arXiv subjects

Efrain Rojas

Publications and source records attributed to Efrain Rojas.

At least 19 recordsLinked to original sources

arXiv2020

Hamiltonian dynamics of gonihedric string theory

We develop in a consistent manner the Ostrogradski-Hamilton framework for gonihedric string theory. The local action describing this model, being invariant under reparametrizations, depends on the modulus of the mean extrinsic curvature of the worldsheet swept out by the string, and thus we are confronted with a genuine second-order in derivatives field theory. In our geometric approach, we consider the embedding functions as the field variables and, even though the highly non-linear dependence of the action on these variables, we are able to complete the classical analysis of the emerging constraints for which, after implementing a Dirac bracket, we are able to identify both the gauge transformations and the proper physical degrees of freedom of the model. The Ostrogradski-Hamilton framework is thus considerable robust as one may recover in a straightforward and consistent manner some existing results reported in the literature. Further, in consequence of our geometrical treatment, we are able to unambiguously recover as a by-product the Hamiltonian approach for a particular relativistic point-particle limit associated with the gonihedric string action, that is, a model linearly depending on the first Frenet-Serret curvature.

hep-th↗

arXiv2020

Hamilton-Jacobi approach for Regge-Teitelboim cosmology

The Hamilton-Jacobi formalism for a geodetic brane-like universe described by the Regge-Teitelboim model is developed. We focus on the description of the complete set of Hamiltonians that ensure the integrability of the model in addition to obtaining the Hamilton principal function $S$. In order to do this, we avoid the second-order in derivative nature of the model by appropriately defining a set of auxiliary variables that yields a first-order Lagrangian. Being a linear in acceleration theory, this scheme unavoidably needs an adequate redefinition of the so-called Generalized Poisson Bracket in order to achieve the right evolution in the reduced phase space. Further this Hamilton-Jacobi framework also enables us to explore the quantum behaviour under a semi-classical approximation of the model. A comparison with the Ostrogradski-Hamilton method for constrained systems is also provided in detail.

gr-qc↗

arXiv2019

Holographic relationships in Lovelock type brane gravity

We show that the Lovelock type brane gravity is naturally holographic by providing a correspondence between bulk and surface terms that appear in the Lovelock-type brane gravity action functional. We prove the existence of relationships between the $\mathcal{L}_{\mbox{\tiny bulk}}$ and $\mathcal{L}_{\mbox{\tiny surf}}$ allowing $\mathcal{L}_{\mbox{\tiny surf}}$ to be determined completely by $\mathcal{L}_{\mbox{\tiny bulk}}$. In the same spirit, we provide relationships among the various conserved tensors that this theory possesses. We further comment briefly on the correspondence between geometric degrees of freedom in both bulk and surface space.

hep-th↗

arXiv2017

Covariant perturbations in the gonihedric string model

We provide a covariant framework to study classically the stability of small perturbations on the so-called gonihedric string model by making precise use of variational techniques. The local action depends of the square root of the quadratic mean extrinsic curvature of the worldsheet swept out by the string, and is reparametrization invariant. A general expression for the worldsheet perturbations, guided by Jacobi equations without any early gauge fixing, is obtained. This is manifested through a set of highly coupled nonlinear differential partial equations where the perturbations are described by scalar fields, $Φ^i$, living in the worldsheet. This model contains, as a special limit, to the linear model in the mean extrinsic curvature. In such a case the Jacobi equations specialize to a single wave-like equation for $Φ$.

hep-th↗

arXiv2016

Covariant approach of perturbations in Lovelock type brane gravity

We develop a covariant scheme to describe the dynamics of small perturbations on Lovelock type extended objects propagating in a flat Minkowski spacetime. The higher-dimensional analogue of the Jacobi equation in this theory becomes a wave type equation for a scalar field $Φ$. Whithin this framework, we analyse the stability of membranes with a de Sitter geometry where we find that the Jacobi equation specializes to a Klein-Gordon (KG) equation for $Φ$ possessing a tachyonic mass. This shows that, to some extent, these type of extended objects share the symmetries of the Dirac-Nambu-Goto (DNG) action which is by no means coincidental because the DNG model is the simplest included in this type of gravity.

gr-qc↗

arXiv2016

Hamiltonian analysis for linearly acceleration-dependent Lagrangians

We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defned quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identifed. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant feld theories.

math-ph↗

arXiv2015

On the flat spacetime Galileons and the Born-Infeld type structures

We show how the flat spacetime Galileon field theories (FSGFT) in arbitrary dimensions can be obtained through a Born-Infeld type structure. This construction involves a brane metric and non-linear combinations of derivatives of a scalar field. Our setup gives rise to some Galileon tensors and vectors useful for the variational analysis which are related to the momentum density of the probe Lovelock branes floating in a $N$-dimensional flat bulk. We find further that the Noether currents associated to these Galileon theories may be written in terms of such tensors.

hep-th↗

arXiv2011

Hamiltonian dynamics for Einstein's action in G$\rightarrow$0 limit

The Hamiltonian analysis for the Einstein's action in $ G\to 0 $ limit is performed. Considering the original configuration space without involve the usual $ADM$ variables we show that the version $ Gto 0 $ for Einstein's action is devoid of physical degrees of freedom. In addition, we will identify the relevant symmetries of the theory such as the extended action, the extended Hamiltonian, the gauge transformations and the algebra of the constraints. As complement part of this work, we develop the covariant canonical formalism where will be constructed a closed and gauge invariant symplectic form. In particular, using the geometric form we will obtain by means of other way the same symmetries that we found using the Hamiltonian analysis.

math-ph↗

arXiv2011

Quantum charged rigid membrane

The early Dirac proposal to model the electron as a charged membrane is reviewed. A rigidity term, instead of the natural membrane tension, involving linearly the extrinsic curvature of the worldvolume swept out by the membrane is considered in the action modeling the bubble in the presence of an electromagnetic field. We set up this model as a genuine second-order derivative theory by considering a non-trivial boundary term which plays a relevant part in our formulation. The Lagrangian in question is linear in the bubble acceleration and by means of the Ostrogradski-Hamiltonian approach we observed that the theory comprises the management of both first- and second-class constraints. We show thus that our second-order approach is robust allowing for a proper quantization. We found an effective quantum potential which permits to compute bounded states for the system. We comment on the possibility of describing brane world universes by invoking this kind of second-order correction terms.

gr-qc↗

arXiv2010

Higher order curvature terms in Born-Infeld type brane theories

The field equations associated to Born-Infeld type brane theories are studied by using an auxiliary variables method. This approach hinges on the fact that the expressions defining the physical and geometrical quantities describing the worldvolume are varied independently. The general structure of the Born-Infeld type theories for branes contains the square root of a determinant of a combined matrix between the induced metric on the worldvolume swept out by the brane and a symmetric/antisymmetric tensor depending of gauge, matter or extrinsic curvature terms taking place on the worldvolume. The higher order curvature terms appearing in the determinant form come to play as competition with other effective brane models. Additionally, we suggest a Born-Infeld-Einstein type action for branes where the higher order curvature content is provided by the worldvolume Ricci tensor. This action provide an alternative description of the dynamics of braneworld scenarios.

hep-th↗

arXiv2010

Greybody factors for topological massless black holes

We study the reflection coefficient, the transmission coefficient and the greybody factors for black holes with topologically non trivial transverse sections in 4 and d-dimensions, in the limit of low energy. Considering a massive scalar field in a topological massless black hole background, which is non minimally coupled to the curvature and assuming the horizon geometry with a negative constant curvature. Mainly, we show that there is range of modes which contribute to the absorption cross section in the zero-frequency limit, at difference of the result existing in the literature. Where, the mode with lowest angular momentum contribute to the absorption cross section. Also we show that the condition that the sum of the reflection coefficient and the transmission coefficient is equal to one is always satisfied for these kind of black holes.

gr-qc↗

arXiv2009

Curvaton reheating in logamediate inflationary model

In a logamediate inflationary universe model we introduce the curvaton field in order to bring this inflationary model to an end. In this approach we determine the reheating temperature. We also outline some interesting constraints on the parameters that describe our models. Thus, we give the parameter space in this scenario.

astro-ph.CO↗

arXiv2009

Ostrogradski approach for the Regge-Teitelboim type cosmology

We present an alternative geometric inspired derivation of the quantum cosmology arising from a brane universe in the context of {\it geodetic gravity}. We set up the Regge-Teitelboim model to describe our universe, and we recover its original dynamics by thinking of such field theory as a second-order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. Our analysis highlights the second-order derivative nature of the RT model and the inherited geometrical aspect of the theory. A canonical transformation brings us to the internal physical geometry of the theory and induces its quantization straightforwardly. By using the Dirac canonical quantization method our approach comprises the management of both first- and second-class constraints where the counting of degrees of freedom follows accordingly. At the quantum level our Wheeler-De Witt Wheeler equation agrees with previous results recently found. On these lines, we also comment upon the compatibility of our approach with the Hamiltonian approach proposed by Davidson and coworkers.

gr-qc↗

arXiv2007

Geometrical dynamics of Born-Infeld objects

We present a geometrical inspired study of the dynamics of $Dp$-branes. We focus on the usual nonpolynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a $D1$-brane immersed in a $AdS_3 \times S^3$ background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation.

hep-th↗

arXiv2007

Null Frenet-Serret Dynamics

We consider the Frenet-Serret geometry of null curves in a three and a four-dimensional Minkowski background. We develop a theory of deformations adapted to the Frenet-Serret frame. We exploit it to provide a Lagrangian description of the dynamics of geometric models for null curves.

math-ph↗

arXiv2005

Hamilton's equations for a fluid membrane: axial symmetry

Consider a homogenous fluid membrane, or vesicle, described by the Helfrich-Canham energy, quadratic in the mean curvature. When the membrane is axially symmetric, this energy can be viewed as an `action' describing the motion of a particle; the contours of equilibrium geometries are identified with particle trajectories. A novel Hamiltonian formulation of the problem is presented which exhibits the following two features: {\it (i)} the second derivatives appearing in the action through the mean curvature are accommodated in a natural phase space; {\it (ii)} the intrinsic freedom associated with the choice of evolution parameter along the contour is preserved. As a result, the phase space involves momenta conjugate not only to the particle position but also to its velocity, and there are constraints on the phase space variables. This formulation provides the groundwork for a field theoretical generalization to arbitrary configurations, with the particle replaced by a loop in space.

cond-mat.soft↗

arXiv2005

Hamilton's equations for a fluid membrane

Consider a homogenous fluid membrane described by the Helfrich-Canham energy, quadratic in the mean curvature of the membrane surface. The shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in the mean curvature. We introduce a Hamiltonian formulation of this equation which dismantles it into a set of coupled first order equations. This involves interpreting the Helfrich-Canham energy as an action; equilibrium surfaces are generated by the evolution of space curves. Two features complicate the implementation of a Hamiltonian framework: (i) The action involves second derivatives. This requires treating the velocity as a phase space variable and the introduction of its conjugate momentum. The canonical Hamiltonian is constructed on this phase space. (ii) The action possesses a local symmetry -- reparametrization invariance. The two labels we use to parametrize points on the surface are themselves physically irrelevant. This symmetry implies primary constraints, one for each label, that need to be implemented within the Hamiltonian. The two lagrange multipliers associated with these constraints are identified as the components of the acceleration tangential to the surface. The conservation of the primary constraints imply two secondary constraints, fixing the tangential components of the momentum conjugate to the position. Hamilton's equations are derived and the appropriate initial conditions on the phase space variables are identified. Finally, it is shown how the shape equation can be reconstructed from these equations.

cond-mat.soft↗

arXiv2005

Supertubes versus superconducting tubes

In this paper we show the relationship between cylindrical D2-branes and cylindrical superconducting membranes described by a generic effective action at the bosonic level. In the first case the extended objects considered, arose as blown up type IIA superstrings to D2-branes, named supertubes. In the second one, the cosmological objects arose from some sort of field theories. The Dirac-Born-Infeld action describing supertubes is shown to be equivalent to the generic effective action describing superconducting membranes via a special transformation.

hep-th↗