Group Field Theory

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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. It can be shown that 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. doi:10.1007/s10773-005-8894-1. Bibcode: 2005IJTP...44.1769F. 
• Oriti, Daniele (2006). The group field theory approach to quantum gravity. Bibcode: 2006gr.qc.....7032O. 
• Oriti, Daniele (2009). The Group Field Theory Approach to Quantum Gravity: A QFT for the Microstructure of Spacetime. http://fqxi.org/data/documents/Oriti Azores Talk.pdf. 
• 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. doi:10.1088/0264-9381/27/15/155012. Bibcode: 2010CQGra..27o5012B. 
• Ben Geloun, J.; Gurau, R.; Rivasseau, V. (2010). "EPRL/FK group field theory". Europhysics Letters 92 (6): 60008. doi:10.1209/0295-5075/92/60008. Bibcode: 2010EL.....9260008B. 
• Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam (2009). "Loop quantum cosmology and spin foams". Physics Letters B 681 (4): 347–352. doi:10.1016/j.physletb.2009.10.042. Bibcode: 2009PhLB..681..347A. 
• 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. doi:10.1088/0264-9381/24/20/021. Bibcode: 2007CQGra..24.5277F. 
• Alexandrov, Sergei; Roche, Philippe (2011). "Critical overview of loops and foams". Physics Reports 506 (3–4): 41–86. doi:10.1016/j.physrep.2011.05.002. Bibcode: 2011PhR...506...41A. 
• Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo (2013). "Cosmology from Group Field Theory Formalism for Quantum Gravity". Physical Review Letters 111 (3): 031301. doi:10.1103/PhysRevLett.111.031301. PMID 23909305. Bibcode: 2013PhRvL.111c1301G. 

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