Group field theory

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

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

• https://web.archive.org/web/20091027184638/http://relativity.livingreviews.org/Articles/lrr-2008-5/ see Sec 6.8 Dynamics: III. Group field theory
• https://arxiv.org/abs/hep-th/0505016
• https://arxiv.org/abs/gr-qc/0607032
• http://fqxi.org/data/documents/Oriti%20Azores%20Talk.pdf
• https://arxiv.org/abs/1002.3592
• https://arxiv.org/abs/1008.0354
• https://arxiv.org/abs/0909.4221
• https://arxiv.org/abs/gr-qc/0702125
• https://arxiv.org/abs/1009.4475
• https://arxiv.org/abs/1303.3576