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Beyond the Standard Model
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v t e

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.

v t e Quantum gravity
Central concepts	AdS/CFT correspondence Batalin–Vilkovisky formalism CA-duality Causal patch Faddeev–Popov ghost Gravitational anomaly Graviton Holographic principle IR/UV mixing Planck units Quantum foam Ryu–Takayanagi conjecture Trans-Planckian problem Weinberg–Witten theorem
Toy models	2+1D topological gravity CGHS model Jackiw–Teitelboim gravity Liouville gravity RST model Topological quantum field theory
Quantum field theory in curved spacetime	Bunch–Davies vacuum Hawking radiation Semiclassical gravity Unruh effect
Black holes	Black hole complementarity Black hole information paradox Black-hole thermodynamics Bekenstein bound Bousso's holographic bound Cosmic censorship hypothesis ER = EPR Firewall (physics) Gravitational singularity
Approaches	String theory Bosonic string theory M-theory Supergravity Superstring theory Canonical quantum gravity Loop quantum gravity Wheeler–DeWitt equation Euclidean quantum gravity Hartle–Hawking state Others Causal dynamical triangulation Causal sets Dual graviton Group field theory Noncommutative geometry Spin foam Superfluid vacuum theory Twistor theory
Applications	Quantum cosmology Eternal inflation FRW/CFT duality Multiverse
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