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SIGMA, 2012, Volume 8, 055, 79 pages (Mi sigma732)  

This article is cited in 37 scientific papers (total in 37 papers)

Spin foams and canonical quantization

Sergei Alexandrovab, Marc Geillerc, Karim Nouidc

a Université Montpellier 2, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France
b CNRS, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France
c Laboratoire APC, Université Paris Diderot Paris 7, 75013 Paris, France
d LMPT, Université François Rabelais, Parc de Grandmont, 37200 Tours, France

Abstract: This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev–Viro spin foam model, and how the Ponzano–Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.

Keywords: spin foam models, loop quantum gravity, canonical quantization.

DOI: https://doi.org/10.3842/SIGMA.2012.055

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Full text: http://emis.mi.ras.ru/.../055
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ArXiv: 1112.1961
MSC: 83C45; 83C05; 83C27
Received: January 30, 2012; in final form August 12, 2012; Published online August 19, 2012
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Citation: Sergei Alexandrov, Marc Geiller, Karim Noui, “Spin foams and canonical quantization”, SIGMA, 8 (2012), 055, 79 pp.

Citation in format AMSBIB
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\by Sergei Alexandrov, Marc Geiller, Karim Noui
\paper Spin foams and canonical quantization
\jour SIGMA
\yr 2012
\vol 8
\papernumber 055
\totalpages 79
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    This publication is cited in the following articles:
    1. Perez A., “The Spin-Foam Approach to Quantum Gravity”, Living Rev. Relativ., 16 (2013), 3  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Alexandrov S., Krasnov K., Speziale S., “Chiral Description of Massive Gravity”, J. High Energy Phys., 2013, no. 6, 068  crossref  mathscinet  zmath  isi  elib  scopus
    3. Dittrich B., Hellmann F., Kaminski W., “Holonomy Spin Foam Models: Boundary Hilbert Spaces and Time Evolution Operators”, Class. Quantum Gravity, 30:8 (2013), 085005  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Daniele Oriti, Matti Raasakka, “Asymptotic Analysis of the Ponzano–Regge Model with Non-Commutative Metric Boundary Data”, SIGMA, 10 (2014), 067, 32 pp.  mathnet  crossref  mathscinet
    5. Dittrich B., Martin-Benito M., Steinhaus S., “Quantum Group Spin Nets: Refinement Limit and Relation to Spin Foams”, Phys. Rev. D, 90:2 (2014), 024058  crossref  mathscinet  adsnasa  isi  scopus
    6. Pranzetti D., “Turaev-Viro Amplitudes From 2+1 Loop Quantum Gravity”, Phys. Rev. D, 89:8 (2014), 084058  crossref  mathscinet  adsnasa  isi  elib  scopus
    7. Hoehn Ph.A., “Quantization of Systems With Temporally Varying Discretization. i. Evolving Hilbert Spaces”, J. Math. Phys., 55:8 (2014), 083508  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Pranzetti D., “Geometric Temperature and Entropy of Quantum Isolated Horizons”, Phys. Rev. D, 89:10 (2014), 104046  crossref  adsnasa  isi  elib  scopus
    9. Wieland W.M., “Hamiltonian Spinfoam Gravity”, Class. Quantum Gravity, 31:2 (2014), 025002  crossref  zmath  adsnasa  isi  elib  scopus
    10. Rivasseau V., “Tensorial Methods and Renormalization in Group Field Theories Introduction and Motivation”: Carrozza, S, Tensorial Methods and Renormalization in Group Field Theories, Springer Theses-Recognizing Outstanding Phd Research, Springer-Verlag Berlin, 2014, 1–15  isi
    11. Rivasseau V., “Two Paths to Group Field Theories”: Carrozza, S, Tensorial Methods and Renormalization in Group Field Theories, Springer Theses, Springer-Verlag Berlin, 2014, 17–47  crossref  isi
    12. Pithis A.G.A., Euler H.-Ch.R., “Anyonic Statistics and Large Horizon Diffeomorphisms For Loop Quantum Gravity Black Holes”, Phys. Rev. D, 91:6 (2015), 064053  crossref  mathscinet  adsnasa  isi  elib  scopus
    13. Carrozza S., “Group Field Theory in Dimension 4-Epsilon”, Phys. Rev. D, 91:6 (2015), 065023  crossref  mathscinet  adsnasa  isi  scopus
    14. Geiller M., Noui K., “Btz Black Hole Entropy and the Turaev-Viro Model”, Ann. Henri Poincare, 16:2 (2015), 609–640  crossref  mathscinet  zmath  adsnasa  isi  scopus
    15. Ben Achour J., Grain J., Noui K., “Loop Quantum Cosmology With Complex Ashtekar Variables”, Class. Quantum Gravity, 32:2 (2015), 025011  crossref  mathscinet  zmath  adsnasa  isi  scopus
    16. Dittrich B., Geiller M., “Flux Formulation of Loop Quantum Gravity: Classical Framework”, Class. Quantum Gravity, 32:13 (2015), 135016  crossref  mathscinet  zmath  adsnasa  isi  scopus
    17. Jibril B.A., Mouchet A., Noui K., “Analytic Continuation of Black Hole Entropy in Loop Quantum Gravity”, J. High Energy Phys., 2015, no. 6, 145  crossref  mathscinet  isi  elib  scopus
    18. Dittrich B., Geiller M., “A New Vacuum For Loop Quantum Gravity”, Class. Quantum Gravity, 32:11 (2015), 112001  crossref  mathscinet  zmath  adsnasa  isi  scopus
    19. Ben Achour J., Geiller M., Noui K., Yu Ch., “Testing the Role of the Barbero-Immirzi Parameter and the Choice of Connection in Loop Quantum Gravity”, Phys. Rev. D, 91:10 (2015), 104016  crossref  mathscinet  adsnasa  isi  scopus
    20. Carrozza S., “Discrete Renormalization Group For Su(2) Tensorial Group Field Theory”, Ann. Inst. Henri Poincare D, 2:1 (2015), 49–112  crossref  mathscinet  zmath  isi  scopus
    21. Chowdhury S. Hasibul Hassan, “On Goldman Bracket For G(2) Gauge Group”, J. High Energy Phys., 2016, no. 2, 001  crossref  mathscinet  isi  elib  scopus
    22. Sylvain Carrozza, “Flowing in Group Field Theory Space: a Review”, SIGMA, 12 (2016), 070, 30 pp.  mathnet  crossref
    23. Steffen Gielen, Lorenzo Sindoni, “Quantum Cosmology from Group Field Theory Condensates: a Review”, SIGMA, 12 (2016), 082, 49 pp.  mathnet  crossref
    24. Celada M., Gonzalez D., Montesinos M., “BF gravity”, Class. Quantum Gravity, 33:21 (2016), 213001  crossref  mathscinet  zmath  isi  elib  scopus
    25. Carrozza S., Tanasa A., “O(N) Random Tensor Models”, Lett. Math. Phys., 106:11 (2016), 1531–1559  crossref  mathscinet  zmath  isi  scopus
    26. Cianfrani F., Kowalski-Glikman J., Pranzetti D., Rosati G., “Symmetries of quantum spacetime in three dimensions”, Phys. Rev. D, 94:8 (2016), 084044  crossref  mathscinet  isi  elib  scopus
    27. Ben Achour J., Noui K., Perez A., “Analytic continuation of the rotating black hole state counting”, J. High Energy Phys., 2016, no. 8, 149  crossref  mathscinet  isi  scopus
    28. Tamaki T., “Holographic bound in covariant loop quantum gravity”, Phys. Rev. D, 94:2 (2016), 024045  crossref  mathscinet  isi  elib  scopus
    29. Oriti D., “Group field theory as the second quantization of loop quantum gravity”, Class. Quantum Gravity, 33:8 (2016), 085005  crossref  mathscinet  zmath  isi  elib  scopus
    30. E. R. Livine, “3d quantum gravity: coarse-graining and $q$-deformation”, Ann. Henri Poincare, 18:4 (2017), 1465–1491  crossref  mathscinet  zmath  isi  scopus
    31. B. Dittrich, M. Geiller, “Quantum gravity kinematics from extended TQFTs”, New J. Phys., 19 (2017), 013003  crossref  isi  scopus
    32. A. Kegeles, D. Oriti, “Continuous point symmetries in group field theories”, J. Phys. A-Math. Theor., 50:12 (2017), 125402  crossref  mathscinet  zmath  isi  scopus
    33. Ya. Li, D. Oriti, M. Zhang, “Group field theory for quantum gravity minimally coupled to a scalar field”, Class. Quantum Gravity, 34:19 (2017), 195001  crossref  mathscinet  zmath  isi  scopus
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    35. M. Montesinos, J. Romero, M. Celada, “Manifestly Lorentz-covariant variables for the phase space of general relativity”, Phys. Rev. D, 97:2 (2018), 024014  crossref  isi  scopus
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