Group Field Theories

Krajewski, Thomas

doi:10.22323/1.140.0005

Cited by 73 publications

(129 citation statements)

References 64 publications

(90 reference statements)

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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%

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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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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“…Define the 2 × 2 complex matrix D(m ) := (m , J m ) having m and J m as columns. 11 It is an element of SU (2). Using the previous notation, it can be written as The Livine-Speziale (LS) coherent states are defined as [35] |m 〉 j := D (j ) (m )|j , j 〉 ≡ D(m ) |j , j 〉, (2.10) where |j , j 〉 is the usual maximal magnetic number state in the standard j -th SU (2) irreducible representation (j ) , and D (j ) (m ) is the representation of the matrix D(m ) acting on (j ) .…”

Section: Spinors Vectors and Bivectorsmentioning

confidence: 99%

Self-energy of the Lorentzian Engle-Pereira-Rovelli-Livine and Freidel-Krasnov model of quantum gravity

Riello

2013

Phys. Rev. D

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We calculate the most divergent contribution to non-degenerate sectorof the self-energy (or "melonic") graph in the context of the Lorentzian EPRL-FK Spin Foam model of Quantum Gravity. We find that such a contribution is logarithmically divergent in the cut-off over the SU (2)-representation spins when one chooses the face amplitude guaranteeing the facesplitting invariance of the foam. We also find that the dependence on the boundary data is different from that of the bare propagator. This fact has its origin in the non-commutativity of the EPRL-FK Y γ -map with the projector onto SL(2, )-invariant states. In the course of the paper, we discuss in detail the approximations used during the calculations, its geometrical interpretation as well as the physical consequences of our result.

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“…-Group Field Theories [1][2][3][4][5] (GFTs) are a particular class of quantum field theories with fields defined over a group manifold and characterised by combinatorially non-local interaction terms. This combinatorial non-locality makes the Feynman diagrams of the theory stranded diagrams dual to cellular complexes (simplicial complexes in the simplest constructions) [1,3].…”

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confidence: 99%

“…Introducing the logarithmic scale t = log k and Γ (2) k := δΓ k /δϕδϕ, the Wetterich equation for tensorial GFT models has the form [45]:…”

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confidence: 99%

Functional Renormalization Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$

Geloun

Martini

Oriti

2015

EPL

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-We study a model of Tensorial Group Field Theory (TGFT) on R 3 from the point of view of the Functional Renormalisation Group. This is the first attempt to apply a renormalisation procedure to a TGFT model defined over a non-compact group manifold. IR divergences (with respect to the metric on R) coming from the non-compactness of the group are regularised via compactification, and a thermodynamic limit is then taken. We identify then IR and UV fixed points of the RG flow and find strong hints of a phase transition of the TGFT system from a symmetric to a broken or condensate phase in the IR.Introduction. -Group Field Theories [1-5] (GFTs) are a particular class of quantum field theories with fields defined over a group manifold and characterised by combinatorially non-local interaction terms. This combinatorial non-locality makes the Feynman diagrams of the theory stranded diagrams dual to cellular complexes (simplicial complexes in the simplest constructions) [1,3]. GFT's historically were born from an attempt to generalise matrix models [6] of 2d gravity to higher dimensions in the form of tensor models [7][8][9]. These models were soon enriched with group theoretic data in such a way that the Feynman amplitudes of specific GFT models coincide with state sum models of topological field theory [9,10]. A connection between GFTs and Loop Quantum Gravity (LQG) [11,12] was immediately pointed out [13] at the level of quantum states, and later enforced at the level of the quantum dynamics. In fact, it was later shown [14] that GFTs provide a formal (complete) definition of spin foams models, a covariant formalism for LQG. For GFTs (and spin foam models) endowed with a discrete geometric interpretation (which requires appropriate group theoretic data and suitable choices of dynamics) there is also a direct link with simplicial quantum gravity path integrals, first manifested in the semiclassical analysis of GFT Feynman (spin foam) amplitudes, where one recovers the Regge action [15], and then shown to be generically manifest in the flux repre-

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Group Field Theories

Cited by 73 publications

References 64 publications

Homogeneous cosmologies as group field theory condensates

Homogeneous cosmologies as group field theory condensates

Self-energy of the Lorentzian Engle-Pereira-Rovelli-Livine and Freidel-Krasnov model of quantum gravity

Functional Renormalization Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$

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