BPS solutions in Type IIB supergravity which are dual to Wilson loops with 16 supersymmetries in N = 4 super Yang-Mills. In a first part, we use the methods of a companion paper to derive the exact general solution of the half-BPS equations on the space AdS 2 x S 2 x S 4 x Σ, with isometry group SO(2, 1) x SO(3) x SO(5) in terms of two locally harmonic functions on a Riemann surface Σ with boundary. These solutions, generally, have varying dilaton and axion, and non-vanishing 3-form fluxes. In a second part, we impose regularity and topology conditions. These non-singular solutions may be parametrized by a genus g ≥ 0 hyperelliptic surface Σ, all of whose branch points lie on the real line. Each genus g solution has only a single asymptotic AdS 5 x S 5 region, but exhibits g homology 3-spheres, and an extra g homology 5-spheres, carrying respectively RR 3-form and RR 5-form charges. For genus 0, we recover AdS 5 x S 5 with 3 free parameters, while for genus g ≥ 1, the solution has 2g+5 free parameters. The genus 1 case is studied in detail. Numerical analysis is used to show that the solutions are regular throughout the g = 1 parameter space. Collapse of a branch cut on Σ subtending either a homology 3-sphere or a homology 5-sphere is non-singular and yields the genus g-1 solution. This behavior is precisely expected of a proper dual to a Wilson loop in gauge theory
Quantum gravity in three dimensions, Witten spinors and the quantisation of length
Wieland, Wolfgang
2018-05-01
In this paper, I investigate the quantisation of length in euclidean quantum gravity in three dimensions. The starting point is the classical hamiltonian formalism in a cylinder of finite radius. At this finite boundary, a counter term is introduced that couples the gravitational field in the interior to a two-dimensional conformal field theory for an SU (2) boundary spinor, whose norm determines the conformal factor between the fiducial boundary metric and the physical metric in the bulk. The equations of motion for this boundary spinor are derived from the boundary action and turn out to be the two-dimensional analogue of the Witten equations appearing in Witten's proof of the positive mass theorem. The paper concludes with some comments on the resulting quantum theory. It is shown, in particular, that the length of a one-dimensional cross section of the boundary turns into a number operator on the Fock space of the theory. The spectrum of this operator is discrete and matches the results from loop quantum gravity in the spin network representation.
Anti-Gravity Loop-shaped heat pipe with graded pore-size wick
International Nuclear Information System (INIS)
Tang Yong; Zhou Rui; Lu Longsheng; Xie Zichun
2012-01-01
An Anti-Gravity Loop-Shaped Heat Pipe (AGLSHP) with a Continuous Graded Pore-Size Wick (CGPSW) was developed for the cooling of electronic devices at the anti-gravity orientation on the ground. At this orientation, heat is transferred toward the direction of the gravitational field. The AGLSHP consists of an evaporator, a condenser, a vapor line and a liquid line. The CGPSW is formed by sintered copper powders and it is filled inside the evaporator and the liquid line. The corresponding test system was developed to investigate the start-up characteristics and heat transfer performance of the AGLSHP at the anti-gravity orientation. The experimental result shows that, the AGLSHP has the capability to start-up reliably without any temperature overshoot or oscillation at the test heat loads. And the AGLSHP is able to keep the temperature of the evaporator below 105 °C and the overall thermal resistance below 0.24 °C/W at the heat load of 100 W. It is also found that the ideal heat load range of the AGLSHP at the anti-gravity orientation is from 30 W to 90 W. In this power range the overall thermal resistance stabilizes at about 0.15 °C/W, and the maximum temperature of the evaporator is lower than 84 °C at the heat load of 90 W. - Highlights: ► We present a loop-shaped heat pipe for the anti-gravity application on the ground. ► We present the continuous graded pore-size wick and its fabrication process. ► We test the start-up and heat transfer performance of this loop-shaped heat pipe. ► This loop-shaped heat pipe starts up reliably and has satisfying heat transfer capability.
Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity
Directory of Open Access Journals (Sweden)
Claudio Cremaschini
2017-07-01
Full Text Available Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015–2017 are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ , which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g μ ν and its quantum conjugate momentum operator.
TCP, quantum gravity, the cosmological constant and all that .
International Nuclear Information System (INIS)
Banks, T.
1985-01-01
We study cosmology from the point of view of quantum gravity. Some light is thrown on the nature of time, and it is suggested that the cosmological arrow of time is generated by a spontaneous breakdown of TCP. Conventional cosmological models in which quantum fields interact with a time-dependent gravitational field are shown to describe an approximation to the quantum gravitational wave function which is valid in the long-wavelength limit. Two problems with initial conditions are resolved in models in which a negative bare cosmological constant is cancelled by the classical excitation of a Bose field eta with a very flat potential. These models can also give a natural explanation for the observed value of the cosmological constant. (orig.)
Black-hole decay and topological stability in quantum gravity
International Nuclear Information System (INIS)
Rodrigues, L.M.C.S.; Soares, I.D.; Zanelli, J.
1988-01-01
In the context of Quantum Gravity, the evolution of Schwarzschild black-holes is studied. The superspace of the theory is restricted to a class of geometries that contains the Schwarzschild solution for different masses as well as other geometries with different topologies. It is shown that, black-holes are topologically stable under quantum fluctuations but unstable under quantum processes of emission and absorption of gravitons. It is found that, the probability of emission behaves as exp (- α (M f - M i ), where M i and M f are the masses associated to the initial and final states, respectively and α is a positive constant of the order of 1. As the black-hole looses mass it evolves towards a state corresponding to a black-hole of very small that cannot be distinguished from a pure graviton state. (author) [pt
Aspects of Nonlocality in Quantum Field Theory, Quantum Gravity and Cosmology
Barvinsky, A O
2015-01-01
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures and the nonperturbative method based on the late time asymptotics of the heat kernel. Euclidean version of the Schwinger-Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter stage of cosmological evolution at an arbitrary value of $\\varLambda$ -- a model of dark energy with its scale played by the dynamical variable that can be fixed by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of gravity theory mediated by a scala...
Operator ordering in quantum mechanics and quantum gravity
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1984-05-01
A non-perturbative approach to the quantization of the canonical algebra of pure gravity is presented. The problem of factor ordering of operators in the constraints H-caretsub(μ)psi=0 is resolved invoking hermiticity under the invariant inner product in hyperspace - the space of all three-dimensional metrics gsub(ij)(x) - and covariance under coordinate transformations. The resulting operators H-caretsub(μ) receive corrections of order h and h 2 only, and the algebra closes up to a conformal anomaly term. It is argued that, by a convenient choice of gauge, the anomalous term can be removed. (author)
Loop quantum cosmology of Bianchi IX: effective dynamics
International Nuclear Information System (INIS)
Corichi, Alejandro; Montoya, Edison
2017-01-01
We study solutions to the effective equations for the Bianchi IX class of spacetimes within loop quantum cosmology (LQC). We consider Bianchi IX models whose matter content is a massless scalar field, by numerically solving the loop quantum cosmology effective equations, with and without inverse triad corrections. The solutions are classified using certain geometrically motivated classical observables. We show that both effective theories—with lapse N = V and N = 1—resolve the big bang singularity and reproduce the classical dynamics far from the bounce. Moreover, due to the positive spatial curvature, there is an infinite number of bounces and recollapses. We study the limit of large field momentum and show that both effective theories reproduce the same dynamics, thus recovering general relativity. We implement a procedure to identify amongst the Bianchi IX solutions, those that behave like k = 0,1 FLRW as well as Bianchi I, II, and VII 0 models. The effective solutions exhibit Bianchi I phases with Bianchi II transitions and also Bianchi VII 0 phases, which had not been studied before. We comment on the possible implications of these results for a quantum modification to the classical BKL behaviour. (paper)
Loop quantum cosmology of Bianchi IX: effective dynamics
Corichi, Alejandro; Montoya, Edison
2017-03-01
We study solutions to the effective equations for the Bianchi IX class of spacetimes within loop quantum cosmology (LQC). We consider Bianchi IX models whose matter content is a massless scalar field, by numerically solving the loop quantum cosmology effective equations, with and without inverse triad corrections. The solutions are classified using certain geometrically motivated classical observables. We show that both effective theories—with lapse N = V and N = 1—resolve the big bang singularity and reproduce the classical dynamics far from the bounce. Moreover, due to the positive spatial curvature, there is an infinite number of bounces and recollapses. We study the limit of large field momentum and show that both effective theories reproduce the same dynamics, thus recovering general relativity. We implement a procedure to identify amongst the Bianchi IX solutions, those that behave like k = 0,1 FLRW as well as Bianchi I, II, and VII0 models. The effective solutions exhibit Bianchi I phases with Bianchi II transitions and also Bianchi VII0 phases, which had not been studied before. We comment on the possible implications of these results for a quantum modification to the classical BKL behaviour.
Low energy description of quantum gravity and complementarity
International Nuclear Information System (INIS)
Nomura, Yasunori; Varela, Jaime; Weinberg, Sean J.
2014-01-01
We consider a framework in which low energy dynamics of quantum gravity is described preserving locality, and yet taking into account the effects that are not captured by the naive global spacetime picture, e.g. those associated with black hole complementarity. Our framework employs a “special relativistic” description of gravity; specifically, gravity is treated as a force measured by the observer tied to the coordinate system associated with a freely falling local Lorentz frame. We identify, in simple cases, regions of spacetime in which low energy local descriptions are applicable as viewed from the freely falling frame; in particular, we identify a surface called the gravitational observer horizon on which the local proper acceleration measured in the observer's coordinates becomes the cutoff (string) scale. This allows for separating between the “low-energy” local physics and “trans-Planckian” intrinsically quantum gravitational (stringy) physics, and allows for developing physical pictures of the origins of various effects. We explore the structure of the Hilbert space in which the proposed scheme is realized in a simple manner, and classify its elements according to certain horizons they possess. We also discuss implications of our framework on the firewall problem. We conjecture that the complementarity picture may persist due to properties of trans-Planckian physics.
The potential of quantum technology gravity sensors in civil engineering
Tuckwell, G.; Metje, N.; Boddice, D.; Usher, C.
2017-12-01
Potential field techniques have advantages over active geophysical techniques as they are not limited to the depth they can image features, provided the signals of interest are detectable amongst the other variations recorded by the instrument. A new generation of gravity instruments based on quantum technology promise greatly increased measurement sensitivity, but with this comes significant challenges in data processing and noise suppression. In the UK Innovate UK funded SIGMA project (http://www.rsksigma.co.uk/) the field of opportunity for a step change in gravity sensor accuracy has been evaluated by comparison with existing geophysical sensors, identifying the range of targets and depths of interest to commercial end users that are currently undetectable and might become visible. Forward modelling was used to quantify the potential of a Quantum Technology (QT) gravity and gravity gradiometer sensor. A substantive improvement in detectability of targets is predicted, which can be considered as a factor of 1.5 to 2 increase in the depth of detectability, or in the reduction of the size of the feature of interest. To take further advantage of new instrument sensitivity, new survey workflows are required. The accuracy of measured gravity maps is limited by environmental vibration noise, and by the accuracy with which tidal variations and terrain signals can be removed. It is still common practice in engineering scale surveys for gravity values to be reduced to Bouguer residuals. However, with a more sensitive instrument comes the need to measure the terrain more accurately. This can be achieved within a commercially viable workflow using a laser scanner for rapid data acquisition and advanced processing to produce an accurate DEM. Initial tests on 4 commercial sites have shown that an improvement of 10s of mGal can be achieved if applying a full digital terrain model correction to the microgravity data even on sites with very minor topographic height variations
Loop algorithms for quantum simulations of fermion models on lattices
International Nuclear Information System (INIS)
Kawashima, N.; Gubernatis, J.E.; Evertz, H.G.
1994-01-01
Two cluster algorithms, based on constructing and flipping loops, are presented for world-line quantum Monte Carlo simulations of fermions and are tested on the one-dimensional repulsive Hubbard model. We call these algorithms the loop-flip and loop-exchange algorithms. For these two algorithms and the standard world-line algorithm, we calculated the autocorrelation times for various physical quantities and found that the ordinary world-line algorithm, which uses only local moves, suffers from very long correlation times that makes not only the estimate of the error difficult but also the estimate of the average values themselves difficult. These difficulties are especially severe in the low-temperature, large-U regime. In contrast, we find that new algorithms, when used alone or in combinations with themselves and the standard algorithm, can have significantly smaller autocorrelation times, in some cases being smaller by three orders of magnitude. The new algorithms, which use nonlocal moves, are discussed from the point of view of a general prescription for developing cluster algorithms. The loop-flip algorithm is also shown to be ergodic and to belong to the grand canonical ensemble. Extensions to other models and higher dimensions are briefly discussed
Exact Path Integral for 3D Quantum Gravity.
Iizuka, Norihiro; Tanaka, Akinori; Terashima, Seiji
2015-10-16
Three-dimensional Euclidean pure gravity with a negative cosmological constant can be formulated in terms of the Chern-Simons theory, classically. This theory can be written in a supersymmetric way by introducing auxiliary gauginos and scalars. We calculate the exact partition function of this Chern-Simons theory by using the localization technique. Thus, we obtain the quantum gravity partition function, assuming that it can be obtained nonperturbatively by summing over partition functions of the Chern-Simons theory on topologically different manifolds. The resultant partition function is modular invariant, and, in the case in which the central charge is expected to be 24, it is the J function, predicted by Witten.
Super-Planckian spatial field variations and quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Klaewer, Daniel; Palti, Eran [Institut für Theoretische Physik, Ruprecht-Karls-Universität,Philosophenweg 19, 69120 Heidelberg (Germany)
2017-01-20
We study scenarios where a scalar field has a spatially varying vacuum expectation value such that the total field variation is super-Planckian. We focus on the case where the scalar field controls the coupling of a U(1) gauge field, which allows us to apply the Weak Gravity Conjecture to such configurations. We show that this leads to evidence for a conjectured property of quantum gravity that as a scalar field variation in field space asymptotes to infinity there must exist an infinite tower of states whose mass decreases as an exponential function of the scalar field variation. We determine the rate at which the mass of the states reaches this exponential behaviour showing that it occurs quickly after the field variation passes the Planck scale.
Loop quantum cosmology of the Bianchi I model: complete quantization
International Nuclear Information System (INIS)
Martín-Benito, M; Garay, L J; Mena Marugán, G A; Wilson-Ewing, E
2012-01-01
We complete the canonical quantization of the vacuum Bianchi I model within the improved dynamics scheme of loop quantum cosmology, characterizing the Hilbert structure of the physical states and providing a complete set of observables acting on them. In order to achieve this task, it has been essential to determine the structure of the separable superselection sectors that arise owing to the polymeric quantization, and to prove that the initial value problem obtained when regarding the Hamiltonian constraint as an evolution equation, interpreting the volume as the evolution parameter, is well-posed.
Stochastic Geometry and Quantum Gravity: Some Rigorous Results
Zessin, H.
The aim of these lectures is a short introduction into some recent developments in stochastic geometry which have one of its origins in simplicial gravity theory (see Regge Nuovo Cimento 19: 558-571, 1961). The aim is to define and construct rigorously point processes on spaces of Euclidean simplices in such a way that the configurations of these simplices are simplicial complexes. The main interest then is concentrated on their curvature properties. We illustrate certain basic ideas from a mathematical point of view. An excellent representation of this area can be found in Schneider and Weil (Stochastic and Integral Geometry, Springer, Berlin, 2008. German edition: Stochastische Geometrie, Teubner, 2000). In Ambjørn et al. (Quantum Geometry Cambridge University Press, Cambridge, 1997) you find a beautiful account from the physical point of view. More recent developments in this direction can be found in Ambjørn et al. ("Quantum gravity as sum over spacetimes", Lect. Notes Phys. 807. Springer, Heidelberg, 2010). After an informal axiomatic introduction into the conceptual foundations of Regge's approach the first lecture recalls the concepts and notations used. It presents the fundamental zero-infinity law of stochastic geometry and the construction of cluster processes based on it. The second lecture presents the main mathematical object, i.e. Poisson-Delaunay surfaces possessing an intrinsic random metric structure. The third and fourth lectures discuss their ergodic behaviour and present the two-dimensional Regge model of pure simplicial quantum gravity. We terminate with the formulation of basic open problems. Proofs are given in detail only in a few cases. In general the main ideas are developed. Sufficiently complete references are given.
The Gravity Makeup on the LORHR Event during Mid-loop Operation for APR1400
Energy Technology Data Exchange (ETDEWEB)
Kim, Cheol Woo; Lee, Yong Hee; Lee, Gyu Cheon; Kim, Shin Whan [KEPCO, Daejeon (Korea, Republic of)
2015-05-15
This paper is to investigate means of the available gravity makeup after the event to prevent or sustain the core uncovery and fuel failure for the typical advanced power reactor nuclear power plants (APR1400). Unlike the OPR1000 (optimized power reactor 1000 nuclear power plants), the refueling water storage tank of APR1400 cannot be used for gravity makeup since it is located on the bottom of the containment with a lower elevation than the reactor vessel. So, the other means of gravity makeup and their effect on the core uncovery are accounted. The use of the water used for the cask loading pit (CLP) during refueling or the safety injection line filling tank (SIFT), which are not designed for gravity makeup during the event, and safety injection tanks (SITs) are considered as the alternative source of makeup feed. The results show that gravity makeup of a SIT provides a sufficient operator action time for the LORHR with the station black out (SBO) during the mid-loop operation for the APR1400. From the LORHR event analysis, the effective means of gravity makeup for APR1400 to cope with this event concurrent loss of all AC power is determined as the gravity feed using SITs. Other means for gravity makeup using CLP or SIFT, which are not designed to mitigate the LORHR event, are evaluated as not effective to the event due to the large flow resistances and the low elevation head to overcome the system pressure increase during the LORHR. The use of one SIT and two SITs for the LORHR provides the core uncovery times as 3 hr 8 min and 4 hr 32 min extending 1 hr 15 min and 2 hr 38 min from the base case, respectively.
Understanding big bang in loop quantum cosmology: Recent advances
Energy Technology Data Exchange (ETDEWEB)
Singh, Parampreet [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)], E-mail: psingh@perimeterinstitute.ca
2008-11-01
We discuss the way non-perturbative quantization of cosmological spacetimes in loop quantum cosmology provides insights on the physics of Planck scale and the resolution of big bang singularity. In recent years, rigorous examination of mathematical and physical aspects of the quantum theory, have singled out a consistent quantization which is physically viable and various early ideas have been shown to be inconsistent. These include 'physical effects' originating from modifications to inverse scale factors in the flat models. The singularity resolution is understood to originate from the non-local nature of curvature in the quantum theory and the underlying polymer representation. Based on insights from extensive numerical simulations, an exactly solvable model involving a small approximation at the quantum level can be developed. The model predicts occurrence of bounce for a dense subspace of the Hilbert space and a supremum for the value of energy density. It also provides answers to the growth of fluctuations, showing that semi-classicality is preserved to an amazing degree across the bounce.
Understanding big bang in loop quantum cosmology: Recent advances
Singh, Parampreet
2008-11-01
We discuss the way non-perturbative quantization of cosmological spacetimes in loop quantum cosmology provides insights on the physics of Planck scale and the resolution of big bang singularity. In recent years, rigorous examination of mathematical and physical aspects of the quantum theory, have singled out a consistent quantization which is physically viable and various early ideas have been shown to be inconsistent. These include 'physical effects' originating from modifications to inverse scale factors in the flat models. The singularity resolution is understood to originate from the non-local nature of curvature in the quantum theory and the underlying polymer representation. Based on insights from extensive numerical simulations, an exactly solvable model involving a small approximation at the quantum level can be developed. The model predicts occurrence of bounce for a dense subspace of the Hilbert space and a supremum for the value of energy density. It also provides answers to the growth of fluctuations, showing that semi-classicality is preserved to an amazing degree across the bounce.
Loop quantum cosmology of k=1 FRW models
International Nuclear Information System (INIS)
Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parampreet; Vandersloot, Kevin
2007-01-01
The closed, k=1, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the k=0 case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semiclassical at some late time, the big bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the ''difficulties'' pointed out by Green and Unruh in the k=1 case do not arise in a more systematic treatment. As in k=0 models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the k=0 case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna's recent work addressed to computational physicists
Understanding big bang in loop quantum cosmology: Recent advances
International Nuclear Information System (INIS)
Singh, Parampreet
2008-01-01
We discuss the way non-perturbative quantization of cosmological spacetimes in loop quantum cosmology provides insights on the physics of Planck scale and the resolution of big bang singularity. In recent years, rigorous examination of mathematical and physical aspects of the quantum theory, have singled out a consistent quantization which is physically viable and various early ideas have been shown to be inconsistent. These include 'physical effects' originating from modifications to inverse scale factors in the flat models. The singularity resolution is understood to originate from the non-local nature of curvature in the quantum theory and the underlying polymer representation. Based on insights from extensive numerical simulations, an exactly solvable model involving a small approximation at the quantum level can be developed. The model predicts occurrence of bounce for a dense subspace of the Hilbert space and a supremum for the value of energy density. It also provides answers to the growth of fluctuations, showing that semi-classicality is preserved to an amazing degree across the bounce.
Modular Theory, Non-Commutative Geometry and Quantum Gravity
Directory of Open Access Journals (Sweden)
Wicharn Lewkeeratiyutkul
2010-08-01
Full Text Available This paper contains the first written exposition of some ideas (announced in a previous survey on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.
Lessons from classical gravity about the quantum structure of spacetime
International Nuclear Information System (INIS)
Padmanabhan, Thanu
2011-01-01
I present the theoretical evidence which suggests that gravity is an emergent phenomenon like gas dynamics or elasticity with the gravitational field equations having the same status as, say, the equations of fluid dynamics/elasticity. This paradigm views a wide class of gravitational theories - including Einstein's theory - as describing the thermodynamic limit of the statistical mechanics of 'atoms of spacetime'. Strong internal evidence in favour of such a point of view is presented using the classical features of the gravitational theories with just one quantum mechanical input, viz. the existence of Davies-Unruh temperature of horizons. I discuss several conceptual ingredients of this approach.
Conformal field theory and 2D quantum gravity
International Nuclear Information System (INIS)
Distler, J.; Kawai, Hikaru
1989-01-01
Inspired by the recent work of Knizhnik, Polyakov and Zamolodchikov on the solution of 2D quantum gravity in the 'light cone' gauge, we present a proposal for solving the theory in the usual conformal gauge. Our results for the critical exponents of the theory agree with the genus-zero results of KPZ. Since our formalism naturally generalizes to higher-genus Riemann surfaces, we obtain the critical exponents for all genera. The corresponding results for the supersymmetric case are presented. We also show how to calculate correlation functions in these theories. (orig.)
Giersch International Symposion 2016 : Week 1 : Experimental Search for Quantum Gravity
Experimental Search for Quantum Gravity
2018-01-01
This book summarizes recent developments in the research area of quantum gravity phenomenology. A series of short and nontechnical essays lays out the prospects of various experimental possibilities and their current status. Finding observational evidence for the quantization of space-time was long thought impossible. In the last decade however, new experimental design and technological advances have changed the research landscape and opened new perspectives on quantum gravity. Formerly dominated by purely theoretical constructions, quantum gravity now has a lively phenomenology to offer. From high precision measurements using macroscopic quantum oscillators to new analysis methods of the cosmic microwave background, no stone is being left unturned in the experimental search for quantum gravity. This book sheds new light on the connection of astroparticle physics with the quantum gravity problem. Gravitational waves and their detection are covered. It illustrates findings from the interconnection between gene...
R 2 inflation to probe non-perturbative quantum gravity
Koshelev, Alexey S.; Sravan Kumar, K.; Starobinsky, Alexei A.
2018-03-01
It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, R + R 2, or shortly R 2, inflation is the most successful in accounting for the latest CMB data from the PLANCK satellite and other experiments. Moreover, recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric space-times. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant. We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local R 2 model. We further compute the full second order perturbed action around any background belonging to that class. We proceed by extracting the key inflationary parameters of our model such as a spectral index ( n s ), a tensor-to-scalar ratio ( r) and a tensor tilt ( n t ). It appears that n s remains the same as in the local R 2 inflation in the leading slow-roll approximation, while r and n t get modified due to modification of the tensor power spectrum. This class of models allows for any value of r complete R 2 gravity a natural target for future CMB probes.
Black holes production in self-complete quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Spallucci, Euro, E-mail: spallucci@ts.infn.it [Dipartimento di Fisica Teorica, Universita di Trieste (Italy); INFN, Sezione di Trieste (Italy); Smailagic, Anais, E-mail: anais@ts.infn.it [INFN, Sezione di Trieste (Italy)
2012-03-19
A regular black hole model, which has been proposed by Hayward (2006) in , is reconsidered in the framework of higher dimensional TeV unification and self-complete quantum gravity scenario (Dvali and Gomez (2010) , Dvali, Folkerts and Germani (2010) , Spallucci and Ansoldi (2011) ). We point out the 'quantum' nature of these objects and compute their cross section production by taking into account the key role played by the existence of a minimal lengthl{sub 0}. We show that the threshold energy is related to l{sub 0}. We recover, in the high energy limit, the standard 'black-disk' form of the cross section, while it vanishes, below threshold, faster than any power of the invariant mass energy {radical}(-s).
Gravity, quantum theory and the evaporation of black holes. [Review
Energy Technology Data Exchange (ETDEWEB)
Wilkins, D C [Tata Inst. of Fundamental Research, Bombay (India)
1977-06-01
Recent developments in blackhole physics are reviewed. It is pointed out that black hole thermodynamics is a theory of exceptional unity and elegance. Starting from the discovery of thermal emission from black holes (evaporation process) by Hawking, the four thermodynamic laws they obey, the nonzero temperature and entropy, angular momentum and charge of the black holes are dealt with. The influence of this thermodynamics on quantum theory and gravitation is discussed in relation to particle creation and quantum gravity. The formation and basic properties of black holes are described in terms of significant milestones. The decade-long development of black hole thermodynamics from 1963-73 is highlighted. The fundamental issues arising in particle physics as a result of these discoveries are discussed.
And what if gravity is intrinsically quantic?
International Nuclear Information System (INIS)
Ziaeepour, Houri
2009-01-01
Since the early days of search for a quantum theory of gravity the attempts have been mostly concentrated on the quantization of an otherwise classical system. The two most contentious candidate theories of gravity, string theory and quantum loop gravity are based on a quantum field theory - the latter is a quantum field theory of connections on a SU(2) group manifold and the former is a quantum field theory in two dimensional spaces. Here we argue that there is a very close relation between quantum mechanics (QM) and gravity. Without gravity, QM becomes ambiguous. We consider this observation as the evidence for an intrinsic relation between these fundamental laws of nature. We suggest a quantum role and definition for gravity in the context of a quantum Universe, and present a preliminary formulation for gravity in a system with a finite number of particles.
Hierarchies in Quantum Gravity: Large Numbers, Small Numbers, and Axions
Stout, John Eldon
Our knowledge of the physical world is mediated by relatively simple, effective descriptions of complex processes. By their very nature, these effective theories obscure any phenomena outside their finite range of validity, discarding information crucial to understanding the full, quantum gravitational theory. However, we may gain enormous insight into the full theory by understanding how effective theories with extreme characteristics--for example, those which realize large-field inflation or have disparate hierarchies of scales--can be naturally realized in consistent theories of quantum gravity. The work in this dissertation focuses on understanding the quantum gravitational constraints on these "extreme" theories in well-controlled corners of string theory. Axion monodromy provides one mechanism for realizing large-field inflation in quantum gravity. These models spontaneously break an axion's discrete shift symmetry and, assuming that the corrections induced by this breaking remain small throughout the excursion, create a long, quasi-flat direction in field space. This weakly-broken shift symmetry has been used to construct a dynamical solution to the Higgs hierarchy problem, dubbed the "relaxion." We study this relaxion mechanism and show that--without major modifications--it can not be naturally embedded within string theory. In particular, we find corrections to the relaxion potential--due to the ten-dimensional backreaction of monodromy charge--that conflict with naive notions of technical naturalness and render the mechanism ineffective. The super-Planckian field displacements necessary for large-field inflation may also be realized via the collective motion of many aligned axions. However, it is not clear that string theory provides the structures necessary for this to occur. We search for these structures by explicitly constructing the leading order potential for C4 axions and computing the maximum possible field displacement in all compactifications of
Dirac Magnon Nodal Loops in Quasi-2D Quantum Magnets.
Owerre, S A
2017-07-31
In this report, we propose a new concept of one-dimensional (1D) closed lines of Dirac magnon nodes in two-dimensional (2D) momentum space of quasi-2D quantum magnetic systems. They are termed "2D Dirac magnon nodal-line loops". We utilize the bilayer honeycomb ferromagnets with intralayer coupling J and interlayer coupling J L , which is realizable in the honeycomb chromium compounds CrX 3 (X ≡ Br, Cl, and I). However, our results can also exist in other layered quasi-2D quantum magnetic systems. Here, we show that the magnon bands of the bilayer honeycomb ferromagnets overlap for J L ≠ 0 and form 1D closed lines of Dirac magnon nodes in 2D momentum space. The 2D Dirac magnon nodal-line loops are topologically protected by inversion and time-reversal symmetry. Furthermore, we show that they are robust against weak Dzyaloshinskii-Moriya interaction Δ DM magnon edge modes.
Multi-leg one-loop gravity amplitudes from gauge theory
International Nuclear Information System (INIS)
Bern, Z.; Dixon, L.; Perelstein, M.; Rozowsky, J.S.
1999-01-01
By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n-graviton scattering amplitudes: the 'maximally helicity-violating' amplitudes in N = 8 supergravity, and the 'all-plus' helicity amplitudes in gravity with any minimally coupled massless matter content. The all-plus amplitudes correspond to self-dual field configurations and vanish in supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT) relations between open and closed string theory amplitudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For n ≤ 6, we determine the all-plus amplitudes explicitly from their unitarity cuts. The KLT relations, applied to the cuts, allow us to extend to gravity a previously found 'dimension-shifting' relation between (the cuts of) the all-plus amplitudes in gauge theory and the maximally helicity-violating amplitudes in N = 4 super-Yang-Mills theory. The gravitational version of the relation lets us determine the n ≤ 6N = 8 supergravity amplitudes from the all-plus gravity amplitudes. We infer the two series of amplitudes for all n from their soft and collinear properties, which can also be derived from gauge theory using the KLT relations
Nonlinear quantum gravity on the constant mean curvature foliation
International Nuclear Information System (INIS)
Wang, Charles H-T
2005-01-01
A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system to be quantized. This permits the Hamiltonian constraint equation to be consistently turned into an expectation value equation on quantization that describes the scale factor on each spatial hypersurface characterized by a constant mean exterior curvature. This expectation value equation augments the dynamical quantum evolution of the unconstrained conformal three-geometry with a transverse traceless momentum tensor density. The resulting quantum theory is inherently nonlinear. Nonetheless, it is unitary and free from a nonlocal and implicit description of the Hamiltonian operator. Finally, by imposing additional homogeneity symmetries, a broad class of Bianchi cosmological models are analysed as nonlinear quantum minisuperspaces in the context of the proposed theory
Quantum fluctuations and thermal dissipation in higher derivative gravity
Directory of Open Access Journals (Sweden)
Dibakar Roychowdhury
2015-08-01
Full Text Available In this paper, based on the AdS2/CFT1 prescription, we explore the low frequency behavior of quantum two point functions for a special class of strongly coupled CFTs in one dimension whose dual gravitational counterpart consists of extremal black hole solutions in higher derivative theories of gravity defined over an asymptotically AdS spacetime. The quantum critical points thus described are supposed to correspond to a very large value of the dynamic exponent (z→∞. In our analysis, we find that quantum fluctuations are enhanced due to the higher derivative corrections in the bulk which in turn increases the possibility of quantum phase transition near the critical point. On the field theory side, such higher derivative effects would stand for the corrections appearing due to the finite coupling in the gauge theory. Finally, we compute the coefficient of thermal diffusion at finite coupling corresponding to Gauss Bonnet corrected charged Lifshitz black holes in the bulk. We observe an important crossover corresponding to z=5 fixed point.
Aquilanti, Vincenzo; Bitencourt, Ana Carla P.; Ferreira, Cristiane da S.; Marzuoli, Annalisa; Ragni, Mirco
2008-11-01
The mathematical apparatus of quantum-mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the underlying combinatorial aspects. SU(2) recoupling theory, involving Wigner's 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, nowadays plays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory—and of its extension to other Lie and quantum groups—by using the collective term of 'spin networks'. Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper, we list and discuss some aspects of these developments—such as for instance the hyperquantization algorithm—as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.
Gravitational wave echoes from macroscopic quantum gravity effects
Energy Technology Data Exchange (ETDEWEB)
Barceló, Carlos [Instituto de Astrofísica de Andalucía (IAA-CSIC),Glorieta de la Astronomía, 18008 Granada (Spain); Carballo-Rubio, Raúl [The Cosmology & Gravity Group and the Laboratory for Quantum Gravity & Strings,Department of Mathematics & Applied Mathematics, University of Cape Town,Private Bag, Rondebosch 7701 (South Africa); Garay, Luis J. [Departamento de Física Teórica II,Universidad Complutense de Madrid, 28040 Madrid (Spain); Instituto de Estructura de la Materia (IEM-CSIC),Serrano 121, 28006 Madrid (Spain)
2017-05-10
New theoretical approaches developed in the last years predict that macroscopic quantum gravity effects in black holes should lead to modifications of the gravitational wave signals expected in the framework of classical general relativity, with these modifications being characterized in certain scenarios by the existence of dampened repetitions of the primary signal. Here we use the fact that non-perturbative corrections to the near-horizon external geometry of black holes are necessary for these modifications to exist, in order to classify different proposals and paradigms with respect to this criterion and study in a neat and systematic way their phenomenology. Proposals that lead naturally to the existence of echoes in the late-time ringdown of gravitational wave signals from black hole mergers must share the replacement of black holes by horizonless configurations with a physical surface showing reflective properties in the relevant range of frequencies. On the other hand, proposals or paradigms that restrict quantum gravity effects on the external geometry to be perturbative, such as black hole complementarity or the closely related firewall proposal, do not display echoes. For the sake of completeness we exploit the interplay between the timescales associated with the formation of firewalls and the mechanism behind the existence of echoes in order to conclude that even unconventional distortions of the firewall concept (such as naked firewalls) do not lead to this phenomenon.
The spin-statistics connection in quantum gravity
International Nuclear Information System (INIS)
Balachandran, A.P.; Batista, E.; Costa e Silva, I.P.; Teotonio-Sobrinho, P.
2000-01-01
It is well known that in spite of sharing some properties with conventional particles, topological geons in general violate the spin-statistics theorem. On the other hand, it is generally believed that in quantum gravity theories allowing for topology change, using pair creation and annihilation of geons, one should be able to recover this theorem. In this paper, we take an alternative route, and use an algebraic formalism developed in previous work. We give a description of topological geons where an algebra of 'observables' is identified and quantized. Different irreducible representations of this algebra correspond to different kinds of geons, and are labeled by a non-abelian 'charge' and 'magnetic flux'. We then find that the usual spin-statistics theorem is indeed violated, but a new spin-statistics relation arises, when we assume that the fluxes are superselected. This assumption can be proved if all observables are local, as is generally the case in physical theories. Finally, we also discuss how our approach fits into conventional formulations of quantum gravity
In search of fundamental discreteness in (2 + 1)-dimensional quantum gravity
Budd, T.G.; Loll, R.
2009-01-01
Inspired by previous work in (2 + 1)-dimensional quantum gravity, which found evidence for a discretization of time in the quantum theory, we reexamine the issue for the case of pure Lorentzian gravity with vanishing cosmological constant and spatially compact universes of genus g ≥ 2. Taking the
2d CDT is 2d Horava-Lifshitz quantum gravity
DEFF Research Database (Denmark)
Ambjørn, J.; Glaser, L.; Sato, Y.
2013-01-01
Causal Dynamical Triangulations (CDT) is a lattice theory where aspects of quantum gravity can be studied. Two-dimensional CDT can be solved analytically and the continuum (quantum) Hamiltonian obtained. In this Letter we show that this continuum Hamiltonian is the one obtained by quantizing two......-dimensional projectable Horava-Lifshitz gravity....
Topology Change and the Emergence of Geometry in Two Dimensional Causal Quantum Gravity
Westra, W.
2007-01-01
Despite many attempts, gravity has vigorously resisted a unification with the laws of quantum mechanics. Besides a plethora of technical issues, one is also faced with many interesting conceptual problems. The study of quantum gravity in lower dimensional models ameliorates the technical
Uncertainty principle in loop quantum cosmology by Moyal formalism
Perlov, Leonid
2018-03-01
In this paper, we derive the uncertainty principle for the loop quantum cosmology homogeneous and isotropic Friedmann-Lemaiter-Robertson-Walker model with the holonomy-flux algebra. The uncertainty principle is between the variables c, with the meaning of connection and μ having the meaning of the physical cell volume to the power 2/3, i.e., v2 /3 or a plaquette area. Since both μ and c are not operators, but rather the random variables, the Robertson uncertainty principle derivation that works for hermitian operators cannot be used. Instead we use the Wigner-Moyal-Groenewold phase space formalism. The Wigner-Moyal-Groenewold formalism was originally applied to the Heisenberg algebra of the quantum mechanics. One can derive it from both the canonical and path integral quantum mechanics as well as the uncertainty principle. In this paper, we apply it to the holonomy-flux algebra in the case of the homogeneous and isotropic space. Another result is the expression for the Wigner function on the space of the cylindrical wave functions defined on Rb in c variables rather than in dual space μ variables.