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 Cosmological constant problem Strong CP problem Neutrino oscillation
Theories Technicolor Kaluza–Klein theory Grand Unified Theory Theory of everything String theory Causal fermion systems Superfluid vacuum theory
Supersymmetry MSSM Superstring theory Supergravity
Quantum gravity String theory Loop quantum gravity Causal dynamical triangulation Causal fermion systems Causal sets Canonical quantum gravity Superfluid vacuum theory
Experiments ANNIE Gran Sasso INO LHC SNO Super-K Tevatron NOνA

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

• http://relativity.livingreviews.org/Articles/lrr-2008-5/ see Sec 6.8 Dynamics: III. Group field theory
• http://arxiv.org/abs/hep-th/0505016
• http://arXiv.org/abs/gr-qc/0607032
• http://fqxi.org/data/documents/Oriti%20Azores%20Talk.pdf
• http://arxiv.org/abs/1002.3592
• http://arxiv.org/abs/1008.0354
• http://arxiv.org/abs/0909.4221
• http://arxiv.org/abs/gr-qc/0702125
• http://arxiv.org/abs/1009.4475
• http://arxiv.org/abs/1303.3576