Group Field Theory: An Overview

By L. Freidel. 2005

376 citations recorded by the source corpus.

We give a brief overview of the properties of a higher-dimensional generalization of matrix model which arise naturally in the context of a background approach to quantum gravity, the so-called group field theory. We show in which sense this theory provides a third quantization point-of-view on quantum gravity.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/18b9f9066c77c62a45f28865aee031b3050fa231

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Colored Group Field Theory (2009, background): “Group Field Theories (GFT) [1–5] are quantum field theories over group manifolds.”
A Renormalizable 4-Dimensional Tensor Field Theory (2011, background): “Group field theory is a special kind of random tensor model in which one adds a Lie group G and a gauge invariance [20, 21, 22, 23, 24](1).”
Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity (2011, background): “Group field theories [1] are quantum field theories showing up as a higher dimensional generalization of matrix models in background independent approaches to quantum gravity [2].”
The Spin-Foam Approach to Quantum Gravity (2012, methodology): “Freidel and Krasnov [175] define a general framework to construct spin foam models corresponding to theories whose action has the general form S(B,A) = ∫ Tr [B ∧ F (A)] + Φ(B), (14) where the first term is the BF action while Φ(B) is a certain polynomial function of the B field.”
A new spin foam model for 4D gravity (2007, methodology): “This way of deriving spin foam models later received a catchy name of ‘group field theory’, see [13] for a review.”
The 1/N Expansion of Colored Tensor Models (2010, background): “To approach a more realistic physical setting, one generalizes them in higher dimensions to random tensor models [10–12] and Group Field Theories (GFT) [ 13 ,14].”
Flipped spinfoam vertex and loop gravity (2007, methodology): “We expect that the model considered here will admit a group field theory formulation [30] and that its vertex can be used to generate the dynamics of loop quantum gravity also in the absence of a fixed triangulation [3].”
Principle of relative locality (2011, methodology): “The curved momentum space was also employed in the context of group field theory, which generates amplitudes for spin foam models of quantum gravity [25].”
Phase space descriptions for simplicial 4D geometries (2008, methodology): “As is pointed out in [21, 39], the understanding of diffeomorphism symmetry is however crucial for the discussion of anomaly freeness and the appearance of (bubble) divergences in these models.”
Loop Quantum Gravity (2003, background): “The subject of group field theory has greatly developed recently, and I refer to the reviews [113, 217, 216] for an update and complete references.”
O(N) Random Tensor Models (2015, background): “spin foam [33, 34] and group field theory models [35, 36] for 3d quantum gravity.”