- #1
- 24,775
- 792
Here's a tentative lineup of papers that could appear in the 3rd quarter MIP poll, in case anyone wants to look it over and comment. BTW I happened to notice this time that by coincidence a fair number of the authors are women: Elena Magliaro, Bianca Dittrich, Francesca Vidotto, Diana Kaminski, Mingyi Zhang, Maité Dupuis. Also a fair number of new QG researchers on the list this time. Not sure, perhaps more than usual. The attempt is to sort out papers that could be important or valuable to future research.
http://arxiv.org/abs/1109.0740
Observables in gravity: a review
Johannes Tambornino
(Submitted on 4 Sep 2011)
We present an overview on observables in gravity mainly from a loop quantum gravity perspective. The gauge group of general relativity is the diffeomorphism group of the underlying manifold. Consequently, general relativity is a totally constrained theory with vanishing canonical Hamiltonian. This fact, often referred to as the problem of time, provides the main conceptual difficulty towards the construction of gauge-invariant local observables. Nevertheless, within the framework of complete observables, that encode relations between dynamical fields, remarkable progress has been made during the last 20 years. Although analytic control over observables for full gravity is still lacking, perturbative calculations have been performed and within de-parameterizable toy models it was possible for the first time to construct a full set of gauge invariant observables for a background independent field theory. We review these developments and comment on their implications for quantum gravity.
31 pages. contribution for a special issue of SIGMA on Loop Quantum Gravity and Cosmology
http://arxiv.org/abs/1109.0499
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
Muxin Han, Mingyi Zhang
(Submitted on 2 Sep 2011)
The present paper studies the large-j asymptotics of the Lorentzian EPRL spinfoam amplitude on a 4d simplicial complex with an arbitrary number of simplices. The asymptotics of the spinfoam amplitude is determined by the critical configurations. Here we show that, given a critical configuration in general, there exists a partition of the simplicial complex into three type of regions RNondeg, RDeg-A, RDeg-B, where the three regions are simplicial sub-complexes with boundaries. The critical configuration implies different types of geometries in different types of regions, i.e. (1) the critical configuration restricted into RNondeg implies a nondegenerate discrete Lorentzian geometry, (2) the critical configuration restricted into RDeg-A is degenerate of type-A in our definition of degeneracy, but implies a nondegenerate discrete Euclidean geometry on RDeg-A, (3) the critical configuration restricted into RDeg-B is degenerate of type-B, and implies a vector geometry on RDeg-B. With the critical configuration, we further make a subdivision of the regions RNondeg and RDeg-A into sub-complexes (with boundary) according to their Lorentzian/Euclidean oriented 4-simplex volume V4(v), such that sgn(V4(v)) is a constant sign on each sub-complex. Then in the each sub-complex, the spinfoam amplitude at the critical configuration gives the Regge action in Lorentzian or Euclidean signature respectively on RNondeg or RDeg-A. The Regge action reproduced here contains a sign factor sgn(V4(v)) of the oriented 4-simplex volume. Therefore the Regge action reproduced here can be viewed a discretized Palatini action with on-shell connection. Finally the asymptotic formula of the spinfoam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated to different type of geometries.
54 pages, 2 figures
http://arxiv.org/abs/1109.0080 (EDIT)
Emergent Braided Matter of Quantum Geometry
Sundance Bilson-Thompson, Jonathan Hackett, Louis Kauffman, Yidun Wan
(Submitted on 1 Sep 2011)
Abstract: We review and present a few new results of the program of emergent matter as braid excitations of quantum geometry that is represented by braided ribbon networks, which are a generalisation of the spin networks proposed by Penrose and those in models of background independent quantum gravity theories, such as Loop Quantum Gravity and Spin Foam models. This program has been developed in two parallel but complimentary schemes, namely the trivalent and tetravalent schemes. The former studies the trivalent braids on trivalent braided ribbon networks, while the latter investigate the tetravalent braids on tetravalent braided ribbon networks. Both schemes have been fruitful. The trivalent scheme has been quite successful at establishing a correspondence between the trivalent braids and Standard Model particles, whereas the tetravalent scheme has naturally substantiated a rich, dynamical theory of interactions and propagation of tetravalent braids, which is ruled by topological conservation laws. Some recent advances in the program indicate that the two schemes may converge to yield a fundamental theory of matter in quantum spacetime.
37 pages
http://arxiv.org/abs/1108.5224
Shape Dynamics
Tim Koslowski
(Submitted on 26 Aug 2011)
General Relativity can be reformulated as a geometrodynamical theory, called Shape Dynamics, that is not based on spacetime (in particular refoliation) symmetry but on spatial diffeomorphism and local spatial conformal symmetry. This leads to a constraint algebra that is (unlike General Relativity) a Lie algebra, where all local constraints are linear in momenta and may thus be quantized as vector fields on the geometrodynamic configuration space. The Hamiltonian of Shape Dynamics is complicated but admits simple expressions whenever spatial derivatives are negligible.
4 pages
http://arxiv.org/abs/1108.4577
Algebras of Quantum Variables for Loop Quantum Gravity, I. Overview
Diana Kaminski
(Submitted on 19 Aug 2011)
The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until now. In the project about 'Algebras of Quantum Variables (AQV) for LQG' the known holonomy-flux *-algebra and the Weyl C*-algebra will be modified and a set of new algebras will be proposed and studied. The idea of the construction of these algebras is to establish a finite set of operators, which generates (in the sense of Woronowicz, Schmüdgen and Inoue) the different O*- or C*-algebras of quantum gravity and to use inductive limits of these algebras. In the Loop Quantum Gravity approach usually the basic classical variables are connections and fluxes. Studying the three constraints appearing in the canonical quantisation of classical general relativity in the ADM-formalism some other variables like curvature appear. Consequently the main difficulty of a quantisation of gravity is to find a suitable replacement of the set of elementary classical variables and constraints. The algebra of quantum gravity is supposed to be generated by a set of the operators associated to holonomies, fluxes and in some cases even the curvature. There are two reasonable choices for this algebra: The set of constraints of Quantum Gravity are contained in or at least the constraints are affilliated with this algebra. Secondly, the algebra of quantum variables is said to be physical if it contains complete observables. In the project of 'Algebras of Quantum Variables for LQG' different algebras will be studied with respect to the property of being a physical algebra. Furthermore the existence of KMS-states on these algebras will be argued.
45 pages
http://arxiv.org/abs/1108.2258
Emergence of gravity from spinfoams
Elena Magliaro, Claudio Perini
(Submitted on 10 Aug 2011)
We find a nontrivial regime of spinfoam quantum gravity that reproduces classical Einstein equations. This is the double scaling limit of small Immirzi parameter (gamma), large spins (j) with physical area (gamma times j) constant. In addition to quantum corrections in the Planck constant, we find new corrections in the Immirzi parameter due to the quantum discreteness of spacetime. The result is a strong evidence that the spinfoam covariant quantization of general relativity possesses the correct classical limit.
http://arxiv.org/abs/1108.1974
Canonical simplicial gravity
Bianca Dittrich, Philipp A Hoehn
(Submitted on 9 Aug 2011)
A general canonical formalism for discrete systems is developed which can handle varying phase space dimensions and constraints. The central ingredient is Hamilton's principle function which generates canonical time evolution and ensures that the canonical formalism reproduces the dynamics of the covariant formulation following directly from the action. We apply this formalism to simplicial gravity and (Euclidean) Regge calculus, in particular. A discrete forward/backward evolution is realized by gluing/removing single simplices step by step to/from a bulk triangulation and amounts to Pachner moves in the triangulated hypersurfaces. As a result, the hypersurfaces evolve in a discrete `multi-fingered' time through the full Regge solution. Pachner moves are an elementary and ergodic class of homeomorphisms and generically change the number of variables, but can be implemented as canonical transformations on naturally extended phase spaces. Some moves introduce a priori free data which, however, may become fixed a posteriori by constraints arising in subsequent moves. The end result is a general and fully consistent formulation of canonical Regge calculus, thereby removing a longstanding obstacle in connecting covariant simplicial gravity models to canonical frameworks. The present scheme is, therefore, interesting in view of many approaches to quantum gravity, but may also prove useful for numerical implementations.
52 pages, 14 figures, 3 tables
http://arxiv.org/abs/1108.0910
The black hole information paradox and relative locality
Lee Smolin
(Submitted on 3 Aug 2011)
We argue that the recently proposed principle of relative locality offers a new way to resolve the black hole information puzzle.
11 pages, one figure
http://arxiv.org/abs/1108.0893
Loop Quantum Cosmology: A Status Report
Abhay Ashtekar, Parampreet Singh
(Submitted on 3 Aug 2011)
The goal of this article is to provide an overview of the current state of the art in loop quantum cosmology for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general; and, cosmologists who wish to apply loop quantum cosmology to probe modifications in the standard paradigm of the early universe. An effort has been made to streamline the material so that each of these communities can read only the sections they are most interested in, without a loss of continuity.
136 pages, 15 figures
http://arxiv.org/abs/1108.0832
On the structure of a background independent quantum theory: Hamilton function, transition amplitudes, classical limit and continuous limit
Carlo Rovelli
(Submitted on 3 Aug 2011)
The Hamilton function is a powerful tool for studying the classical limit of quantum systems, which remains meaningful in background-independent systems. In quantum gravity, it clarifies the physical interpretation of the transitions amplitudes and their truncations.
7 pages
http://arxiv.org/abs/1108.0369
Twistor Networks and Covariant Twisted Geometries
Etera R. Livine, Simone Speziale, Johannes Tambornino
(Submitted on 1 Aug 2011)
We study the symplectic reduction of the phase space of two twistors to the cotangent bundle of the Lorentz group. We provide expressions for the Lorentz generators and group elements in terms of the spinors defining the twistors. We use this to define twistor networks as a graph carrying the phase space of two twistors on each edge. We also introduce simple twistor networks, which provide a classical version of the simple projected spin networks living on the boundary Hilbert space of EPRL/FK spin foam models. Finally, we give an expression for the Haar measure in terms of spinors.
18 pages
http://arxiv.org/abs/1107.5274
Holomorphic Lorentzian Simplicity Constraints
Maité Dupuis, Laurent Freidel, Etera R. Livine, Simone Speziale
(Submitted on 26 Jul 2011)
We develop an Hamiltonian representation of the sl(2,C) algebra on a phase space consisting of N copies of twistors, or bi-spinors. We identify a complete set of global invariants, and show that they generate a closed algebra including gl(N,C) as a subalgebra. Then, we define the linear and quadratic simplicity constraints which reduce the spinor variables to (framed) 3d spacelike polyhedra embedded in Minkowski spacetime. Finally, we introduce a new version of the simplicity constraints which (i) are holomorphic and (ii) Poisson-commute with each other, and show their equivalence to the linear and quadratic constraints.
20 pages
http://arxiv.org/abs/1107.5185
Feynman diagrammatic approach to spin foams
Marcin Kisielowski, Jerzy Lewandowski, Jacek Puchta
(Submitted on 26 Jul 2011)
"The Spin Foams for People Without the 3d/4d Imagination" could be an alternative title of our work. We derive spin foams from operator spin network diagrams} we introduce. Our diagrams are the spin network analogy of the Feynman diagrams. Their framework is compatible with the framework of Loop Quantum Gravity. For every operator spin network diagram we construct a corresponding operator spin foam. Admitting all the spin networks of LQG and all possible diagrams leads to a clearly defined large class of operator spin foams. In this way our framework provides a proposal for a class of 2-cell complexes that should be used in the spin foam theories of LQG. Within this class, our diagrams are just equivalent to the spin foams. The advantage, however, in the diagram framework is, that it is self contained, all the amplitudes can be calculated directly from the diagrams without explicit visualization of the corresponding spin foams. The spin network diagram operators and amplitudes are consistently defined on their own. Each diagram encodes all the combinatorial information. We illustrate applications of our diagrams: we introduce a diagram definition of Rovelli's surface amplitudes as well as of the canonical transition amplitudes. Importantly, our operator spin network diagrams are defined in a sufficiently general way to accommodate all the versions of the EPRL or the FK model, as well as other possible models. The diagrams are also compatible with the structure of the LQG Hamiltonian operators, what is an additional advantage. Finally, a scheme for a complete definition of a spin foam theory by declaring a set of interaction vertices emerges from the examples presented at the end of the paper.
36 pages, 23 figures
http://arxiv.org/abs/1107.2633
Many-nodes/many-links spinfoam: the homogeneous and isotropic case
Francesca Vidotto
(Submitted on 13 Jul 2011)
I compute the Lorentzian EPRL/FK/KKL spinfoam vertex amplitude for regular graphs, with an arbitrary number of links and nodes, and coherent states peaked on a homogeneous and isotropic geometry. This form of the amplitude can be applied for example to a dipole with an arbitrary number of links or to the 4-simplex given by the compete graph on 5 nodes. All the resulting amplitudes have the same support, independently of the graph used, in the large j (large volume) limit. This implies that they all yield the Friedmann equation: I show this in the presence of the cosmological constant. This result indicates that in the semiclassical limit quantum corrections in spinfoam cosmology do not come from just refining the graph, but rather from relaxing the large j limit.
http://arxiv.org/abs/1107.1540
Observational test of inflation in loop quantum cosmology
Martin Bojowald, Gianluca Calcagni, Shinji Tsujikawa
(Submitted on 8 Jul 2011)
We study in detail the power spectra of scalar and tensor perturbations generated during inflation in loop quantum cosmology (LQC). After clarifying in a novel quantitative way how inverse-volume corrections arise in inhomogeneous settings, we show that they can generate large running spectral indices, which generally lead to an enhancement of power at large scales. We provide explicit formulas for the scalar/tensor power spectra under the slow-roll approximation, by taking into account corrections of order higher than the runnings. We place observational bounds on the inverse-volume quantum correction δ ~ a-σ (σ >0, a is the scale factor) and the slow-roll parameter εV for power-law potentials as well as exponential potentials by using the data of WMAP 7yr combined with other observations. We derive the constraints on δ for two pivot wavenumbers k0 for several values of δ. The quadratic potential can be compatible with the data even in the presence of the LQC corrections, but the quartic potential is in tension with observations. We also find that the upper bounds on δ (k0) for given σ and k0 are insensitive to the choice of the inflaton potentials.
37 pages, 6 figures, 1 table
http://arxiv.org/abs/1107.1320
Black hole entropy and isolated horizons thermodynamics
Amit Ghosh, Alejandro Perez
(Submitted on 7 Jul 2011)
We present a statistical mechanical calculation of the thermodynamical properties of (non rotating) isolated horizons. The introduction of Planck scale allows for the definition of an universal horizon temperature (independent of the mass of the black hole) and a well-defined notion of energy (as measured by suitable local observers) proportional to the horizon area in Planck units. The microcanonical and canonical ensembles associated with the system are introduced. Black hole entropy and other thermodynamical quantities can be consistently computed in both ensembles and results are in agreement with Hawking's semiclassical analysis for all values of the Immirzi parameter.
5 pages
http://arxiv.org/abs/1107.0709
The Plebanski sectors of the EPRL vertex
Jonathan Engle
(Submitted on 4 Jul 2011)
Modern spin-foam models of four dimensional gravity are based on a discrete version of the Spin(4) Plebanski formulation. Beyond what is already in the literature, we clarify the meaning of different Plebanski sectors in this classical discrete model. We show that the linearized simplicity constraints used in the EPRL and FK models are not sufficient to impose a restriction to a single Plebanski sector, but rather, three Plebanski sectors are mixed. We propose this as the reason for certain extra 'undesired' terms in the asymptotics of the EPRL vertex analyzed by Barrett et al. This explanation for the extra terms is new and different from that sometimes offered in the spin-foam literature thus far.
17 pages
http://arxiv.org/abs/1109.0740
Observables in gravity: a review
Johannes Tambornino
(Submitted on 4 Sep 2011)
We present an overview on observables in gravity mainly from a loop quantum gravity perspective. The gauge group of general relativity is the diffeomorphism group of the underlying manifold. Consequently, general relativity is a totally constrained theory with vanishing canonical Hamiltonian. This fact, often referred to as the problem of time, provides the main conceptual difficulty towards the construction of gauge-invariant local observables. Nevertheless, within the framework of complete observables, that encode relations between dynamical fields, remarkable progress has been made during the last 20 years. Although analytic control over observables for full gravity is still lacking, perturbative calculations have been performed and within de-parameterizable toy models it was possible for the first time to construct a full set of gauge invariant observables for a background independent field theory. We review these developments and comment on their implications for quantum gravity.
31 pages. contribution for a special issue of SIGMA on Loop Quantum Gravity and Cosmology
http://arxiv.org/abs/1109.0499
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
Muxin Han, Mingyi Zhang
(Submitted on 2 Sep 2011)
The present paper studies the large-j asymptotics of the Lorentzian EPRL spinfoam amplitude on a 4d simplicial complex with an arbitrary number of simplices. The asymptotics of the spinfoam amplitude is determined by the critical configurations. Here we show that, given a critical configuration in general, there exists a partition of the simplicial complex into three type of regions RNondeg, RDeg-A, RDeg-B, where the three regions are simplicial sub-complexes with boundaries. The critical configuration implies different types of geometries in different types of regions, i.e. (1) the critical configuration restricted into RNondeg implies a nondegenerate discrete Lorentzian geometry, (2) the critical configuration restricted into RDeg-A is degenerate of type-A in our definition of degeneracy, but implies a nondegenerate discrete Euclidean geometry on RDeg-A, (3) the critical configuration restricted into RDeg-B is degenerate of type-B, and implies a vector geometry on RDeg-B. With the critical configuration, we further make a subdivision of the regions RNondeg and RDeg-A into sub-complexes (with boundary) according to their Lorentzian/Euclidean oriented 4-simplex volume V4(v), such that sgn(V4(v)) is a constant sign on each sub-complex. Then in the each sub-complex, the spinfoam amplitude at the critical configuration gives the Regge action in Lorentzian or Euclidean signature respectively on RNondeg or RDeg-A. The Regge action reproduced here contains a sign factor sgn(V4(v)) of the oriented 4-simplex volume. Therefore the Regge action reproduced here can be viewed a discretized Palatini action with on-shell connection. Finally the asymptotic formula of the spinfoam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated to different type of geometries.
54 pages, 2 figures
http://arxiv.org/abs/1109.0080 (EDIT)
Emergent Braided Matter of Quantum Geometry
Sundance Bilson-Thompson, Jonathan Hackett, Louis Kauffman, Yidun Wan
(Submitted on 1 Sep 2011)
Abstract: We review and present a few new results of the program of emergent matter as braid excitations of quantum geometry that is represented by braided ribbon networks, which are a generalisation of the spin networks proposed by Penrose and those in models of background independent quantum gravity theories, such as Loop Quantum Gravity and Spin Foam models. This program has been developed in two parallel but complimentary schemes, namely the trivalent and tetravalent schemes. The former studies the trivalent braids on trivalent braided ribbon networks, while the latter investigate the tetravalent braids on tetravalent braided ribbon networks. Both schemes have been fruitful. The trivalent scheme has been quite successful at establishing a correspondence between the trivalent braids and Standard Model particles, whereas the tetravalent scheme has naturally substantiated a rich, dynamical theory of interactions and propagation of tetravalent braids, which is ruled by topological conservation laws. Some recent advances in the program indicate that the two schemes may converge to yield a fundamental theory of matter in quantum spacetime.
37 pages
http://arxiv.org/abs/1108.5224
Shape Dynamics
Tim Koslowski
(Submitted on 26 Aug 2011)
General Relativity can be reformulated as a geometrodynamical theory, called Shape Dynamics, that is not based on spacetime (in particular refoliation) symmetry but on spatial diffeomorphism and local spatial conformal symmetry. This leads to a constraint algebra that is (unlike General Relativity) a Lie algebra, where all local constraints are linear in momenta and may thus be quantized as vector fields on the geometrodynamic configuration space. The Hamiltonian of Shape Dynamics is complicated but admits simple expressions whenever spatial derivatives are negligible.
4 pages
http://arxiv.org/abs/1108.4577
Algebras of Quantum Variables for Loop Quantum Gravity, I. Overview
Diana Kaminski
(Submitted on 19 Aug 2011)
The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until now. In the project about 'Algebras of Quantum Variables (AQV) for LQG' the known holonomy-flux *-algebra and the Weyl C*-algebra will be modified and a set of new algebras will be proposed and studied. The idea of the construction of these algebras is to establish a finite set of operators, which generates (in the sense of Woronowicz, Schmüdgen and Inoue) the different O*- or C*-algebras of quantum gravity and to use inductive limits of these algebras. In the Loop Quantum Gravity approach usually the basic classical variables are connections and fluxes. Studying the three constraints appearing in the canonical quantisation of classical general relativity in the ADM-formalism some other variables like curvature appear. Consequently the main difficulty of a quantisation of gravity is to find a suitable replacement of the set of elementary classical variables and constraints. The algebra of quantum gravity is supposed to be generated by a set of the operators associated to holonomies, fluxes and in some cases even the curvature. There are two reasonable choices for this algebra: The set of constraints of Quantum Gravity are contained in or at least the constraints are affilliated with this algebra. Secondly, the algebra of quantum variables is said to be physical if it contains complete observables. In the project of 'Algebras of Quantum Variables for LQG' different algebras will be studied with respect to the property of being a physical algebra. Furthermore the existence of KMS-states on these algebras will be argued.
45 pages
http://arxiv.org/abs/1108.2258
Emergence of gravity from spinfoams
Elena Magliaro, Claudio Perini
(Submitted on 10 Aug 2011)
We find a nontrivial regime of spinfoam quantum gravity that reproduces classical Einstein equations. This is the double scaling limit of small Immirzi parameter (gamma), large spins (j) with physical area (gamma times j) constant. In addition to quantum corrections in the Planck constant, we find new corrections in the Immirzi parameter due to the quantum discreteness of spacetime. The result is a strong evidence that the spinfoam covariant quantization of general relativity possesses the correct classical limit.
http://arxiv.org/abs/1108.1974
Canonical simplicial gravity
Bianca Dittrich, Philipp A Hoehn
(Submitted on 9 Aug 2011)
A general canonical formalism for discrete systems is developed which can handle varying phase space dimensions and constraints. The central ingredient is Hamilton's principle function which generates canonical time evolution and ensures that the canonical formalism reproduces the dynamics of the covariant formulation following directly from the action. We apply this formalism to simplicial gravity and (Euclidean) Regge calculus, in particular. A discrete forward/backward evolution is realized by gluing/removing single simplices step by step to/from a bulk triangulation and amounts to Pachner moves in the triangulated hypersurfaces. As a result, the hypersurfaces evolve in a discrete `multi-fingered' time through the full Regge solution. Pachner moves are an elementary and ergodic class of homeomorphisms and generically change the number of variables, but can be implemented as canonical transformations on naturally extended phase spaces. Some moves introduce a priori free data which, however, may become fixed a posteriori by constraints arising in subsequent moves. The end result is a general and fully consistent formulation of canonical Regge calculus, thereby removing a longstanding obstacle in connecting covariant simplicial gravity models to canonical frameworks. The present scheme is, therefore, interesting in view of many approaches to quantum gravity, but may also prove useful for numerical implementations.
52 pages, 14 figures, 3 tables
http://arxiv.org/abs/1108.0910
The black hole information paradox and relative locality
Lee Smolin
(Submitted on 3 Aug 2011)
We argue that the recently proposed principle of relative locality offers a new way to resolve the black hole information puzzle.
11 pages, one figure
http://arxiv.org/abs/1108.0893
Loop Quantum Cosmology: A Status Report
Abhay Ashtekar, Parampreet Singh
(Submitted on 3 Aug 2011)
The goal of this article is to provide an overview of the current state of the art in loop quantum cosmology for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general; and, cosmologists who wish to apply loop quantum cosmology to probe modifications in the standard paradigm of the early universe. An effort has been made to streamline the material so that each of these communities can read only the sections they are most interested in, without a loss of continuity.
136 pages, 15 figures
http://arxiv.org/abs/1108.0832
On the structure of a background independent quantum theory: Hamilton function, transition amplitudes, classical limit and continuous limit
Carlo Rovelli
(Submitted on 3 Aug 2011)
The Hamilton function is a powerful tool for studying the classical limit of quantum systems, which remains meaningful in background-independent systems. In quantum gravity, it clarifies the physical interpretation of the transitions amplitudes and their truncations.
7 pages
http://arxiv.org/abs/1108.0369
Twistor Networks and Covariant Twisted Geometries
Etera R. Livine, Simone Speziale, Johannes Tambornino
(Submitted on 1 Aug 2011)
We study the symplectic reduction of the phase space of two twistors to the cotangent bundle of the Lorentz group. We provide expressions for the Lorentz generators and group elements in terms of the spinors defining the twistors. We use this to define twistor networks as a graph carrying the phase space of two twistors on each edge. We also introduce simple twistor networks, which provide a classical version of the simple projected spin networks living on the boundary Hilbert space of EPRL/FK spin foam models. Finally, we give an expression for the Haar measure in terms of spinors.
18 pages
http://arxiv.org/abs/1107.5274
Holomorphic Lorentzian Simplicity Constraints
Maité Dupuis, Laurent Freidel, Etera R. Livine, Simone Speziale
(Submitted on 26 Jul 2011)
We develop an Hamiltonian representation of the sl(2,C) algebra on a phase space consisting of N copies of twistors, or bi-spinors. We identify a complete set of global invariants, and show that they generate a closed algebra including gl(N,C) as a subalgebra. Then, we define the linear and quadratic simplicity constraints which reduce the spinor variables to (framed) 3d spacelike polyhedra embedded in Minkowski spacetime. Finally, we introduce a new version of the simplicity constraints which (i) are holomorphic and (ii) Poisson-commute with each other, and show their equivalence to the linear and quadratic constraints.
20 pages
http://arxiv.org/abs/1107.5185
Feynman diagrammatic approach to spin foams
Marcin Kisielowski, Jerzy Lewandowski, Jacek Puchta
(Submitted on 26 Jul 2011)
"The Spin Foams for People Without the 3d/4d Imagination" could be an alternative title of our work. We derive spin foams from operator spin network diagrams} we introduce. Our diagrams are the spin network analogy of the Feynman diagrams. Their framework is compatible with the framework of Loop Quantum Gravity. For every operator spin network diagram we construct a corresponding operator spin foam. Admitting all the spin networks of LQG and all possible diagrams leads to a clearly defined large class of operator spin foams. In this way our framework provides a proposal for a class of 2-cell complexes that should be used in the spin foam theories of LQG. Within this class, our diagrams are just equivalent to the spin foams. The advantage, however, in the diagram framework is, that it is self contained, all the amplitudes can be calculated directly from the diagrams without explicit visualization of the corresponding spin foams. The spin network diagram operators and amplitudes are consistently defined on their own. Each diagram encodes all the combinatorial information. We illustrate applications of our diagrams: we introduce a diagram definition of Rovelli's surface amplitudes as well as of the canonical transition amplitudes. Importantly, our operator spin network diagrams are defined in a sufficiently general way to accommodate all the versions of the EPRL or the FK model, as well as other possible models. The diagrams are also compatible with the structure of the LQG Hamiltonian operators, what is an additional advantage. Finally, a scheme for a complete definition of a spin foam theory by declaring a set of interaction vertices emerges from the examples presented at the end of the paper.
36 pages, 23 figures
http://arxiv.org/abs/1107.2633
Many-nodes/many-links spinfoam: the homogeneous and isotropic case
Francesca Vidotto
(Submitted on 13 Jul 2011)
I compute the Lorentzian EPRL/FK/KKL spinfoam vertex amplitude for regular graphs, with an arbitrary number of links and nodes, and coherent states peaked on a homogeneous and isotropic geometry. This form of the amplitude can be applied for example to a dipole with an arbitrary number of links or to the 4-simplex given by the compete graph on 5 nodes. All the resulting amplitudes have the same support, independently of the graph used, in the large j (large volume) limit. This implies that they all yield the Friedmann equation: I show this in the presence of the cosmological constant. This result indicates that in the semiclassical limit quantum corrections in spinfoam cosmology do not come from just refining the graph, but rather from relaxing the large j limit.
http://arxiv.org/abs/1107.1540
Observational test of inflation in loop quantum cosmology
Martin Bojowald, Gianluca Calcagni, Shinji Tsujikawa
(Submitted on 8 Jul 2011)
We study in detail the power spectra of scalar and tensor perturbations generated during inflation in loop quantum cosmology (LQC). After clarifying in a novel quantitative way how inverse-volume corrections arise in inhomogeneous settings, we show that they can generate large running spectral indices, which generally lead to an enhancement of power at large scales. We provide explicit formulas for the scalar/tensor power spectra under the slow-roll approximation, by taking into account corrections of order higher than the runnings. We place observational bounds on the inverse-volume quantum correction δ ~ a-σ (σ >0, a is the scale factor) and the slow-roll parameter εV for power-law potentials as well as exponential potentials by using the data of WMAP 7yr combined with other observations. We derive the constraints on δ for two pivot wavenumbers k0 for several values of δ. The quadratic potential can be compatible with the data even in the presence of the LQC corrections, but the quartic potential is in tension with observations. We also find that the upper bounds on δ (k0) for given σ and k0 are insensitive to the choice of the inflaton potentials.
37 pages, 6 figures, 1 table
http://arxiv.org/abs/1107.1320
Black hole entropy and isolated horizons thermodynamics
Amit Ghosh, Alejandro Perez
(Submitted on 7 Jul 2011)
We present a statistical mechanical calculation of the thermodynamical properties of (non rotating) isolated horizons. The introduction of Planck scale allows for the definition of an universal horizon temperature (independent of the mass of the black hole) and a well-defined notion of energy (as measured by suitable local observers) proportional to the horizon area in Planck units. The microcanonical and canonical ensembles associated with the system are introduced. Black hole entropy and other thermodynamical quantities can be consistently computed in both ensembles and results are in agreement with Hawking's semiclassical analysis for all values of the Immirzi parameter.
5 pages
http://arxiv.org/abs/1107.0709
The Plebanski sectors of the EPRL vertex
Jonathan Engle
(Submitted on 4 Jul 2011)
Modern spin-foam models of four dimensional gravity are based on a discrete version of the Spin(4) Plebanski formulation. Beyond what is already in the literature, we clarify the meaning of different Plebanski sectors in this classical discrete model. We show that the linearized simplicity constraints used in the EPRL and FK models are not sufficient to impose a restriction to a single Plebanski sector, but rather, three Plebanski sectors are mixed. We propose this as the reason for certain extra 'undesired' terms in the asymptotics of the EPRL vertex analyzed by Barrett et al. This explanation for the extra terms is new and different from that sometimes offered in the spin-foam literature thus far.
17 pages
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