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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.


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ArXiv: 1204.5394
MSC: 83C27; 83C45
Received: April 25, 2012; in final form August 6, 2012; Published online August 13, 2012

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
\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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    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
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    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
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  • Symmetry, Integrability and Geometry: Methods and Applications
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