Group field theory

Quantum field theory with a Lie group base manifold

Not to be confused with group theory. This article is about group field theory as a candidate theory of quantum gravity.

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

Supersymmetry

* MSSM
* NMSSM
* Superstring theory
* M-theory
* Supergravity
* Supersymmetry breaking
* Extra dimensions
* Large extra dimensions

Quantum gravity

* False vacuum
* String theory
* Spin foam
* Quantum foam
* Quantum geometry
* Loop quantum gravity
* Quantum cosmology
* Loop quantum cosmology
* Causal dynamical triangulation
* Causal fermion systems
* Causal sets
* Canonical quantum gravity
* Semiclassical gravity
* Superfluid vacuum theory

Experiments

* ANNIE
* Gran Sasso
* INO
* LHC
* SNO
* Super-K
* Tevatron
* NOvA

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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

[edit]

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

## References

[edit]

* 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 118543391.3–4&rft.pages=41-86&rft.date=2011&rft_id=info:arxiv/1009.4475&rft_id=https://api.semanticscholar.org/CorpusID:118543391#id-name=S2CID&rft_id=info:doi/10.1016/j.physrep.2011.05.002&rft_id=info:bibcode/2011PhR...506...41A&rft.aulast=Alexandrov&rft.aufirst=Sergei&rft.au=Roche,+Philippe&rfr_id=info:sid/en.wikipedia.org:Group+field+theory" class="Z3988">
* 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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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

See also: Template:Quantum mechanics topics

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