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Juan Margalef-Bentabol

Publications and source records attributed to Juan Margalef-Bentabol.

32 records · Page 2Linked to original sources
arXiv2019

Generalizations of the Pontryagin and Husain-Kuchař actions to manifolds with boundary

In this paper we study a family of generalizations of the Pontryagin and Husain-Kuchař actions on manifolds with boundary. In some cases, they describe well-known models---either at the boundary or in the bulk---such as 3-dimensional Euclidean general relativity with a cosmological constant or the Husain-Kuchař model. We will use Hamiltonian methods in order to disentangle the physical and dynamical content of the systems that we discuss here. This will be done by relying on a geometric implementation of the Dirac algorithm in the presence of boundaries recently proposed by the authors.

gr-qc↗
arXiv2019

Towards general relativity through parametrized theories

Boundaries, GNH, and parametrized theories. It takes three to tango. This is the motto of my doctoral thesis and the common thread of it. The thesis is structured as follows: after some acknowledgments and a brief introduction, chapter one is devoted to establishing the mathematical background necessary for the rest of the thesis (with special emphasis in the space of embeddings and the Fock construction). Chapter two is based on our papers arXiv:1701.00735, arXiv:1611.09603, and arXiv:1501.05114. We study carefully a system consisting of a string with two masses attached to the ends and try to establish if we can identify degrees of freedom at the boundary both classically and quantically (spoiler alert: it is not possible). The next chapter is a brief introduction to the parametrized theories with the simple example of the parametrized classical mechanics. The 4th chapter deals with the parametrized electromagnetism with boundaries, a generalization of our paper arXiv:1511.00826. The following chapter focuses on the parametrized scalar field with boundaries (see arXiv:1507.05438). The 6th chapter deals with the parametrized Maxwell-Chern-Simons and Chern-Simons theories with boundaries. Chapter seven delves into the theory of general relativity using the GNH algorithm, showing that the Hamiltonian formulation (ADM) can be obtained in a more direct and simple way. The same study is performed over the unimodular gravity. In the last chapter we gather the conclusions and some hints about the future work. Finally, an appendix is included with some additional mathematical topics as well as explicit computations.

math-ph↗
arXiv2017

On the distribution of the eigenvalues of the area operator in loop quantum gravity

We study the distribution of the eigenvalues of the area operator in loop quantum gravity concentrating on the part of the spectrum relevant for isolated horizons. We first show that the approximations relying on integer partitions are not sufficient to obtain the asymptotic behaviour of the eigenvalue distribution for large areas. We then develop a method, based on Laplace transforms, that provides a very accurate solution to this problem. The representation that we get is valid for any area and can be used to obtain its asymptotics in the large area limit.

gr-qc↗
arXiv2017

Boundary Hilbert spaces and trace operators

We discuss the introduction of boundary Hilbert spaces for a class of physical systems for which it is not possible to factor their state spaces as tensor products of Hilbert spaces naturally associated to their boundaries and bulks respectively. In order to do this we make use of the so called trace operators that play a relevant role in the analysis of PDE's in bounded regions. By taking advantage of these operators and some functorial aspects of the construction of Fock spaces, we will show how to obtain quantum dynamics at the boundaries defined in appropriate Hilbert spaces associated with them.

gr-qc↗
arXiv2016

Hamiltonian description of the parametrized scalar field in bounded spatial regions

We study the Hamiltonian formulation for a parametrized scalar field in a regular bounded spatial region subject to Dirichlet, Neumann and Robin boundary conditions. We generalize the work carried out by a number of authors on parametrized field systems to the interesting case where spatial boundaries are present. The configuration space of our models contains both smooth scalar fields defined on the spatial manifold and spacelike embeddings from the spatial manifold to a target spacetime endowed with a fixed Lorentzian background metric. We pay particular attention to the geometry of the infinite dimensional manifold of embeddings and the description of the relevant geometric objects: the symplectic form on the primary constraint submanifold and the Hamiltonian vector fields defined on it.

gr-qc↗
arXiv2015

Hamiltonian dynamics of the parametrized electromagnetic field

We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.

hep-th↗
arXiv2015

Quantization of scalar fields coupled to point-masses

We study the Fock quantization of a compound classical system consisting of point masses and a scalar field. We consider the Hamiltonian formulation of the model by using the geometric constraint algorithm of Gotay, Nester and Hinds. By relying on this Hamiltonian description, we characterize in a precise way the real Hilbert space of classical solutions to the equations of motion and use it to rigorously construct the Fock space of the system. We finally discuss the structure of this space, in particular the impossibility of writing it in a natural way as a tensor product of Hilbert spaces associated with the point masses and the field, respectively.

math-ph↗
arXiv2015

Realization problems for limit cycles of planar polynomial vector fields

We show that for any finite configuration of closed curves $Γ\subset \mathbb{R}^2$, one can construct an explicit planar polynomial vector field that realizes $Γ$, up to homeomorphism, as the set of its limit cycles with prescribed periods, multiplicities and stabilities. The only obstruction given on this data is the obvious compatibility relation between the stabilities and the parity of the multiplicities. The constructed vector fields are Darboux integrable and admit a polynomial inverse integrating factor.

math.DS↗
arXiv2014

Topology of the Misner Space and its g-boundary

The Misner space is a simplified $2$-dimensional model of the $4$-dimensional Taub-NUT space that reproduces some of its pathological behaviours. In this paper we provide an explicit base of the topology of the complete Misner space $\mathbb{R}^{1,1}/boost$. Besides we prove that some parts of this space, that behave like topological boundaries, are equivalent to the $g$-boundaries of the Misner space.

gr-qc↗
arXiv2013

Evolution of the Cosmological Horizons in a Concordance Universe

The particle and event horizons are widely known and studied concepts, but the study of their properties, in particular their evolution, have only been done so far considering a single state equation in a decelerating universe. This paper is the first of two where we study this problem from a general point of view. Specifically, this paper is devoted to the study of the evolution of these cosmological horizons in an accelerated universe with two state equations, cosmological constant and dust. We have obtained closed-form expressions for the horizons, which have allowed us to compute their velocities in terms of their respective recession velocities that generalize the previous results for one state equation only. With the equations of state considered, it is proved that both velocities remain always positive.

astro-ph.CO↗
arXiv2013

Evolution of the Cosmological Horizons in a Universe with Countably Infinitely Many State Equations

This paper is the second of two papers devoted to the study of the evolution of the cosmological horizons (particle and event horizons). Specifically, in this paper we consider the extremely general case of an accelerated universe with countably infinitely many constant state equations, and we obtain simple expressions in terms of their respective recession velocities that generalize the previous results for one and two state equations. We also provide a qualitative study of the values of the horizons and their velocities at the origin of the universe and at the far future, and we prove that these values only depend on one dominant state equation. Finally, we compare both horizons and determine when one is larger that the other.

astro-ph.CO↗
arXiv2008

Contractions of low-dimensional nilpotent Jordan algebras

In this paper we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among them. In particular, we prove that J2 and J3 are irreducible and that J4 is the union of the Zariski closures of two rigid Jordan algebras.

math.RA↗