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SIGMA, 2012, Volume 8, 052, 31 pages (Mi sigma729)  

This article is cited in 20 scientific papers (total in 20 papers)

Discrete gravity models and Loop Quantum Gravity: a short review

Maïté Dupuisa, James P. Ryanb, Simone Spezialec

a Institute for Theoretical Physics III, University of Erlangen-Nürnberg, Erlangen, Germany
b MPI für Gravitationsphysik, Am Mühlenberg 1, D-14476 Potsdam, Germany
c Centre de Physique Théorique, CNRS-UMR 7332, Luminy Case 907, 13288 Marseille, France

Abstract: We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the spin foam formalism, with particular attention to the definition of the simplicity constraints.

Keywords: Loop Quantum Gravity, discrete gravity, Regge calculus, simplicity constraints, twisted geometries.

DOI: https://doi.org/10.3842/SIGMA.2012.052

Full text: PDF file (642 kB)
Full text: http://emis.mi.ras.ru/.../052
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Bibliographic databases:

ArXiv: 1204.5394
MSC: 83C27; 83C45
Received: April 25, 2012; in final form August 6, 2012; Published online August 13, 2012
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Citation: Maïté Dupuis, James P. Ryan, Simone Speziale, “Discrete gravity models and Loop Quantum Gravity: a short review”, SIGMA, 8 (2012), 052, 31 pp.

Citation in format AMSBIB
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\by Ma{\"\i}t\'e Dupuis, James P. Ryan, Simone Speziale
\paper Discrete gravity models and Loop Quantum Gravity: a short review
\jour SIGMA
\yr 2012
\vol 8
\papernumber 052
\totalpages 31
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\crossref{https://doi.org/10.3842/SIGMA.2012.052}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bogacz L., Burda Z., Waclaw B., “Quantum Widening of a Causal Dynamical Triangulations Universe”, Phys. Rev. D, 86:10 (2012), 104015  crossref  adsnasa  isi  scopus
    2. Eugenio Bianchi, Frank Hellmann, “The Construction of Spin Foam Vertex Amplitudes”, SIGMA, 9 (2013), 008, 22 pp.  mathnet  crossref  mathscinet
    3. Haggard H.M., Rovelli C., Wieland W., Vidotto F., “Spin Connection of Twisted Geometry”, Phys. Rev. D, 87:2 (2013), 024038  crossref  adsnasa  isi  elib  scopus
    4. El-Nabulsi R.A., “Nonstandard Fractional Exponential Lagrangians, Fractional Geodesic Equation, Complex General Relativity, and Discrete Gravity”, Can. J. Phys., 91:8 (2013), 618–622  crossref  adsnasa  isi  scopus
    5. Calcagni G., Oriti D., Thuerigen J., “Laplacians on Discrete and Quantum Geometries”, Class. Quantum Gravity, 30:12 (2013), 125006  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Livine E.R., Tambornino J., “Holonomy Operator and Quantization Ambiguities on Spinor Space”, Phys. Rev. D, 87:10 (2013), 104014  crossref  mathscinet  adsnasa  isi  scopus
    7. Kaminski W., Oriti D., Ryan J.P., “Towards a Double Scaling Limit for Tensor Models: Probing Sub-Dominant Orders”, New J. Phys., 16 (2014), 063048  crossref  isi  scopus
    8. Dittrich B. Steinhaus S., “Time Evolution as Refining, Coarse Graining and Entangling”, New J. Phys., 16 (2014), 123041  crossref  isi  scopus
    9. Carlo Rovelli, “Quantum Spacetime”, Springer Handbook of Spacetime, 2014, 751–757  crossref  mathscinet  scopus
    10. Ariwahjoedi S., Kosasih J.S., Rovelli C., Zen F.P., “Curvatures and Discrete Gauss-Codazzi Equation in (2+1)-Dimensional Loop Quantum Gravity”, Int. J. Geom. Methods Mod. Phys., 12:10 (2015), 1550112  crossref  mathscinet  zmath  isi  scopus
    11. Charles Ch., Livine E.R., “Closure Constraints For Hyperbolic Tetrahedra”, Class. Quantum Gravity, 32:13 (2015), 135003  crossref  mathscinet  zmath  adsnasa  isi  scopus
    12. Liu R.G., Williams R.M., “Regge Calculus Models of the Closed Vacuum Lambda-Flrw Universe”, Phys. Rev. D, 93:2 (2016), 024032  crossref  mathscinet  adsnasa  isi  scopus
    13. Charles Ch. Livine E.R., “The Fock space of loopy spin networks for quantum gravity”, Gen. Relativ. Gravit., 48:8 (2016), 113  crossref  mathscinet  zmath  isi  elib  scopus
    14. A. Feller, E. R. Livine, “Quantum surface and intertwiner dynamics in loop quantum gravity”, Phys. Rev. D, 95:12 (2017), 124038  crossref  mathscinet  isi  scopus
    15. N. Chakravarty, L. Mullick, P. Bandyopadhyay, “Fermions, loop quantum gravity and geometry”, Int. J. Mod. Phys. D, 26:11 (2017), 1750122  crossref  mathscinet  zmath  isi  scopus
    16. E. R. Livine, “Intertwiner entanglement on spin networks”, Phys. Rev. D, 97:2 (2018), 026009  crossref  mathscinet  isi  scopus
    17. Goeller Ch., Livine E.R., “Probing the Shape of Quantum Surfaces: the Quadrupole Moment Operator”, Class. Quantum Gravity, 35:21 (2018), 215004  crossref  mathscinet  isi  scopus
    18. Albalate G., Manuel Carmona J., Luis Cortes J., Javier Relancio J., “Twin Peaks: a Possible Signal in the Production of Resonances Beyond Special Relativity”, Symmetry-Basel, 10:10 (2018), 432  crossref  mathscinet  isi  scopus
    19. Livine E.R., “Hamiltonian Flows of Lorentzian Polyhedra: Kapovich-Millson Phase Space and Su(1,1) Intertwiners”, J. Math. Phys., 60:1 (2019), 012301  crossref  mathscinet  zmath  isi  scopus
    20. Freidel L., Livine E.R., “Bubble Networks: Framed Discrete Geometry For Quantum Gravity”, Gen. Relativ. Gravit., 51:1 (2019), 9  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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