Related papers: Group field theories for all loop quantum gravity
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, and discuss briefly the current status…
This Editorial introduces the Special Issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms" which includes a number of research and review articles covering results in the group field theory (GFT) formalism for…
The observation that spacetime and quantum fields on it have to be dynamically produced in any theory of quantum gravity implies that quantum gravity should be defined on the configuration space of fields rather than spacetime. Such a…
We construct a generalization of pure lattice gauge theory (LGT) where the role of the gauge group is played by a tensor category. The type of tensor category admissible (spherical, ribbon, symmetric) depends on the dimension of the…
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such…
We present the case for a fundamentally discrete quantum spacetime and for Group Field Theories as a candidate consistent description of it, briefly reviewing the key properties of the GFT formalism. We then argue that the outstanding…
We present a new group field theory model, generalising the Boulatov model, which incorporates both 3-dimensional gravity and matter coupled to gravity. We show that the Feynman diagram amplitudes of this model are given by Riemannian…
This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
We discuss motivation and goals of renormalization analyses of group field theory models of simplicial 4d quantum gravity, and review briefly the status of this research area. We present some new computations of perturbative GFT (spin foam)…
In this series of papers, we propose a new rendition of 3d and 4d state sum models based upon the group field theory (GFT) approach to non-perturbative quantum gravity. We will see that the group field theories investigated in the…
We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with…
We consider quantum transition amplitudes, partition functions and observables for 3D spin foam models within $SU(2)$ quantum group deformation symmetry, where the deformation parameter is a complex fifth root of unity. By considering…
New progress in loop gravity has lead to a simple model of `general-covariant quantum field theory'. I sum up the definition of the model in self-contained form, in terms accessible to those outside the subfield. I emphasize its formulation…
Group field theories (GFT) are higher dimensional generalizations of matrix models whose Feynman diagrams are dual to triangulations. Here we propose a modification of GFT models that includes extra field indices keeping track of the…
We discuss the notion of symmetries in non-local field theories characterized by integro-differential equations of motion, from a geometric perspective. We then focus on Group Field Theory (GFT) models of quantum gravity and provide a…
Spin foam models of quantum gravity are based on Plebanski's formulation of general relativity as a constrained BF theory. We give an alternative formulation of gravity as BF theory plus a certain potential term for the B-field. When the…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…