Group Field Theory: An Overview

Freidel, Laurent

doi:10.1007/s10773-005-8894-1

Cited by 329 publications

(600 citation statements)

References 38 publications

(74 reference statements)

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“…This was suggested in [4,23], following the results of [14]. Indeed Ward identities in quantum field theory relate the amplitudes of different Feynman diagrams.…”

Section: Jhep02(2007)092mentioning

confidence: 89%

Coupling of spacetime atoms in 4D spin foam models from group field theory

Livine

Oriti

2007

J. High Energy Phys.

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We study the issue of coupling among 4-simplices in the context of spin foam models obtained from a group field theory formalism. We construct a generalisation of the Barrett-Crane model in which an additional coupling between the normals to tetrahedra, as defined in different 4-simplices that share them, is present. This is realised through an extension of the usual field over the group manifold to a five argument one. We define a specific model in which this coupling is parametrised by an additional real parameter that allows to tune the degree of locality of the resulting model, interpolating between the usual Barrett-Crane model and a flat BF-type one. Moreover, we define a further extension of the group field theory formalism in which the coupling parameter enters as a new variable of the field, and the action presents derivative terms that lead to modified classical equations of motion. Finally, we discuss the issue of renormalisation of spin foam models, and how the new coupled model can be of help regarding this. Contents

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“…This was suggested in [4,23], following the results of [14]. Indeed Ward identities in quantum field theory relate the amplitudes of different Feynman diagrams.…”

Section: Jhep02(2007)092mentioning

confidence: 89%

Coupling of spacetime atoms in 4D spin foam models from group field theory

Livine

Oriti

2007

J. High Energy Phys.

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“…However, to understand better the motivation of the GFT approach, let us explain more closely the relation of group field theories [22][23][24][25][26][27][28] to loop quantum gravity (LQG) [14][15][16] and specifically its spin foam corner [17,18], which has in fact provided the impetus for the development of group field theories. More details on this are given in a separate publication [29] but we illuminate the most important points here.…”

Section: Jhep06(2014)013mentioning

confidence: 99%

“…In order to turn this expression into the GFT path integral, we introduce then a second quantised basis of eigenstates of the GFT quantum field operator, |ϕ = exp 25) or equivalentlyφ 26) and a completeness relation as is usual for such coherent states,…”

Section: Jhep06(2014)013mentioning

confidence: 99%

Homogeneous cosmologies as group field theory condensates

Gielen

Oriti

Sindoni

2014

J. High Energ. Phys.

140

256

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We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the 'condensate wavefunction' which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.

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“…on their representation and intertwiner labels, that can be interpreted as the quantum analog of the Plebanski constraints in the classical B variables of BF theory, and thus to characterize the spin network quantum states of 4D gravity. In the new spin foam models of [22,[24][25][26], the crucial intermediate step is to rewrite the same spin network states of BF theory in terms of coherent states of SO (4), whose defining parameters are interpreted as the quantum labels corresponding to the B variables. Second, one follows the steps leading to the BF spin foam amplitudes, but starting the newly defined candidate 4D gravity states, arriving at a proposal for the 4-simplex gravity amplitude.…”

Section: C(b F ⊂E ) E I F Tr(b F H F (G E∈∂f ))mentioning

confidence: 99%

“…The key ingredient is the non-trivial propagator, the inverse of the kinetic term 4. This being a product of Klein-Gordon operators on the homogeneous space S 3 Spin(4)/SU (2), thanks to the projection operators P h , its inverse is taken to be the product of the Feynman propagator on the same homogeneous space, in turn equal to the propagators on the group SU (2), due to the isomorphism between the two spaces, with variable mass given by b 2 i − m 2 4 . From now on we set m 2 = 1 because this simplifies the resulting formulae.…”

Section: Feynman Amplitudes: Discrete Gravity Path Integralsmentioning

confidence: 99%

Group field theory and simplicial quantum gravity

Oriti¹

2010

Class. Quantum Grav.

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We present a new group field theory for 4D quantum gravity. It incorporates the constraints that give gravity from BF theory and has quantum amplitudes with the explicit form of simplicial path integrals for first-order gravity. The geometric interpretation of the variables and of the contributions to the quantum amplitudes is manifest. This allows a direct link with other simplicial gravity approaches, like quantum Regge calculus, in the form of the amplitudes of the model, and dynamical triangulations, which we show to correspond to a simple restriction of the same.

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Group Field Theory: An Overview

Cited by 329 publications

References 38 publications

Coupling of spacetime atoms in 4D spin foam models from group field theory

Coupling of spacetime atoms in 4D spin foam models from group field theory

Homogeneous cosmologies as group field theory condensates

Group field theory and simplicial quantum gravity

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