Related papers: Tensors and Algebras: An Algebraic Spacetime Inter…
Loop Quantum Gravity (LQG) is an attempt to describe the quantum gravity regime. Introducing a non-zero cosmological constant $\Lambda$ in this context has been a withstanding problem. Other approaches, such as Chern-Simons gravity, suggest…
We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is…
We use the polygon representation of 2+1--dimensional gravity to explicitly carry out the canonical quantization of a universe with the topology of a torus. The mapping-class-invariant wave function for a quantum ''big bounce'', is…
To understand spacetime dynamics in the canonical tensor model of quantum gravity for the positive cosmological constant case, we analytically and numerically study the phase profile of its exact wave function in a coordinate…
This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains,…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
Deformations of maximal supergravity theories induced by gauging non-abelian subgroups of the duality group reveal the presence of charged M-theory degrees of freedom that are not necessarily contained in supergravity. The relation with…
The aim of this paper is to discuss a kinematical algebraic structure of a theory of gravity, that would be unitary, renormalizable and coupled in the same manner to both spinorial and tensorial matter fields. An analysis of the common…
In any space-time, it is possible to have a family of observers who have access to only part of the space-time manifold, because of the existence of a horizon. We demand that \emph{physical theories in a given coordinate system must be…
The quest for a consistent theory which describes the quantum microstructure of spacetime seems to require some departure from the paradigms that have been followed in the construction of quantum theories for the other fundamental…
Recentely, it is shown that the quantum effects of matter determine the conformal degree of freedom of the space-time metric. This was done in the framework of a scalar-tensor theory with one scalar field. A point with that theory is that…
We study the scalar-tensor theory of gravity profoundly in the action level as well as in the thermodynamic level. Contrary to the usual description in the literature about the equivalence in the two conformally connected frames, this paper…
The lack of a well-established solution for the gravitational energy problem might be one of the reasons why a clear road to quantum gravity does not exist. In this paper, the gravitational energy is studied in detail with the help of the…
We review quantum gravity model building using the new formalism of `quantum Riemannian geometry' to construct this on finite discrete spaces and on fuzzy ones such as matrix algebras. The formalism starts with a `differential structure' as…
Tensor-scalar theories of gravitation are commonly employed as extensions of General Relativity that allow to describe a much wider phenomenology. They are also naturally generated as low energy limit of higher-dimensional or unified…
Semi-classical gravity is an approximation to quantum gravity where gravity is treated classically and matter quantum mechanically. Matter is described by quantum field theory on curved space-time, whereas gravity is described by a…
Three-dimensional topologically massive AdS gravity has a complicated constraint algebra, making it difficult to count nonperturbative degrees of freedom. I show that a new choice of variables greatly simplifies this algebra, and confirm…
Area metric manifolds emerge as a refinement of symplectic and metric geometry in four dimensions, where in numerous situations of physical interest they feature as effective matter backgrounds. In this article, this prompts us to identify…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…