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SIGMA, 2012, Volume 8, 015, 44 pages (Mi sigma692)  

This article is cited in 10 scientific papers (total in 10 papers)

Learning about quantum gravity with a couple of nodes

Enrique F. Borjaab, Iñaki Garayac, Francesca Vidottode

a Institute for Theoretical Physics III, University of Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
b Departamento de Física Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Facultad de Física, Universidad de Valencia, Burjassot-46100, Valencia, Spain
c Departamento de Física Teórica, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
d Laboratoire de Physique Subatomique et de Cosmologie, 53 rue des Martyrs, 38026 Grenoble, France
e Centre de Physique Théorique de Luminy, Case 907, 13288 Marseille, France

Abstract: Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a simple graph, formed by only two nodes. We review the $\mathrm{U}(N)$ framework, which provides a powerful tool for the canonical study of this model, and a formulation of the system based on spinors. We consider also the covariant theory, which permits to derive the model from a more complex formulation, paying special attention to the cosmological interpretation of the theory.

Keywords: discrete gravity, canonical quantization, spinors, spinfoam, quantum cosmology.


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ArXiv: 1110.3020
MSC: 83C27; 83C45; 83C60; 83F05
Received: October 8, 2011; in final form March 12, 2012; Published online March 25, 2012

Citation: Enrique F. Borja, Iñaki Garay, Francesca Vidotto, “Learning about quantum gravity with a couple of nodes”, SIGMA, 8 (2012), 015, 44 pp.

Citation in format AMSBIB
\by Enrique F. Borja, I{\~n}aki Garay, Francesca Vidotto
\paper Learning about quantum gravity with a couple of nodes
\jour SIGMA
\yr 2012
\vol 8
\papernumber 015
\totalpages 44

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    This publication is cited in the following articles:
    1. F. Vidotto, “Many-node/many-link spinfoam: the homogeneous and isotropic case”, CLASSICAL AND QUANTUM GRAVITY, 28:24 (2011), 245005  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. E. F. Borja, J. Diaz-Polo, L. Freidel, I. Garay, E. R. Livine, “New tools for loop quantum gravity with applications to a simple model”, Towards New Paradigms: Proceeding of the Spanish Relativity Meeting 2011, AIP Conf. Proc., 1458, eds. J. Jimenez, J. Cembranos, A. Dobado, A. Maroto, A. Dombriz, Amer. Inst. Phys., 2012, 339–342  crossref  isi  scopus
    3. Kisielowski M., Lewandowski J., Puchta J., “One Vertex Spin-Foams with the Dipole Cosmology Boundary”, Class. Quantum Gravity, 30:2 (2013), 025007  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Alesci E., Cianfrani F., Rovelli C., “Quantum-Reduced Loop Gravity: Relation with the Full Theory”, Phys. Rev. D, 88:10 (2013), 104001  crossref  mathscinet  adsnasa  isi  scopus
    5. Rovelli, C.; Vidotto, F., “Covariant loop quantum gravity: An elementary introduction to quantum gravity and spinfoam theory”, Cambridge University Press, 2015, 254 pp.  crossref  scopus
    6. Rovelli C., Vidotto F., “Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory”, Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory, Cambridge Univ Press, 2015, 1–254  isi
    7. de Cesare M., Pithis A.G.A., Sakellariadou M., “Cosmological implications of interacting group field theory models: Cyclic universe and accelerated expansion”, Phys. Rev. D, 94:6 (2016), 064051  crossref  mathscinet  isi  scopus
    8. F. Vidotto, “Relational quantum cosmology”, Philosophy of Cosmology, eds. K. Chamcham, J. Silk, J. Barrow, S. Saunders, Cambridge Univ Press, 2017, 297–316  crossref  isi
    9. G. Sarno, S. Speziale, G. V. Stagno, “2-vertex Lorentzian spin foam amplitudes for dipole transitions”, Gen. Relativ. Gravit., 50:4 (2018), 43  crossref  mathscinet  isi  scopus
    10. Pithis A.G.A. Sakellariadou M., “Group Field Theory Condensate Cosmology: An Appetizer”, Universe, 5:6 (2019), 147  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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