Related papers: Tensors and Algebras: An Algebraic Spacetime Inter…
Developing a theory for quantum gravity is one of the big open questions in theoretical high-energy physics. Recently, a tensor model approach has been considered that treats tensors as the generators of commutative non-associative…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
Space-time measurements and gravitational experiments are made by using objects, matter fields or particles and their mutual relationships. As a consequence, any operationally meaningful assertion about space-time is in fact an assertion…
It is well known that for a given Poisson structure one has infinitely many star products related through the Kontsevich gauge transformations. These gauge transformations have an infinite functional dimension (i.e., correspond to an…
Recently, it was shown that the quantum effects of the matter, could be used to determine the conformal degree of freedom of the space-time metric. So both gravity and quantum are geometrical features. Gravity determines the causal…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
The paper studies the possible interplay between matter and geometry in scalar tensor theories of gravitation where the energy--momentum tensor is directly coupled with the Einstein tensor. After obtaining the scalar tensor representation…
This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder like deformation in the background of the Kepler problem. In order to accomplish that task, a newtonian spacetime is…
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
The canonical tensor model (CTM) is a tensor model in Hamilton formalism and is studied as a model for gravity in both classical and quantum frameworks. Its dynamical variables are a canonical conjugate pair of real symmetric three-index…
A non-geometrical (but with curved space) theory of gravitation characterized by a vector field representing gravitational matter and a metric tensor presenting space is presented. It is derived from a more general theory of matter and…
The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…
The tensor rank decomposition is a useful tool for the geometric interpretation of the tensors in the canonical tensor model (CTM) of quantum gravity. In order to understand the stability of this interpretation, it is important to be able…
Tensor models are measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as additionally to the…
One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…
We will argue in this paper that the type classification of v.Neumann algebras play an important role in a theory of quantum gravity and quantum space-time physics. We provide arguments that type $II_{\infty}$ and its representation as a…
f(T) gravity is a generalization of the teleparallel equivalent of general relativity (TEGR), where T is the torsion scalar made up of the Weitzenb\"{o}ck connection. This connection describes a spacetime with zero curvature but with…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
The paper is constructed in two parts.In the first part we introduce the concept of the algebra of Q-meromorphic functions on the quantum plane.The A (q)-algebra of Q-analytic functions considered in[6]is seen as a proper subalgebra. In the…
We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x,t]=\lambda x drastically reduce the moduli of possible metrics g up to normalisation to a…