Related papers: Aspects of Group Field Theory
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…
Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any…
We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…
I describe the history of my attempts to arrive at a discrete substratum underlying the spacetime manifold, culminating in the hypothesis that the basic structure has the form of a partial-order (i.e. that it is a causal set).
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…
Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in…
We construct a group field theory model for quantum gravity minimally coupled to relativistic scalar fields, defining as well a corresponding discrete gravity path integral (and, implicitly, a coupled spin foam model) in its Feynman…
The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as…
This paper presents reflections on the validity of a series of mathematical methods and technical assumptions that are encrusted in macrophysics (related to gravitational interaction), that seem to have little or no physical significance.…
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…
A new unifying theory was recently proposed by the author in the publication "Arrangement field theory - beyond strings and loop gravity -". Such theory describes all fields (gravitational, gauge and matter fields) as entries in a matricial…
Here we present an overview on the various works, in which many collaborators have contributed, regarding the interesting dipole of noncommutativity and physics. In brief, we present the features that noncommutativity triggers both in the…
We present an introduction to Group Field Theory models, motivating them on the basis of their relationship with discretized BF models of gravity. We derive the Feynmann rules and compute quantum corrections in the coherent states basis.
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…
We provide a short and non-technical summary of our current knowledge and some possible perspectives on the group field theory formalism for quantum gravity, in the form of a (partial) FAQ (with answers). Some of the questions and answers…
The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces…
The tensor track approach to quantum gravity is based on a new class of quantum field theories, called tensor group field theories (TGFTs). We provide a brief review of recent progress and list some desirable properties of TGFTs. In order…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
A generalization of the matrix model idea to quantum gravity in three and higher dimensions is known as group field theory (GFT). In this paper we study generalized GFT models that can be used to describe 3D quantum gravity coupled to point…
This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of…