Group field theory

Beyond the Standard Model
Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons
Standard Model
Evidence Hierarchy problem Dark matter Dark energy Quintessence Phantom energy Dark radiation Dark photon Cosmological constant problem Strong CP problem Neutrino oscillation
Theories Brans–Dicke theory Cosmic censorship hypothesis Fifth force F-theory Theory of everything Unified field theory Grand Unified Theory Technicolor Kaluza–Klein theory 6D (2,0) superconformal field theory Noncommutative quantum field theory Quantum cosmology Brane cosmology String theory Superstring theory M-theory Mathematical universe hypothesis Mirror matter Randall–Sundrum model N = 4 supersymmetric Yang–Mills theory Twistor string theory Dark fluid Doubly special relativity de Sitter invariant special relativity Causal fermion systems Black hole thermodynamics Unparticle physics Graviphoton Graviscalar Graviton Gravitino Massive gravity Gauge gravitation theory Gauge theory gravity CPT symmetry
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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. 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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