Searcharxiv⌕ Search

arXiv subjects

J. Fernando Barbero

Publications and source records attributed to J. Fernando Barbero.

14 recordsLinked to original sources
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↗
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↗
arXiv2002

Diff-invariant Kinetic Terms in Arbitrary Dimensions

We study the physical content of quadratic diff-invariant Lagrangians in arbitrary dimensions by using covariant symplectic techniques. This paper extends previous results in dimension four. We discuss the difference between the even and odd dimensional cases.

hep-th↗
arXiv1995

Minisuperspace Examples of Quantization Using Canonical Variables of the Ashtekar Type: Structure and Solutions

The Ashtekar variables have been use to find a number of exact solutions in quantum gravity and quantum cosmology. We investigate the origin of these solutions in the context of a number of canonical transformations (both complex and real) of the basic Hamiltonian variables of general relativity. We are able to present several new solutions in the minisuperspace (quantum cosmology) sector. The meaning of these solutions is then discussed.

gr-qc↗
arXiv1995

Homogeneous 2+1 Dimensional Gravity in the Ashtekar Formulation

The constraint hypersurfaces defining the Witten and Ashtekar formulations for 2+1 gravity are very different. In particular the constraint hypersurface in the Ashtekar case is not a manifold but consists of several sectors that intersect each other in a complicated way. The issue of how to define a consistent dynamics in such a situation is then rather non-trivial. We discuss this point by working out the details in a simplified (finite dimensional) homogeneous reduction of 2+1 gravity in the Ashtekar formulation.

gr-qc↗
arXiv1994

Solving the Constraints of General Relativity

I show in this letter that it is possible to solve some of the constraints of the $SO(3)$-ADM formalism for general relativity by using an approach similar to the one introduced by Capovilla, Dell and Jacobson to solve the vector and scalar constraints in the Ashtekar variables framework. I discuss the advantages of using the ADM formalism and compare the result with similar proposals for different Hamiltonian formulations of general relativity.

gr-qc↗
arXiv1994

Reality Conditions and Ashtekar Variables: a Different Perspective

We give in this paper a modified self-dual action that leads to the $SO(3)$-ADM formalism without having to face the difficult second class constraints present in other approaches (for example if one starts from the Hilbert-Palatini action). We use the new action principle to gain some new insights into the problem of the reality conditions that must be imposed in order to get real formulations from complex general relativity. We derive also a real formulation for Lorentzian general relativity in the Ashtekar phase space by using the modified action presented in the paper.

gr-qc↗
arXiv1994

Real Ashtekar Variables for Lorentzian Signature Space-times

I suggest in this letter a new strategy to attack the problem of the reality conditions in the Ashtekar approach to classical and quantum general relativity. By writing a modified Hamiltonian constraint in the usual $SO(3)$ Yang-Mills phase space I show that it is possible to describe space-times with Lorentzian signature without the introduction of complex variables. All the features of the Ashtekar formalism related to the geometrical nature of the new variables are retained; in particular, it is still possible, in principle, to use the loop variables approach in the passage to the quantum theory. The key issue in the new formulation is how to deal with the more complicated Hamiltonian constraint that must be used in order to avoid the introduction of complex fields.

gr-qc↗
arXiv1993

A Real Polynomial Formulation of General Relativity in terms of Connections

I show in this letter that it is possible to construct a Hamiltonian description for Lorentzian General Relativity in terms of two real $SO(3)$ connections. The constraints are simple polynomials in the basic variables. The present framework gives us a new formulation of General Relativity that keeps some of the interesting features of the Ashtekar formulation without the complications associated with the complex character of the latter.

gr-qc↗
arXiv1993

General Relativity as a Theory of Two Connections

We show in this paper that it is possible to formulate General Relativity in a phase space coordinatized by two $SO(3)$ connections. We analyze first the Husain-Kuchař model and find a two connection description for it. Introducing a suitable scalar constraint in this phase space we get a Hamiltonian formulation of gravity that is close to the Ashtekar one, from which it is derived, but has some interesting features of its own. Among them a possible mechanism for dealing with the degenerate metrics and a neat way of writing the constraints of General Relativity.

gr-qc↗
arXiv1993

The Phase Space of 2+1 Dimensional Gravity in the Ashtekar Formulation

The Ashtekar formulation of 2+1 gravity differs from the geometrodynamical and Witten descriptions when the 2-metric is degenerate. We study the phase space of 2+1 gravity in the Ashtekar formulation to understand these degenerate solutions to the field equations. In the process we find two new systems of first class constraints which describe part of the degenerate sectors of the Ashtekar formulation. One of them also generalizes the Witten constraints. Finally we argue that the Ashtekar formulation has an arbitrarily large number of degrees of freedom in contrast to the usual descriptions. TO GET THE FIGURES CONTACT Barbero@suhep.phy.syr.edu or Madhavan@suhep.phy.syr.edu

gr-qc↗