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Group field theory (GFT) is a quantum field theory in which the base manifold is taken to be a Lie group. It is closely related to background independent quantum gravity approaches such as loop quantum gravity, the spin foam formalism and causal dynamical triangulation. Its perturbative expansion can be interpreted as spin foams and simplicial pseudo-manifolds (depending on the representation of the fields). Thus, its partition function defines a non-perturbative sum over all simplicial topologies and geometries, giving a path integral formulation of quantum spacetime.

See also

• Shape dynamics
• Causal Sets
• Fractal cosmology
• Loop quantum gravity
• Planck scale
• Quantum gravity
• Regge calculus
• Simplex
• Simplicial manifold
• Spin foam

References

• Wayback Machine see Sec 6.8 Dynamics: III. Group field theory
• Freidel, L. (2005). "Group Field Theory: An Overview". International Journal of Theoretical Physics. 44 (10): 1769–1783. arXiv: hep-th/0505016 . Bibcode:2005IJTP...44.1769F. doi:10.1007/s10773-005-8894-1. S2CID   119099369.
• Oriti, Daniele (2006). "The group field theory approach to quantum gravity". arXiv: gr-qc/0607032 . Bibcode:2006gr.qc.....7032O.{{cite journal}}: Cite journal requires |journal= (help)
• Oriti, Daniele (2009). "The Group Field Theory Approach to Quantum Gravity: A QFT for the Microstructure of Spacetime" (PDF). arXiv: 0912.2441 .{{cite journal}}: Cite journal requires |journal= (help)
• Geloun, Joseph Ben; Krajewski, Thomas; Magnen, Jacques; Rivasseau, Vincent (2010). "Linearized group field theory and power-counting theorems". Classical and Quantum Gravity. 27 (15) 155012. arXiv: 1002.3592 . Bibcode:2010CQGra..27o5012B. doi:10.1088/0264-9381/27/15/155012. S2CID   29020457.
• Ben Geloun, J.; Gurau, R.; Rivasseau, V. (2010). "EPRL/FK group field theory". Europhysics Letters. 92 (6) 60008. arXiv: 1008.0354 . Bibcode:2010EL.....9260008B. doi:10.1209/0295-5075/92/60008. S2CID   119247896.
• Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam (2009). "Loop quantum cosmology and spin foams". Physics Letters B. 681 (4): 347–352. arXiv: 0909.4221 . Bibcode:2009PhLB..681..347A. doi:10.1016/j.physletb.2009.10.042. S2CID   56281948.
• Fairbairn, Winston J.; Livine, Etera R. (2007). "3D spinfoam quantum gravity: Matter as a phase of the group field theory". Classical and Quantum Gravity. 24 (20): 5277–5297. arXiv: gr-qc/0702125 . Bibcode:2007CQGra..24.5277F. doi:10.1088/0264-9381/24/20/021. S2CID   119369221.
• Alexandrov, Sergei; Roche, Philippe (2011). "Critical overview of loops and foams". Physics Reports. 506 (3–4): 41–86. arXiv: 1009.4475 . Bibcode:2011PhR...506...41A. doi:10.1016/j.physrep.2011.05.002. S2CID   118543391.
• Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo (2013). "Cosmology from Group Field Theory Formalism for Quantum Gravity". Physical Review Letters. 111 (3) 031301. arXiv: 1303.3576 . Bibcode:2013PhRvL.111c1301G. doi:10.1103/PhysRevLett.111.031301. PMID   23909305. S2CID   14203682.

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