Group field theory

Short description: Quantum field theory with a Lie group base manifold

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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

* Theory of everything
* Mathematical universe hypothesis
* Grand Unified Theory
* Technicolor
* Kaluza–Klein theory
* Quantum field theory
* Quantum field theory in curved spacetime
* Thermal quantum field theory
* Topological quantum field theory
* Conformal field theory
* Two-dimensional conformal field theory
* Liouville field theory
* 6D (2,0) superconformal field theory
* Quantum mechanics
* Quantum cosmology
* Brane cosmology
* String theory
* Superstring theory
* M-theory
* Randall–Sundrum model
* de Broglie–Bohm theory
* Stochastic electrodynamics
* Eigenstate thermalization hypothesis
* Yang–Mills theory
* N = 4 supersymmetric Yang–Mills theory
* Twistor string theory
* Dark fluid
* Superfluid vacuum theory
* Doubly special relativity
* de Sitter invariant special relativity
* Causal fermion systems
* Quantum thermodynamics
* Black hole thermodynamics
* Digital physics
* Unparticle physics
* Gauge theory
* Gauge gravitation theory
* Gauge theory gravity
* Hidden-variable theory
* Pilot wave theory
* CPT symmetry

Supersymmetry

* MSSM
* NMSSM
* Superstring theory
* M-theory
* Supergravity
* Supersymmetry breaking

Quantum gravity

* String theory
* Loop quantum gravity
* Loop quantum cosmology
* Causal dynamical triangulation
* Causal fermion systems
* Causal sets
* Event symmetry
* Canonical quantum 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

* 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). 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). 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). doi:10.1103/PhysRevLett.111.031301. PMID 23909305. Bibcode: 2013PhRvL.111c1301G.

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Quantum gravity

Central concepts|

* AdS/CFT correspondence
* Causal patch
* Gravitational anomaly
* Graviton
* Holographic principle
* IR/UV mixing
* Planck scale
* Quantum foam
* 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
* Bousso's holographic bound
* ER=EPR
* Firewall (physics)
* Gravitational singularity

Approaches|

| String theory|

* Bosonic string theory
* M-theory
* Supergravity
* Superstring theory

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Canonical quantum gravity|

* Loop quantum gravity
* Wheeler-DeWitt equation

Euclidean quantum gravity|

* Hartle-Hawking state

Others|

* Causal dynamical triangulation
* Causal sets
* Noncommutative geometry
* Spin foam
* Group field theory
* Superfluid vacuum theory
* Twistor theory
* Dual graviton

Applications|

* Quantum cosmology
* Eternal inflation
* Multiverse
* FRW/CFT duality

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