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Effective Field Theory from Spin Foam Models :3D Example
Effective field theory from spin Foam models :3d example Laurent Freidel Pennstate 2007 Background independent Loop Quantum Gravity in a nutshell Background independence: what the quantum geometry is at Planck scale cannot be postulated its needs to be determined dynamically •Hamiltonian quantisation: gravity is a gauge theory 2 SU(2) Yang-mills phase space (A,E) + constraints i1 (Γ, j , i ) (15) •Kinematical Hilbert space is spannede v by j1 j5 j2 spin network: graph colored by su(2) rep j6 j4 i4 Wave function i3 Ψ(Γ,je,iv)(A) i2 j3 (16) •Eigenstates of Geometrical operators, Area, Vol = trj(h (A)) (17) discrete spectra quantized space◦ geometry s’ 2 •Dynamics:Area !encodedΨΓ,je,i vin= spin8πγ foamlP modelsje(j eallowing+ 1) ΨΓ ,jthee,iv (18) e R Γ + ... computation of transition amplitudes∈!∪ "between Spin networks states: quantum spacetime geometry s 2 Area!Ψ(Γ,je,iv) = 8πγlP je(je + 1) Ψ(Γ,je,iv) (19) # e R Γ ( ∈!∪ " $ %& ' 3 2 VolΨΓ,je,iv = 8πγlP vje,iv ΨΓ,je,iv (20) # v R Γ ( * ∈!∪ ) F (A) E (21) ∝ Area(! H) = A (22) H = tr([E, E]F (A)) (23) Hj(i) (24) i ! i S(g) Dg e lP (25) + K (j) k (l d ) (26) F ∝ F P j ! k [Xi , Xj] = ilP #ijkX (27) m sin(κm)/κ (28) → S3 SU(2) (29) ∼ X ∂ (30) ∼ P 2 (Γ, je, iv) (15) Ψ(Γ,je,iv)(A) (16) v v Ue Pe + [Ωe, Pe] = 0 (0.32) = trj(h (A)) (17) ◦ ∂!e=v 2 S = tr(XeGe) (0.33) Area!ΨΓ,je,iv = 8πγlP je(je +T1ra)nsΨitioΓn,jaem,ipvlitudes between spin network state(1s a8)re defined by e e R Γ s, s! = A[ ], (11) ∈ ∪ ! "phys F ! " ! F:s→s! v v ! δXe = Ue Φwhvere the[nΩotaeti,onΦanvtic]ip=ates t0he interpretation of such amplitudes as defining the physical (0.34) scala−r product. -
The Black Hole Information Paradox and Relative Locality Arxiv
The black hole information paradox and relative locality Lee Smolin∗ Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2J 2Y5, Canada October 24, 2018 Abstract We argue that the recently proposed principle of relative locality offers a new way to resolve the black hole information puzzle. Contents 1 Introduction 2 2 A possible resolution of the BH information paradox 5 2.1 The usual statement of the black hole information paradox . 5 2.2 The point of view of an observer at the formation of the black hole . 6 2.3 The point of view of the observer at the final evaporation . 7 arXiv:1108.0910v1 [gr-qc] 3 Aug 2011 3 Conclusion 8 ∗[email protected] 1 1 Introduction The black hole information paradox1 has challenged theorists of quantum gravity since first proposed by Hawking[1]. One much discussed view has been that some kind of non- locality is required to resolve the puzzle[4]. A recently proposed framework for quantum gravity phenomenology, called relative locality[5, 6, 7, 8] does feature a very controlled form of non-locality. We argue here that the kind and scale of non-locality implied by relative locality is sufficient to resolve the black hole information paradox. Whatever the quantum theory of gravity that describes nature is, we have good reason to suspect that it involves a dissolving of the usual notion of locality in spacetime. It is therefore of interest to characterize exactly how non-locality first appears in physical phenomena in experimental regimes where one of the Planck scales becomes evident. -
Quantum Theory of Geometry I: Area Operators
The Erwin Schrodinger International Boltzmanngasse ESI Institute for Mathematical Physics A Wien Austria Quantum Theory of Geometry I Area Op erators Abhay Ashtekar Jerzy Lewandowski Vienna Preprint ESI August Supp orted by Federal Ministry of Science and Research Austria Available via httpwwwesiacat Quantum Theory of Geometry I Area Op erators Abhay Ashtekar and Jerzy Lewandowski August Center for Gravitational Physics and Geometry Physics Department Penn State University Park PA USA Institute of Theoretical Physics Warsaw University ul Hoza Warsaw Poland Max Planck Institut fur Gravitationphysik Schlaatzweg Potsdam Germany Abstract A new functional calculus develop ed recently for a fully nonp erturbative treatment of quantum gravity is used to b egin a systematic construction of a quantum theory of geometry Regulated op erators corresp onding to areas of surfaces are intro duced and shown to b e selfadjoint on the underlying kinematical Hilb ert space of states It is shown that their sp ectra are purely discrete indicating that the underlying quantum geometry is far from what the continuum picture might suggest Indeed the fundamental excitations of quantum geometry are dimensional rather like p olymers and the dimensional continuum geometry emerges only on coarse graining The full Hilb ert space admits an orthonormal decomp osition into nite dimensional subspaces which can b e interpreted as the spaces of states of spin systems Using this prop erty the complete sp ectrum of the area op erators is evaluated The -
At the Corner of Space and Time
At the Corner of Space and Time by Barak Shoshany A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Physics Waterloo, Ontario, Canada, 2019 c Barak Shoshany 2019 Examining Committee Membership The following served on the Examining Committee for this thesis. The decision of the Examining Committee is by majority vote. External Examiner: Karim Noui Associate Professor University of Tours Supervisors: Laurent Freidel Faculty Perimeter Institute for Theoretical Physics Robert Myers Faculty Perimeter Institute for Theoretical Physics Internal Members: Robert Mann Professor University of Waterloo John Moffat Professor Emeritus University of Toronto Internal-External Member: Florian Girelli Associate Professor University of Waterloo ii Author’s Declaration This thesis consists of material all of which I authored or co-authored: see Statement of Contributions included in the thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. iii Statement of Contributions This thesis is based on the papers [1], co-authored with Laurent Freidel and Florian Girelli, the papers [2, 3], of which I am the sole author, and additional unpublished material, of which I am the sole author. iv Abstract We perform a rigorous piecewise-flat discretization of classical general relativity in the first-order formulation, in both 2+1 and 3+1 dimensions, carefully keeping track of curvature and torsion via holonomies. We show that the resulting phase space is precisely that of spin networks, the quantum states of discrete spacetime in loop quan- tum gravity, with additional degrees of freedom called edge modes, which control the gluing between cells. -
Redalyc.Physics of Deformed Special Relativity: Relativity Principle Revisited
Brazilian Journal of Physics ISSN: 0103-9733 [email protected] Sociedade Brasileira de Física Brasil Girelli, Florian; Livine, Etera R. Physics of deformed special relativity: relativity principle revisited Brazilian Journal of Physics, vol. 35, núm. 2B, junio, 2005, pp. 432-438 Sociedade Brasileira de Física Sâo Paulo, Brasil Available in: http://www.redalyc.org/articulo.oa?id=46415793011 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative 432 Brazilian Journal of Physics, vol. 35, no. 2B, June, 2005 Physics of Deformed Special Relativity: Relativity Principle Revisited Florian Girelli and Etera R. Livine Perimeter Institute, 31 Caroline Street North Waterloo, Ontario Canada N2L 2Y5 Received on 23 December, 2004 In many different ways, Deformed Special Relativity (DSR) has been argued to provide an effective limit of quantum gravity in almost-flat regime. Unfortunately, DSR is up to now plagued by many conceptual problems (in particular how it describes macroscopic objects) which forbids a definitive physical interpretation and clear predictions. Here we propose a consistent framework to interpret DSR. We extend the principle of relativity: the same way that Special Relativity showed us that the definition of a reference frame requires to specify its speed, we show that DSR implies that we must also take into account its mass. We further advocate a 5- dimensional point of view on DSR physics and the extension of the kinematical symmetry from the Poincare´ group to the Poincare-de´ Sitter group (ISO(4; 1)). -
Emergence of Time in Loop Quantum Gravity∗
Emergence of time in Loop Quantum Gravity∗ Suddhasattwa Brahma,1y 1 Center for Field Theory and Particle Physics, Fudan University, 200433 Shanghai, China Abstract Loop quantum gravity has formalized a robust scheme in resolving classical singu- larities in a variety of symmetry-reduced models of gravity. In this essay, we demon- strate that the same quantum correction which is crucial for singularity resolution is also responsible for the phenomenon of signature change in these models, whereby one effectively transitions from a `fuzzy' Euclidean space to a Lorentzian space-time in deep quantum regimes. As long as one uses a quantization scheme which re- spects covariance, holonomy corrections from loop quantum gravity generically leads to non-singular signature change, thereby giving an emergent notion of time in the theory. Robustness of this mechanism is established by comparison across large class of midisuperspace models and allowing for diverse quantization ambiguities. Con- ceptual and mathematical consequences of such an underlying quantum-deformed space-time are briefly discussed. 1 Introduction It is not difficult to imagine a mind to which the sequence of things happens not in space but only in time like the sequence of notes in music. For such a mind such conception of reality is akin to the musical reality in which Pythagorean geometry can have no meaning. | Tagore to Einstein, 1920. We are yet to come up with a formal theory of quantum gravity which is mathematically consistent and allows us to draw phenomenological predictions from it. Yet, there are widespread beliefs among physicists working in fundamental theory regarding some aspects of such a theory, once realized. -
The EPRL Intertwiners and Corrected Partition Function Wojciech Kamiski, Marcin Kisielowski, Jerzy Lewandowski
The EPRL intertwiners and corrected partition function Wojciech Kamiski, Marcin Kisielowski, Jerzy Lewandowski To cite this version: Wojciech Kamiski, Marcin Kisielowski, Jerzy Lewandowski. The EPRL intertwiners and corrected partition function. Classical and Quantum Gravity, IOP Publishing, 2010, 27 (16), pp.165020. 10.1088/0264-9381/27/16/165020. hal-00616260 HAL Id: hal-00616260 https://hal.archives-ouvertes.fr/hal-00616260 Submitted on 21 Aug 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Confidential: not for distribution. Submitted to IOP Publishing for peer review 31 May 2010 The EPRL intertwiners and corrected partition function Wo jciech Kami´nski, Marcin Kisielowski, Jerzy Lewandowski Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, ul. Ho˙za 69, 00-681 Warszawa (Warsaw), Polska (Poland) Abstract Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the sim- plicity constraint? What is a complete form of the partition function written in terms of this parametrization? We prove that the EPRL map is injective in the general n-valent vertex case for the Barbero-Immirzi parameter less then 1. We find, however, that the EPRL map is not isomet- ric. -
On the Consistency of the Constraint Algebra in Spin Network Quantum
SU-GP-97/10-2 On the consistency of the constraint algebra in spin network quantum gravity Rodolfo Gambini∗ Instituto de F´ısica, Facultad de Ciencias, Tristan Narvaja 1674, Montevideo,CGPG-97-10/1 Uruguay gr-qc/9710018 Jerzy Lewandowski† Max-Planck-Institut f¨ur Gravitationsphysik Schlaatzweg 1 D-14473 Potsdam, Germany Donald Marolf Physics Department, Syracuse University, Syracuse, NY 13244-1130 Jorge Pullin Center for Gravitational Physics and Geometry, Department of Physics, 104 Davey Lab, The Pennsylvania State University, University Park, PA 16802 Abstract We point out several features of the quantum Hamiltonian constraints re- arXiv:gr-qc/9710018v1 2 Oct 1997 cently introduced by Thiemann for Euclidean gravity. In particular we dis- cuss the issue of the constraint algebra and of the quantum realization of the ab object q Vb, which is classically the Poisson Bracket of two Hamiltonians. I. INTRODUCTION In a remarkable series of papers [1–4] by Thiemann, the loop approach to the quantiza- tion of general relativity reached a new level. Using ideas related to those of Rovelli and ∗Associate member of ICTP. †On leave from Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, ul. Ho˙za 69, 00-681 Warszawa, Poland 1 Smolin [8], Thiemann proposed a definition of the quantum Hamiltonian (Wheeler-DeWitt) constraint of Einstein-Hilbert gravity which is a densely defined operator on a certain Hilbert space and which is (in a certain sense [1]) anomaly free on diffeomorphism invariant states. The fact that the proposed constraints imply the existence of a self-consistent, well defined theory is very impressive. However, it is still not clear whether the resulting theory is con- nected with the physics of gravity. -
Loop Quantum Gravity
QUANTUM GRAVITY Loop gravity combines general relativity and quantum theory but it leaves no room for space as we know it – only networks of loops that turn space–time into spinfoam Loop quantum gravity Carlo Rovelli GENERAL relativity and quantum the- ture – as a sort of “stage” on which mat- ory have profoundly changed our view ter moves independently. This way of of the world. Furthermore, both theo- understanding space is not, however, as ries have been verified to extraordinary old as you might think; it was introduced accuracy in the last several decades. by Isaac Newton in the 17th century. Loop quantum gravity takes this novel Indeed, the dominant view of space that view of the world seriously,by incorpo- was held from the time of Aristotle to rating the notions of space and time that of Descartes was that there is no from general relativity directly into space without matter. Space was an quantum field theory. The theory that abstraction of the fact that some parts of results is radically different from con- matter can be in touch with others. ventional quantum field theory. Not Newton introduced the idea of physi- only does it provide a precise mathemat- cal space as an independent entity ical picture of quantum space and time, because he needed it for his dynamical but it also offers a solution to long-stand- theory. In order for his second law of ing problems such as the thermodynam- motion to make any sense, acceleration ics of black holes and the physics of the must make sense. -
2+1D Loop Quantum Gravity on the Edge,” Phys
2+1D Loop Quantum Gravity on the Edge Laurent Freidel∗ and Barak Shoshany† Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada, N2L 2Y5 Florian Girelli‡ Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada, N2L 3G1 April 3, 2020 Abstract We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space structure into elementary cells, we obtain the loop gravity phase space coupled to a collection of effective particles carrying mass and spin, which measure the curvature and torsion of the geometry. We show that the new degrees of freedom associated to the particle-like elements can be understood as edge modes, which appear in the decomposition of the continuum theory into subsystems and do not cancel out in the gluing of cells along codimension 2 defects. These new particle-like edge modes are gravitationally dressed in an explicit way. This provides a detailed explanation of the relations and differences between the loop gravity phase space and the one deduced from the continuum theory. Contents 1 Introduction 2 arXiv:1811.04360v4 [gr-qc] 1 Apr 2020 2 Piecewise-DG-Flat Manifolds in Two Dimensions 6 2.1 TheCellularDecomposition . ........... 6 2.2 TheDGConnectionInsidetheCells . ........... 7 2.3 The DG Connection Inside the Disks . ........... 8 2.4 Continuity Conditions Between Cells . ............. 12 2.5 Continuity Conditions Between Disks and Cells . ............... 13 2.6 Summary......................................... ..... 14 2.7 The Chern-Simons Symplectic Potential . -
New Tools for Loop Quantum Gravity with Applications to a Simple Model Enrique F
New tools for Loop Quantum Gravity with applications to a simple model Enrique F. Borja, Jacobo Díaz-Polo, Laurent Freidel, Iñaki Garay, and Etera R. Livine Citation: AIP Conf. Proc. 1458, 339 (2012); doi: 10.1063/1.4734429 View online: http://dx.doi.org/10.1063/1.4734429 View Table of Contents: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=1458&Issue=1 Published by the American Institute of Physics. Additional information on AIP Conf. Proc. Journal Homepage: http://proceedings.aip.org/ Journal Information: http://proceedings.aip.org/about/about_the_proceedings Top downloads: http://proceedings.aip.org/dbt/most_downloaded.jsp?KEY=APCPCS Information for Authors: http://proceedings.aip.org/authors/information_for_authors Downloaded 07 Nov 2012 to 131.188.201.33. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions New tools for Loop Quantum Gravity with applications to a simple model Enrique F. Borja∗,†, Jacobo Díaz-Polo∗∗, Laurent Freidel‡, Iñaki Garay§,∗ and Etera R. Livine¶,‡ ∗Institute for Theoretical Physics III, University of Erlangen-Nürnberg, Staudtstraße 7, D-91058 Erlangen (Germany). †Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC. Facultad de Física, Universidad de Valencia, Burjassot-46100, Valencia (Spain). ∗∗Department of Physics and Astronomy, Louisiana State University.Baton Rouge, LA,70803-4001. ‡Perimeter Institute for Theoretical Physics, 31 Caroline St N, Waterloo ON,Canada N2L2Y5. §Departamento de Física Teórica, Universidad del País Vasco, Apdo. 644, 48080 Bilbao (Spain). ¶Laboratoire de Physique, ENS Lyon, CNRS-UMR 5672, 46 Allée d’Italie, Lyon 69007, France. Abstract. Loop Quantum Gravity is now a well established approach to quantum gravity. -
Amplitudes in the Spin Foam Approach to Quantum Gravity
Amplitudes in the Spin Foam Approach to Quantum Gravity by Lin-Qing Chen A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Physics Waterloo, Ontario, Canada, 2017 c Lin-Qing Chen 2017 Examining Committee Membership The following served on the Examining Committee for this thesis. The decision of the Examining Committee is by majority vote. External Examiner Jesus Fernando Barbero Gonzalez Prof. Supervisor Lee Smolin Prof. Co-supervisor Laurent Freidel Prof. Internal Member Niayesh Afshordi Prof. Committee Member Bianca Dittrich Prof. Internal-external Examiner Eduardo Martin-Martinez Prof. ii This thesis consists of material all of which I authored or co-authored: see Statement of Con- tributions included in the thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. iii Statement of Contributions The construction of the holomorphic Spin Foam model and the calculation of Pachner Moves have been done in collaboration with Andrzej Banburski and Jeff Hnybida, which was supervised by Laurent Freidel. The asymptotics is based on work in collaboration with Andrzej Banburski. The rest of the original results are based solely on my own work. The publications related with this thesis: L. Q. Chen, “Bulk amplitude and degree of divergence in 4d spin foams,” Phys. Rev. D 94, no. 10, 104025 (2016) A. Banburski and L. Q. Chen, “Simpler way of imposing simplicity constraints,” Phys. Rev. D 94, no. 10, 104003 (2016) A.