Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

IMPACT FACTOR 2018: 1.005

CiteScore 2018: 1.01

SCImago Journal Rank (SJR) 2018: 0.237
Source Normalized Impact per Paper (SNIP) 2018: 0.541

ICV 2017: 162.45

Open Access
See all formats and pricing
More options …
Volume 9, Issue 4


Volume 13 (2015)

Wilson loops, geometric operators and fermions in 3d group field theory

R. Dowdall
Published Online: 2011-04-30 | DOI: https://doi.org/10.2478/s11534-010-0137-2


Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin network grasping operators which require the introduction of vector fields on the group. We then use this to define group field theories that give a previously defined spin foam model for fermion fields coupled to gravity, and the simpler “quenched” approximation, by using tensor fields on the group. The group field theory naturally includes the sum over fermionic loops at each order of the perturbation theory.

Keywords: spin foam; loop quantum gravity; fermion; group field theory

  • [1] C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, 2004) http://dx.doi.org/10.1017/CBO9780511755804CrossrefGoogle Scholar

  • [2] D. Oriti, arXiv:gr-qc/0607032 Web of ScienceGoogle Scholar

  • [3] L. Freidel, Int. J. Theor. Phys. 44, 1769 (2005) http://dx.doi.org/10.1007/s10773-005-8894-1CrossrefGoogle Scholar

  • [4] L. Freidel, D. Louapre, Classical Quant. Grav. 21, 5685 (2004) http://dx.doi.org/10.1088/0264-9381/21/24/002CrossrefGoogle Scholar

  • [5] W.J. Fairbairn, A. Perez, Phys. Rev. D 78, 024013 (2008) http://dx.doi.org/10.1103/PhysRevD.78.024013CrossrefGoogle Scholar

  • [6] L. Freidel, E.R. Livine, Classical Quant. Grav. 23, 2021 (2006) http://dx.doi.org/10.1088/0264-9381/23/6/012CrossrefGoogle Scholar

  • [7] D. Oriti, J. Ryan, Classical Quant. Grav. 23, 6543 (2006) http://dx.doi.org/10.1088/0264-9381/23/22/027CrossrefGoogle Scholar

  • [8] W.J. Fairbairn, E.R. Livine, Classical Quant. Grav. 24, 5277 (2007) http://dx.doi.org/10.1088/0264-9381/24/20/021CrossrefGoogle Scholar

  • [9] W.J. Fairbairn, Gen. Rel. Gravit. 39, 427 (2007) http://dx.doi.org/10.1007/s10714-006-0395-xCrossrefGoogle Scholar

  • [10] L. Freidel, D. Louapre, arXiv:gr-qc/0410141 Web of ScienceGoogle Scholar

  • [11] D.V. Boulatov, Mod. Phys. Lett. A 7, 1629 (1992) http://dx.doi.org/10.1142/S0217732392001324CrossrefGoogle Scholar

  • [12] L. Freidel, K. Krasnov, Adv. Theor. Math. Phys. 2, 1183 (1999) Google Scholar

  • [13] J. Hackett, S. Speziale, Classical Quant. Grav. 24, 1525 (2007) http://dx.doi.org/10.1088/0264-9381/24/6/010CrossrefGoogle Scholar

  • [14] D. Oriti, T. Tlas, Classical Quant. Grav. 25, 085011 (2008) http://dx.doi.org/10.1088/0264-9381/25/8/085011CrossrefGoogle Scholar

  • [15] R. Gurau, arXiv:0907.2582v1 [hep-th] Google Scholar

About the article

Published Online: 2011-04-30

Published in Print: 2011-08-01

Citation Information: Open Physics, Volume 9, Issue 4, Pages 1043–1056, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-010-0137-2.

Export Citation

© 2011 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Yang Li, Daniele Oriti, and Mingyi Zhang
Classical and Quantum Gravity, 2017, Volume 34, Number 19, Page 195001
Daniele Oriti, Lorenzo Sindoni, and Edward Wilson-Ewing
Classical and Quantum Gravity, 2016, Volume 33, Number 22, Page 224001
Gianluca Calcagni
Physical Review D, 2014, Volume 90, Number 6
Steffen Gielen, Daniele Oriti, and Lorenzo Sindoni
Journal of High Energy Physics, 2014, Volume 2014, Number 6

Comments (0)

Please log in or register to comment.
Log in