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J. Manuel Garcia-Islas

Publications and source records attributed to J. Manuel Garcia-Islas.

16 recordsLinked to original sources
arXiv2019

Quantum Geometry I : Basics of Loop Quantum Gravity. The Quantum Polyhedra

General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are responsible of this subject. Unfortunately, most mathematicians are not aware of this beautiful area of study. Here we give a basic introduction to what quantum geometry means to a community working in a theory known as loop quantum gravity. It is directed towards graduate or upper students of physics and mathematics. We do it from a point of view of a mathematician.

gr-qc↗
arXiv2015

2D Naked Singularity in General Relativity

We present a novel example of a 2-dimensional space-time naked singularity. The solution has a gravity singularity and no-horizon. This example is only a toy model and as such its motivation is mathematical. In the physical sense it is very helpful to understand in simple terms what naked singularities are and the properties they may have.

gr-qc↗
arXiv2015

Entropic Motion in Loop Quantum Gravity

Entropic forces result from an increase of the entropy of a thermodynamical physical system. It has been proposed that gravity is such a phenomenon and many articles have appeared on the literature concerning this problem. Loop quantum gravity has also considered such possibility. We propose a new method in loop quantum gravity which reproduces an entropic force. By considering the interaction between a fixed gravity state space and a particle state in loop quantum gravity, we show that it leads to a mathematical description of a random walk of such particle. The random walk in special situations, can be seen as an entropic motion in such a way that the particle will move towards a location where entropy increases. This may prove that such theory can reproduce gravity as it is expected.

gr-qc↗
arXiv2014

The four particles paradox in special relativity

We present a novel paradox in special relativity together with its solution. We call it the four particles paradox. The purpose of this paradox is pedagogical and therefore directed towards students and lecturers of physics. Even if most paradoxes in special relativity theory are very interrelated and some are special cases of others, the paradox we present here is original and illuminates on the very nice subject and the literature of special relativity.

physics.class-ph↗
arXiv2013

Measurements and Information in Spin Foam Models

We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy associated to the corresponding information. We present a general definition, compute the Shannon entropy of some examples, and find some interesting inequalities.

gr-qc↗
arXiv2011

A very simple solution to the OPERA neutrino velocity problem

Scientists from the OPERA experiment have measured neutrinos supposedly travelling at a velocity faster than light contrary to the theory of relativity. Even when the measurements are precise, the interpretation of this problem is being misunderstood. Here it is very easily solved and explained within the theory of relativity itself proving that neutrinos are not travelling faster than the speed of light and the early time arrival is due to the the presence of a gravitational field.

physics.gen-ph↗
arXiv2010

Entropy in Spin Foam Models: The Statistical Calculation

Recently an idea for computing the entropy of black holes in the spin foam formalism has been introduced. Particularly complete calculations for the three dimensional euclidean BTZ black hole were done. The whole calculation is based on observables living at the horizon of the black hole universe. Departing from this idea of observables living at the horizon, we now go further and compute the entropy of BTZ black hole in the spirit of statistical mechanics. We compare both calculations and show that they are very interrelated and equally valid. This latter behaviour is certainly due to the importance of the observables.

gr-qc↗
arXiv2008

BTZ Black Hole Entropy: A spin foam model description

We present a microscopical explanation of the entropy of the BTZ black hole using discrete spin foam models of quantum gravity. The entropy of a black hole is given in geometrical terms which lead us to think that its statistical description must be given in terms of a quantum geometry. In this paper we present it in terms of spin foam geometrical observables at the horizon of the black hole.

gr-qc↗
arXiv2008

Graphs on Surfaces and the Partition Function of String Theory

Graphs on surfaces is an active topic of pure mathematics belonging to graph theory. It has also been applied to physics and relates discrete and continuous mathematics. In this paper we present a formal mathematical description of the relation between graph theory and the mathematical physics of discrete string theory. In this description we present problems of the combinatorial world of real importance for graph theorists. The mathematical details of the paper are as follows: There is a combinatorial description of the partition function of bosonic string theory. In this combinatorial description the string world sheet is thought as simplicial and it is considered as a combinatorial graph. It can also be said that we have embeddings of graphs in closed surfaces. The discrete partition function which results from this procedure gives a sum over triangulations of closed surfaces. This is known as the vacuum partition function. The precise calculation of the partition function depends on combinatorial calculations involving counting all non-isomorphic triangulations and all spanning trees of a graph. The exact computation of the partition function turns out to be very complicated, however we show the exact expressions for its computation for the case of any closed orientable surface. We present a clear computation for the sphere and the way it is done for the torus, and for the non-orientable case of the projective plane.

math-ph↗
arXiv2007

Observables in the Turaev-Viro and Crane-Yetter models

We define an invariant of graphs embedded in a three-manifold and a partition function for 2-complexes embedded in a triangulated four-manifold by specifying the values of variables in the Turaev-Viro and Crane-Yetter state sum models. In the case of the three-dimensional invariant, we prove a duality formula relating its Fourier transform to another invariant defined via the coloured Jones polynomial. In the case of the four-dimensional partition function, we give a formula for it in terms of a regular neighbourhood of the 2-complex and the signature of its complement. Some examples are computed which show that the partition function determines an invariant which can detect non locally-flat surfaces in a four-manifold.

math.QA↗
arXiv2004

Observables in 3-dimensional quantum gravity and topological invariants

In this paper we report some results on the expectation values of a set of observables introduced for 3-dimensional Riemannian quantum gravity with positive cosmological constant, that is, observables in the Turaev-Viro model. Instead of giving a formal description of the observables, we just formulate the paper by examples. This means that we just show how an idea works with particular cases and give a way to compute 'expectation values' in general by a topological procedure.

gr-qc↗
arXiv2004

Spin Foam Models of n-dimensional Quantum Gravity and Non-Archimedean and Non-Commutative Formulations

This paper is twofold. First of all a complete unified picture of $n$-dimensional quantum gravity is proposed in the following sense: In spin foam models of quantum gravity the evaluation of spin networks play a very important role. These evaluations correspond to amplitudes which contribute in a state sum model of quantum gravity. In \cite{fk}, the evaluation of spin networks as integrals over internal spaces was described. This evaluation was restricted to evaluations of spin networks in $n$-dimensional Euclidean quantum gravity. Here we propose that a similar method can be considered to include Lorentzian quantum gravity. We therefore describe the the evaluation of spin networks in the Lorentzian framework of spin foam models. We also include a limit of the Euclidean and Lorentzian spin foam models which we call Newtonian. This Newtonian limit was also considered in \cite{jm}. Secondly, we propose an alternative formulation of spin foam models of quantum gravity with its corresponding evaluation of spin networks. This alternative formulation is a non-archimedean or $p$-adic spin foam model. The interest on this description is that it is based on a discrete space-time, which is the expected situation we might have at the Planck length; this description might lead us to an alternative regularisation of quantum gravity. Moreover a non-commutative formulation follows from the non-archimedean one.

gr-qc↗
arXiv2003

(2+1)-dimensional quantum gravity, spin networks and asymptotics

A method to evaluate spin networks for (2+1)-dimensional quantum gravity is given. We analyse the evaluation of spin networks for Lorentzian, Euclidean and a new limiting case of Newtonian quantum gravity. Particular attention is paid to the tetrahedron and to the study of its asymptotics. Moreover, we propose that all this technique can be extended to spin networks for quantum gravity in any dimension.

gr-qc↗