The quantum geometry of tensorial group field theories

@inproceedings{Oriti2012TheQG,
  title={The quantum geometry of tensorial group field theories},
  author={Daniele Oriti},
  year={2012}
}
  • D. Oriti
  • Published 1 November 2012
  • Computer Science
We remark the importance of adding suitable pre-geometric content to tensormodels, obtaining what has recently been called tensorial group field theories,to have a formalism that could describe the structure and dynamics of quantumspacetime. We also review briefly some recent results concerning the definitionof such pre-geometric content, and of models incorporating it. 

The Multi-Orientable Random Tensor Model, a Review

After its introduction (initially within a group eld theory framework) in A. Tanasa, J. Phys. A 45 (2012) 165401, the multi-orientable (MO) tensor model grew over the last years into a solid

On the relation of canonical and covariant formulations of Loop Quantum Gravity

Loop Quantum Gravity (LQG) is a background independent approach towards a quantum theory of gravity that splits into a canonical and a covariant branch the latter of which is also often called spin

$(D+1)$-Colored Graphs - a Review of Sundry Properties

We review the combinatorial, topological, algebraic and metric properties sup- ported by (D + 1)-colored graphs, with a focus on those that are pertinent to the study of tensor model theories. We

Linking covariant and canonical LQG II: spin foam projector

In a seminal paper, Kaminski et al for the first time extended the definition of spin foam models to arbitrary boundary graphs. This is a prerequisite in order to make contact to the canonical

On the finite amplitudes for open graphs in Abelian dynamical colored Boulatov–Ooguri models

In the work (Ben Geloun and Bonzom 2011 Int. J. Theor. Phys. 50 2819), it has been proved that the radiative corrections of the 2-point function in the SU(2) Boulatov tensor model generates a

GEMs and amplitude bounds in the colored Boulatov model

In this paper, we construct a methodology for separating divergencies due to different topological manifolds dual to Feynman graphs in a colored group field theory. After having introduced the

Quartic Tensor Models

Les modeles de tenseurs sont des mesures de probabilite sur des espaces de tenseurs aleatoires. Ils generalisent les modeles de matrices et furent developpes pour l’etude de la geometrie aleatoire en

References

SHOWING 1-10 OF 29 REFERENCES

The microscopic dynamics of quantum space as a group field theory

We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity,

Group field theory with noncommutative metric variables.

A dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest, and a new definition of the Barrett-Crane model for gravity is given.

The Group field theory approach to quantum gravity

We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local

Towards Renormalizing Group Field Theory

We review some aspects of non commutative quantum eld theory and group eld theory, in particular recent progress on the systematic study of the scaling and renormalization properties of group eld

Discrete Gravity Models and Loop Quantum Gravity: a Short Review

We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries

The Spin-Foam Approach to Quantum Gravity

  • A. Perez
  • Physics
    Living reviews in relativity
  • 2013
The present status of the spin-foam approach to the quantization of gravity is reviewed and the pedagogical presentation of the recently-introduced new models for four-dimensional quantum gravity is paid to.

Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions

We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for

Effective Hamiltonian constraint from group field theory

Spinfoam models provide a covariant formulation of the dynamics of loop quantum gravity. They are non-perturbatively defined in the group field theory (GFT) framework; the GFT partition function

The 1/N expansion of colored tensor models in arbitrary dimension

In this paper we extend the 1/N expansion introduced in Gurau R., Ann. Henri Poincaré, 12 (2011) 829, to group field theories in arbitrary dimension and prove that only graphs corresponding to

The Complete 1/N Expansion of Colored Tensor Models in Arbitrary Dimension

In this paper we generalize the results of Gurau (arXiv:1011. 2726 [gr-qc], 2011), Gurau and Rivasseau (arXiv:1101.4182 [gr-qc], 2011) and derive the full 1/N expansion of colored tensor models in