Searcharxiv⌕ Search

arXiv subjects

L. F. Urrutia

Publications and source records attributed to L. F. Urrutia.

At least 37 records · Page 2Linked to original sources
arXiv2016

Electro and magneto statics of topological insulators as modeled by planar, spherical and cylindrical $θ$ boundaries: Green function approach

The Green function (GF) method is used to analyze the boundary effects produced by a Chern Simons (CS) extension to electrodynamics. We consider the electromagnetic field coupled to a $θ$ term that is piecewise constant in different regions of space, separated by a common interface $Σ$, the $θ$ boundary, model which we will refer to as $θ$ electrodynamics ($θ$ ED). This model provides a correct low energy effective action for describing topological insulators (TI). In this work we construct the static GF in $θ$ ED for different geometrical configurations of the $θ$ boundary, namely: planar, spherical and cylindrical $θ$ interfaces. Also we adapt the standard Green theorem to include the effects of the $θ$ boundary. These are the most important results of our work, since they allow to obtain the corresponding static electric and magnetic fields for arbitrary sources and arbitrary boundary conditions in the given geometries. Also, the method provides a well defined starting point for either analytical or numerical approximations in the cases where the exact analytical calculations are not possible. Explicit solutions for simple cases in each of the aforementioned geometries for $θ$ boundaries are provided. The adapted Green theorem is illustrated by studying the problem of a point like electric charge interacting with a planar TI with prescribed boundary conditions. Our generalization, when particularized to specific cases, is successfully compared with previously reported results, most of which have been obtained by using the methods of images.

cond-mat.mes-hall↗
arXiv2015

Green's function approach to Chern-Simons extended electrodynamics: an effective theory describing topological insulators

Boundary effects produced by a Chern-Simons (CS) extension to electrodynamics are analyzed exploiting the Green's function (GF) method. We consider the electromagnetic field coupled to a $θ$-term in a way that has been proposed to provide the correct low energy effective action for topological insulators (TI). We take the $θ$-term to be piecewise constant in different regions of space separated by a common interface $Σ$, to be called the $θ$-boundary. Features arising due to the presence of the boundary, such as magnetoelectric effects, are already known in CS extended electrodynamics and solutions for some experimental setups have been found with specific configuration of sources. In this work we illustrate a method to construct the GF that allows to solve the CS modified field equations for a given $θ$-boundary with otherwise arbitrary configuration of sources. The method is illustrated by solving the case of a planar $θ$-boundary but can also be applied for cylindrical and spherical geometries for which the $θ$-boundary can be characterized by a surface where a given coordinate remains constant. The static fields of a point-like charge interacting with a planar TI, as described by a planar discontinuity in $θ$, are calculated and successfully compared with previously reported results. We also compute the force between the charge and the $θ$-boundary by two different methods, using the energy momentum tensor approach and the interaction energy calculated via the GF. The infinitely straight current-carrying wire is also analyzed.

cond-mat.other↗
arXiv2015

Photons emerging as Goldstone bosons from spontaneous Lorentz symmetry breaking: The Abelian Nambu model

After imposing current conservation together with the Gauss law as initial conditions on the Abelian Nambu model, we prove that the resulting theory is equivalent to standard QED in the non-linear gauge $\left(A_{μ}A^{μ}-n^{2}M^{2}\right)=0$, to all orders in perturbation theory. We show this by writing both models in terms of the same variables, which produce identical Feynman rules for the interactions and propagators. A crucial point is to verify that the Faddeev-Popov ghosts arising from the gauge fixing procedure in the QED sector decouple to all orders. We verify this decoupling by following a method like that employed in Yang-Mills theories when investigating the behavior of axial gauges. The equivalence between the two theories supports the idea that gauge particles can be envisaged as the Goldstone bosons originating from spontaneous Lorentz symmetry breaking.

hep-ph↗
arXiv2015

Conditions for the emergence of gauge bosons from spontaneous Lorentz symmetry breaking

The emergence of gauge particles (e.g., photons and gravitons) as Goldstone bosons arising from spontaneous symmetry breaking is an interesting hypothesis which would provide a dynamical setting for the gauge principle. We investigate this proposal in the framework of a general $% SO(N)$ non-abelian Nambu model (NANM), effectively providing spontaneous Lorentz symmetry breaking in terms of the corresponding Goldstone bosons. Using a non-perturbative Hamiltonian analysis, we prove that the $SO(N)$ Yang--Mills theory is equivalent to the corresponding NANM, after current conservation together with the Gauss laws are imposed as initial conditions for the latter. This equivalence is independent of any gauge fixing in the YM theory. A substantial conceptual and practical improvement in the analysis arises by choosing a particular parametrization that solves the non-linear constraint defining the NANM. This choice allows us to show that the relation between the NANM canonical variables and the corresponding ones of the YM theory, $A_{i}^{a}$ and $E^{bj}$, is given by a canonical transformation. In terms of the latter variables, the NANM Hamiltonian has the same form as the YM Hamiltonian, except that the Gauss laws do not arise as first class constraints. The dynamics of the NANM further guarantees that it is sufficient to impose them only as initial conditions, in order to recover the full equivalence. It is interesting to observe that this particular parametrization exhibits the NANM as a regular theory, thus providing a substantial simplification in the calculations.

hep-ph↗
arXiv2015

The Polymer Bouncer

Polymer Quantization (PQ) is a background independent quantization scheme that is deployed in Loop Quantum Gravity. This framework leads to a new short-distance (discretized) structure characterized by a fundamental length. In this paper we use PQ to analyze the problem of a particle bouncing on a perfectly reflecting surface under the influence of Earth's gravitational field, what we have called "\textit{The Polymer Bouncer}". In this scenario, deviations from the usual quantum effects are induced by the spatial discreteness, but not by a new short-range gravitational interaction. We solve the polymer Schrödinger equation in an analytical fashion, and we evaluate numerically the corresponding energy levels. We find that the polymer energy spectrum exhibits a negative shift compared to the obtained for the quantum bouncer. The comparison of our results with those obtained in the GRANIT experiment leads to an upper bound for the fundamental length scale, namely $λ\ll 0.6 \buildrel _{\circ} \over {\mathrm{A}}$. We find polymer corrections to the probability of transitions between levels, induced by small vibrations, together with the probability of spontaneous emission in the quadrupole approximation.

quant-ph↗
arXiv2014

The Goldstone Theorem in non-linear electrodynamics

We construct a non-linear electrodynamics arising from the spontaneous Lorentz symmetry breaking triggered by a non-zero vacuum expectation value of the electromagnetic field strength, instead of the electromagnetic potential. The expansion of the corresponding action in terms of the physical photon excitations is naturally written in terms of generalized permeabilities, in a manner similar to when the polarization is expanded in terms of the susceptibilities when studying non-linear effects in standard optics. The new version of the Goldstone theorem is investigated and implies that the lowest order permeability, been the analogous of the mass matrix in the standard case, has zero modes. These are interpreted as the corresponding Goldstone modes of the model and they are explicitly constructed for one of the two choices of vacua that the theory admits. Further iterations of the method employed to obtain such theorem yield relationships among the generalized permeabilities. Some preliminary results regarding the splitting of the two degrees of freedom of the model into Goldstone and non-Goldstone modes are presented.

hep-th↗
arXiv2013

A Five Dimensional Perspective on Many Particles in the Snyder basis of Double Special Relativity

After a brief summary of Double Special Relativity (DSR), we concentrate on a five dimensional procedure, which consistently introduce coordinates and momenta in the corresponding four-dimensional phase space, via a Hamiltonian approach. For the one particle case, the starting point is a de Sitter momentum space in five dimensions, with an additional constraint selected to recover the mass shell condition in four dimensions. Different basis of DSR can be recovered by selecting specific gauges to define the reduced four dimensional degrees of freedom. This is shown for the Snyder basis in the one particle case. We generalize the method to the many particles case and apply it again to this basis. We show that the energy and momentum of the system, given by the dynamical variables that are generators of translations in space and time and which close the Poincaré algebra, are additive magnitudes. From this it results that the rest energy (mass) of a composite object does not have an upper limit, as opposed to a single component particle which does.

hep-th↗
arXiv2013

Jaynes-Cummings model in a finite Kerr medium

We introduce a spin model which exhibits the main properties of a Kerr medium to describe an intensity dependent coupling between a two-level atom and the radiation field. We select a unitary irreducible representation of the su(2) Lie algebra such that the number of excitations of the field is bounded from above. We analyze the behavior of both the atomic and the field quantum properties and its dependence on the maximal number of excitations.

quant-ph↗
arXiv2012

Emergent electrodynamics from the Nambu model for spontaneous Lorentz symmetry breaking

After imposing the Gauss law constraint as an initial condition upon the Hilbert space of the Nambu model, in all its generic realizations, we recover QED in the corresponding non-linear gauge A_μA^μ=n^{2}M^{2}. Our result is non-perturbative in the parameter M for n^{2}\neq 0 and can be extended to the n^{2}=0 case. This shows that in the Nambu model, spontaneous Lorentz symmetry breaking dynamically generates gauge invariance, provided the Gauss law is imposed as an initial condition. In this way electrodynamics is recovered, with the photon being realized as the Nambu-Goldstone modes of the spontaneously broken symmetry, which finally turns out to be non-observable

hep-th↗
arXiv2011

Perturbative Hamiltonian constraints for higher order theories

We present a method for constructing a consistent low energy canonical formalism for higher order time-derivative theories, extending the Dirac method to include perturbative Hamiltonian constraints. We apply it to two paradigmatic examples: the Pais-Uhlenbeck oscillator and the Bernard-Duncan scalar field. We also compare the results, both at the classical and quantum level, with the ones corresponding to a direct perturbative construction applied to the exact higher order theory. This comparison highligths the soundness of the present formalism.

hep-th↗
arXiv2011

Relativistic Two-Body Coulomb-Breit Hamiltonian in an External Weak Gravitational Field

A construction of the Coulomb-Breit Hamiltonian for a pair of fermions, considered as a quantum two-body system, immersed in an arbitrary background gravitational field described by Einstein's General Relativity is presented. Working with Fermi normal coordinates for a freely falling observer in a spacetime region where there are no background sources and ignoring the gravitational back-reaction of the system, the effective Coulomb-Breit Hamiltonian is obtained starting from the S-matrix element corresponding to the one-photon exchange between the charged fermionic currents. The contributions due to retardation are considered up to order (v/c)^2 and they are subsequently written as effective operators in the relativistic quantum mechanical Hilbert space of the system. The final Hamiltonian includes effects linear in the curvature and up to order (v/c)^2.

gr-qc↗
arXiv2010

Spontaneous Lorentz symmetry breaking in nonlinear electrodynamics

We review some of the basic features and predictions of a gauge invariant spontaneous Lorentz symmetry breaking model arising from the nonzero vacuum expectation value of the electromagnetic tensor and leading to a nonlinear electrodynamics. The model is stable in the small Lorentz invariance violation approximation. The speed of light is independent of the frequency and one of the propagating modes is highly anisotropic. The bound (Delta c)/c < 10^{-32} is obtained for such anisotropy measured in perpendicular directions.

hep-ph↗
arXiv2009

An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator

Our purpose in this paper is to analyze the Pais-Uhlenbeck (PU) oscillator using complex canonical transformations. We show that starting from a Lagrangian approach we obtain a transformation that makes the extended PU oscillator, with unequal frequencies, to be equivalent to two standard second order oscillators which have the original number of degrees of freedom. Such extension is provided by adding a total time derivative to the PU Lagrangian together with a complexification of the original variables further subjected to reality conditions in order to maintain the required number of degrees of freedom. The analysis is accomplished at both the classical and quantum levels. Remarkably, at the quantum level the negative norm states are eliminated, as well as the problems of unbounded below energy and non-unitary time evolution. We illustrate the idea of our approach by eliminating the negative norm states in a complex oscillator. Next, we extend the procedure to the Pais-Uhlenbeck oscillator. The corresponding quantum propagators are calculated using Schwinger's quantum action principle. We also discuss the equal frequency case at the classical level.

math-ph↗
arXiv2009

The Photon Sector in the Quantum Myers-Pospelov Model: An improved description

The quantization of the electromagnetic sector of the Myers-Pospelov model coupled to standard fermions is studied. Our main objective is to construct an effective quantum theory that results in a genuine perturbation of QED, such that setting zero the Lorentz invariance violation (LIV) parameters will reproduce it. This is achieved by introducing an additional low energy scale $M$, together with a physically motivated prescription to take the QED limit. The prescription is successfully tested in the calculation of the electron self-energy in the one loop approximation. The LIV radiative corrections turn out to be properly scaled by very small factors for any reasonable values of the parameters, no fine-tuning problems are found at this stage and the choice for $M$ to be of the order of the electroweak symmetry breaking scale is consistent with the stringent bounds for the LIV parameters, in particular with those arising from induced dimension three operators.

hep-ph↗
arXiv2008

Quantization of the Myers-Pospelov model: the photon sector interacting with standard fermions as a perturbation of QED

We study the quantization of the electromagnetic sector of the Myers-Pospelov model coupled to standard fermions. Our main objective, based upon experimental and observational evidence, is to construct an effective theory which is a genuine perturbation of QED, such that setting zero the Lorentz invariance violation parameters will reproduce it. To this end we provide a physically motivated prescription, based on the effective character of the model, regarding the way in which the model should be constructed and how the QED limit should be approached. This amounts to the introduction of an additional coarse-graining physical energy scale $M$, under which we can trust the effective field theory formulation. The prescription is successfully tested in the calculation of the Lorentz invariance violating contributions arising from the electron self-energy. Such radiative corrections turn out to be properly scaled by very small factors for any reasonable values of the parameters and no fine-tuning problems are found. Microcausality violations are highly suppressed and occur only in a space-like region extremely close to the light-cone. The stability of the model is guaranteed by restricting to concordant frames satisfying $1-|\mathbf{v}_{max}|> 6.5\times10^{-11}$.

hep-ph↗
arXiv2008

Duality for massive spin two theories in arbitrary dimensions

Using the parent Lagrangian approach we construct a dual formulation, in the sense originally proposed by Curtright and Freund, of a massive spin two Fierz-Pauli theory in arbitrary dimensions $D$. This is achieved in terms of a mixed symmetry tensor $T_{A[B_{1}B_{2}... B_{D-2}]}$, without the need of auxiliary fields. The relation of this method with an alternative formulation based on a gauge symmetry principle proposed by Zinoviev is elucidated. We show that the latter formulation in four dimensions, with a given gauge fixing together with a definite sequence of auxiliary fields elimination via their equations of motion, leads to the parent Lagrangian already considered by West completed by a Fierz-Pauli mass term, which in turns yields the Curtright-Freund action. This motivates our generalization to arbitrary dimensions leading to the corresponding extension of the four dimensional result. We identify the transverse true degrees of freedom of the dual theory and verify that their number is in accordance with those of the massive Fierz-Pauli field.

hep-th↗
arXiv2005

Synchrotron Radiation in Lorentz-violating Electrodynamics: the Myers-Pospelov model

We develop a detailed analysis of synchrotron radiation in the effective Lorentz invariance violating (LIV) model of Myers-Pospelov, considering explicitly both the dynamics of the charge producing the radiation and the dynamics of the electromagnetic field itself. Within the radiation approximation we compute exact expressions in the LIV parameters for the electric and magnetic fields, the angular distribution of the power spectrum, the total emitted power in the m-th harmonic and the polarization. We also perform expansions of the exact results in terms of the LIV parameters to identify the dominant effects, and study the main features of the high energy limit of the spectrum. A very interesting consequence is the appearance of rather unexpected and large amplifying factors associated with the LIV effects, which go along with the usual contributions of the expansion parameter. This opens up the possibility of looking for astrophysical sources where these amplifying factors are important to further explore the constraints imposed upon the LIV parameters by synchrotron radiation measurements. We briefly sketch some phenomenological applications in the case of SNRs and GRBs.

hep-ph↗