arXiv subjects

C. A. Escobar

Publications and source records attributed to C. A. Escobar.

At least 19 recordsLinked to original sources

arXiv2026

Propagation of Laguerre-Gaussian and Bessel-Gaussian scalar beams in an effective anisotropic background

We investigate the propagation of structured scalar optical beams in an effective anisotropic background inspired by the scalar sector of the Standard-Model Extension and controlled by a single dimensionless parameter $\lambda$. The physically relevant configuration is a transverse radial director field that modifies the radial part of the Helmholtz operator while preserving axial symmetry. Starting from the Green-function representation, we cast the propagation problem as an initial-value spectral reconstruction of a prescribed finite-aperture entrance profile at $z=0$ and verify that this profile is recovered at the launch plane across the values of $\lambda$ used in the analysis, within small numerical error. We use the Laguerre--Gaussian mode $L_3$ as the representative vortex-free Laguerre case, retain $L_4$ only as a quantitative benchmark for radial-order dependence, and compare both with a Bessel--Gaussian beam of input order $m=0$. The effective anisotropy produces a systematic redistribution of radial intensity, determines whether the central peak remains dominant or is overtaken by off-axis maxima as propagation advances, and controls the radial displacement of the dominant side lobes. For the finite-aperture Bessel--Gaussian beam, the same parameter quantifies how the approximately diffraction-resistant ring structure broadens for negative $\lambda$ and compresses for positive $\lambda$ during propagation.

physics.optics↗

arXiv2026

Effective-metric formulation of Casimir energies in nonlinear scalar and electromagnetic theories

We study the Casimir effect in nonlinear field theories through the effective geometries that \mbox{govern} their linearized fluctuations. Previous analyses of Lorentz-violating scalar fields showed that a constant kinetic background modifies the parallel-plate Casimir energy by a rescaling of the plate separation and an overall determinant factor. We show that this structure is not merely a consequence of diagonalizing the reduced Green function. It follows from a common Schur-complement structure: after Fourier reduction parallel to the plates, the same reduced quadratic form controls the spectral denominator of the reduced Green function and the numerator generated by the energy-density insertion. This observation allows the Lorentz-violating scalar result to be used as an effective-metric prescription for regular fluctuation sectors arising from the linearization of nonlinear theories around constant backgrounds. In nonlinear scalar theories, the effective tensor is the Hessian of the Lagrangian evaluated on a constant-gradient background. In nonlinear electrodynamics $\mathcal{L}(\mathcal{F})$, a constant magnetic background splits the fluctuations into an ordinary Maxwell branch and an extraordinary optical branch. For this electromagnetic sector, we compute the parallel-plate Casimir energy both by direct mode summation and by applying the effective-metric formula branch by branch, finding exact agreement. The resulting energy depends on the orientation of the magnetic background relative to the plates, providing a concrete anisotropic Casimir response in a regular nonlinear electromagnetic sector.

hep-th↗

arXiv2026

Casimir effect in Pleba\'nski nonlinear electrodynamics with spontaneously Lorentz-breaking magnetic vacua

We study the Casimir effect in a class of gauge-invariant nonlinear electrodynamics models designed to admit spontaneously Lorentz-breaking magnetic vacua. The theory is formulated in the Pleba\'nski first-order representation, with a single-invariant Hamiltonian potential $\widehat V(P)$ as the fundamental nonlinear object. In this formulation, nontrivial magnetic vacua are stationary points of the reduced effective Hamiltonian. The symmetry-breaking condition is controlled by $\Sm(P)\equiv\widehat V_P(P)+2P\widehat V_{PP}(P)$, which also controls the rank of the longitudinal magnetic response and of the Hamiltonian constraint structure. Taking this Lorentz-breaking nonlinear electrodynamics as the model under study, we analyze how the distinction between the regular constant-rank sector and the degenerate magnetic vacuum enters the parallel-plate Casimir spectrum. Linearization around a regular magnetic background $\bar P$, with $\Sm(\bar P)\neq0$, yields an ordinary Maxwell-like branch and an extraordinary anisotropic branch controlled by $\alpha(\bar P)=\widehat V_P(\bar P)/\Sm(\bar P)$. We compute the regularized Casimir energy for magnetic backgrounds perpendicular and parallel to the plates. In the regular-sector limit $\bar P\to P_\star$, with $\Sm(P_\star)=0$, the extraordinary branch becomes singular and the parallel-configuration energy diverges. This divergence is not an infinite physical Casimir force; it signals that the regular two-branch optical description cannot be continued uniformly to the rank-changing magnetic vacuum. Direct analysis on the degenerate surface shows that the extraordinary branch does not survive as an independent propagating mode for generic momenta. Thus, quantizing the regular theory and then taking $\Sm\to0$ is not equivalent to imposing $\Sm(P_\star)=0$ before quantization.

hep-th↗

arXiv2026

Constitutive Origin of Hamiltonian Degeneracy in Nonlinear Electrodynamics with Spontaneous Lorentz Symmetry Breaking

In Pleba\'nski nonlinear electrodynamics with spontaneous Lorentz symmetry breaking, nontrivial magnetic backgrounds are selected by stationary points of an effective Hamiltonian. Previous branchwise Hamiltonian analyses showed that this same stationarity requirement coincides with the vanishing of the determinant of the Poisson-bracket matrix among the second-class constraints, but the structural origin of this coincidence was not manifest. We show that it follows from the constitutive origin of the theory. The structural potential $V(P,Q)$ generates the electromagnetic constitutive relations, while the effective Hamiltonian for magnetic vacua is the complementary energy associated with the magnetic response at fixed $\Dvec$. Moreover, because the first-order constitutive relation enters the Dirac constraint structure, the magnetic constitutive Jacobian appears as a local block of the Poisson-bracket matrix among the second-class constraints. This complementary-energy structure implies that every nontrivial magnetic stationary point lies on a surface where the linearized map $\delta\Hvec\mapsto\delta\Bvec$, at fixed $\Dvec$, loses rank. We use this interpretation to formulate the reduced linearized theory at the vacuum, discuss the removal of the radial mode in the vacuum-restricted theory, and clarify why electric and mixed stationary branches are obstructed in single-invariant models.

hep-th↗

arXiv2026

Stable Magnetic Lorentz-Violating Vacua in Gauge-Invariant Nonlinear Electrodynamics

We investigate gauge-invariant nonlinear electrodynamics in the Pleba\'nski first-order Hamiltonian formulation, taking the single-invariant potential $\hat V(P)$ as the primary object. Our focus is on the existence of stable Lorentz-violating magnetic vacua. For three explicit two-parameter models -- rational asymmetric, logarithmic, and exponential -- we determine the regions of parameter space in which nontrivial constant electromagnetic vacua are compatible with an effective Hamiltonian bounded from below and a positive-semidefinite Hessian. In all three cases, physically admissible Lorentz-violating vacua are realized in the magnetic branch. We further discuss the electric branch and several additional one-parameter models, illustrating that Hamiltonian boundedness by itself does not ensure spontaneous Lorentz symmetry breaking. We also comment on how the symmetry-breaking conditions are related to known strong-field causality criteria.

hep-th↗

arXiv2025

Casimir effect between semitransparent mirrors in a Lorentz-violating background

We investigate the Casimir effect for a massless scalar field confined between two parallel semitransparent mirrors in a vacuum modified by spontaneous Lorentz symmetry breaking. Using Green's function techniques and a point-splitting evaluation of the stress-energy tensor, we compute the vacuum expectation value of the energy density $T_{00}$. After a suitable renormalization, the Casimir energy is obtained as the difference between the vacuum configurations with and without the mirrors. We derive closed-form expressions that generalize the conventional result by simultaneously incorporating the mirror transparency and the Lorentz-violating background. Our analysis shows that the effect of transparency and Lorentz violation consists of a multiplicative correction and an effective rescaling of the plate separation, thereby modifying the functional dependence of the energy on the distance. Beyond the formal derivation, we discuss possible physical realizations of this framework, emphasizing anisotropic media such as nematic liquid crystals (e.g., 5CB), where uniaxial dielectric properties could emulate the Lorentz-violating background. Numerical estimates for such systems illustrate the phenomenological impact of our results and open the possibility of constraining Lorentz-violating coefficients through precision Casimir measurements.

hep-th↗

arXiv2022

Optical scalar beam propagation in nontrivial spacetime backgrounds

We study the propagation of structured optical scalar beams in a spacetime background parameterized by a second-rank symmetric tensor. An analytic expression for the Green's function in a cylindrical coordinate system is obtained for particular choices of such a tensor. This facilitates the numerical exploration of the propagation of apertured Gaussian beams in this nontrivial background. Unusual focusing properties are found along with a decrease in the Gouy phase compared to that in standard vacuum. In the case of apertured Bessel beams, the medium allows to overcome finite aperture effects so that the corresponding diffraction length is increased; besides, the central spot of a zero order Bessel concentrates an increased fraction of the energy of the beam. Multiple scenarios beyond an electromagnetic field in the presence of an anisotropic medium could support the results reported here. They include a bosonic field in a weak gravitational field or a nontrivial spacetime background arising from Lorentz symmetry breaking. In particular, our results could illustrate how optically transparent multiferroic materials offer unprecedented opportunities to tailor structured beam propagation, as well as to simulate nontrivial spacetime backgrounds.

physics.optics↗

arXiv2022

Spontaneous symmetry breaking in models with second-class constraints

In this work the spontaneous symmetry breaking in certain nonlinear theories with second-class constraints is explored. Using the Dirac's method we perform an analysis of the constraints and the counting of the degrees of freedom. The corresponding effective Hamiltonian is constructed explicitly. It is shown that on the surfaces where the effective Hamiltonian takes critical values the symplectic structure becomes degenerate. In particular, we demonstrate that under the condition of spontaneous symmetry breaking, which implies non trivial vacuum surfaces, second-class constraints behave as first-class ones on certain regions of the phase space, leading to undefined Dirac's brackets and to the modification of the number of degrees of freedom. As a physical consequence, these models can suffer from certain pathologies such as the existence of modes with an acausal propagation. Concrete examples where this phenomena occurs are described in detail.

hep-th↗

arXiv2022

Testing the scalar sector of the Standard-Model Extension with neutron gravity experiments

In the present study we analyse, within the scalar sector of the Standard-Model Extension (SME) framework, the influence of a spontaneous Lorentz symmetry breaking on gravitational quantum states of ultracold neutrons. The model is framed according to the laboratory conditions of the recent high-sensitivity GRANIT and $q$Bounce experiments. The high-precision data achieved in such experiments allow us to set bounds on the symmetry breaking parameters of the model. The effective Hamiltonian governing the neutron's motion along the axis of free fall is derived explicitly. It describes a particle in a gravitational field with an effective gravitational constant controlled non-trivially by the Lorentz-violating parameters. In particular, using the exact wave functions and the energy spectrum, we evaluate both the heights associated with the quantum states and the transition frequencies between neighborhoring quantum states. By comparing our theoretical results with those reported in the GRANIT and the $q$Bounce experiments, upper bounds on the Lorentz-violating parameters are determined. We also consider for the first time the gravity-induced interference pattern in a COW-type experiment to test Lorenz-invariance. In this case, an upper bound for the parameters is established as well.

hep-ph↗

arXiv2021

Hamiltonian analysis of ModMax nonlinear electrodynamics in the first order formalism

In this work we study the so-called ModMax nonlinear electrodynamics, which is a novel model designed to preserve duality rotations and conformal transformations, such as the Maxwell's equations do. This model allows to study diverse gravitational phenomena when is coupled to General Relativity, in particular charged black holes and gravitational waves. In the present work we focus in the dynamics and Hamiltonian analysis of the model. Specifically, we analyze the propagation of the discontinuities of the field and obtain the corresponding dispersion relations. To perform the Hamiltonian analysis we adopt the first order formalism develop by Plebański and follow the Dirac method for theories with constraints. We derive the effective Hamiltonian, classify all the constraints and identify the degrees of freedom. We prove that the effective Hamiltonian is strictly bounded from below and investigate the existence of non trivial minima.

hep-th↗

arXiv2020

On the four-body problem in the Born-Oppenheimer approximation

The quantum problem of four particles in $\mathbb{R}^d$ ($d\geq 3$), with arbitrary masses $m_1,m_2,m_3$ and $m_4$, interacting through an harmonic oscillator potential is considered. This model allows exact solvability and a critical analysis of the Born-Oppenheimer approximation. The study is restricted to the ground state level. We pay special attention to the case of two equally heavy masses $m_1=m_2=M$ and two light particles $m_3=m_4=m$. It is shown that the sum of the first two terms of the Puiseux series, in powers of the dimensionless parameter $σ=\frac{m}{M}$, of the exact phase $Φ$ of the wave function $ψ_0=e^{-Φ}$ and the corresponding ground state energy $E_0$, coincide exactly with the values obtained in the Born-Oppenheimer approximation. A physically relevant rough model of the $H_2$ molecule and of the chemical compound $H_2O_2$ (Hydrogen peroxide) is described in detail. The generalization to an arbitrary number of particles $n$, with $d$ degrees of freedom ($d\geq n-1$), interacting through an harmonic oscillator potential is briefly discussed as well.

quant-ph↗

arXiv2020

Lorentz violating scalar Casimir effect for a $D$-dimensional sphere

We investigate the Casimir effect, due to the confinement of a scalar field in a $D$-dimensional sphere, with Lorentz symmetry breaking. The Lorentz-violating part of the theory is described by the term $λ(u \cdot \partial ϕ) ^{2}$, where the parameter $λ$ and the background vector $u^μ$ codify the breakdown of Lorentz symmetry. We compute, as a function of $D$, the Casimir stress by using Green's function techniques for two specific choices of the vector $u ^μ$. In the timelike case, $u ^μ = (1,0,...,0)$, the Casimir stress can be factorized as the product of the Lorentz invariant result times the factor $(1 + λ) ^{-1/2}$. For the radial spacelike case, $u ^μ = (0,1,0,...,0)$, we obtain an analytical expression for the Casimir stress which nevertheless does not admit a factorization in terms of the Lorentz invariant result. For the radial spacelike case we find that there exists a critical value $λ_{c} = λ_{c} (D)$ at which the Casimir stress transits from a repulsive behavior to an attractive one for any $D> 2$. The physically relevant case $D = 3$ is analyzed in detail where the critical value $λ_{c}|_{\small D=3} = 0.0025$ was found. As in the Lorentz symmetric case, the force maintains the divergent behavior at positive even integer values of $D$.

hep-th↗

arXiv2020

A non-perturbative approach to the scalar Casimir effect with Lorentz symmetry violation

We determine the effect of Lorentz invariance violation in the vacuum energy and stress between two parallel plates separated by a distance $L$, in the presence of a massive real scalar field. We parametrize the Lorentz-violation in terms of a symmetric tensor $h^{\,μν}$ that represents a constant background. Through the Green's function method, we obtain the global Casimir energy, the Casimir force between the plates and the energy density in a closed analytical form without resorting to perturbative methods. With regards to the pressure, we find that $\mathcal{F}_c(L)=\mathcal{F}_0(\tilde{L})/\sqrt{-{\rm det}\, h^{\,μν}}$, where $\mathcal{F}_0$ is the Lorentz-invariant expression, and $\tilde{L}$ is the plate separation rescaled by the component of $h^{\,μν}$ normal to the plates, $\tilde{L}=L/\sqrt{-h^{nn}}$. We also analyze the Casimir stress including finite-temperature corrections. The local behavior of the Casimir energy density is also discussed.

hep-th↗

arXiv2020

Casimir effect in Lorentz-violating scalar field theory: a local approach

We study the Casimir effect in the classical geometry of two parallel conductive plates, separated by a distance $L$, for a Lorentz-breaking extension of the scalar field theory. The Lorentz-violating part of the theory is characterized by the term $λ\left( u \cdot \partial ϕ\right )^{2}$, where the parameter $λ$ and the background four-vector $u ^μ$ codify Lorentz symmetry violation. We use Green's function techniques to study the local behavior of the vacuum stress-energy tensor in the region between the plates. Closed analytical expressions are obtained for the Casimir energy and pressure. We show that the energy density $\mathcal{E}_{C}$ (and hence the pressure) can be expressed in terms of the Lorentz-invariant energy density $\mathcal{E}_{0}$ as follows \begin{align} \mathcal{E}_{C} (L) = \sqrt{\frac{1-λu_{n} ^{2}}{1 + λu ^{2}}} \mathcal{E}_{0} (\tilde{L}) , \notag \end{align} where $\tilde{L} = L / \sqrt{1-λu_{n} ^{2}}$ is a rescaled plate-to-plate separation and $u_{n}$ is the component of $\vec{u}$ along the normal to the plates. As usual, divergences of the local Casimir energy do not contribute to the pressure.

hep-th↗

arXiv2020

Nonlinear vacuum electrodynamics and spontaneous breaking of Lorentz symmetry

We study nonlinear vacuum electrodynamics in a first-order formulation proposed by Plebański. By applying a Dirac constraint analysis, we derive an effective Hamiltonian, together with the equations of motion. We show that there exists a large class of potentials for which the effective Hamiltonian is bounded from below, while at the same time possessing stationary points in which the field strength acquires a nonzero vacuum expectation value. The associated spontaneous breaking of Lorentz symmetry can in principle be detected by coupling the model to a suitable external current, or to gravity. We show that the possible vacua can be classified in four classes. We study some of their properties, using explicit examples for illustration.

hep-th↗

arXiv2020

Degenerate behavior in nonlinear vacuum electrodynamics

We study nonlinear vacuum electrodynamics in the first-order formulation proposed by Plebański. We analyze in detail the equations of motion, and identify conditions for which a singularity can occur for the time derivative of one of the field components. The resulting degenerate behavior can give rise to a shock wave with a reduction of the local number of degrees of freedom. We use an example model to illustrate the occurrence of superluminal propagation for field values approaching the singularity.

hep-ph↗

arXiv2020

Casimir effect in polymer scalar field theory

In this paper, we study the Casimir effect in the classical geometry of two parallel conducting plates, separated by a distance $L$, due to the presence of a minimal length $λ$ arising from a background independent (polymer) quantization scheme. To this end, we polymer-quantize the classical Klein-Gordon Hamiltonian for a massive scalar field confined between the plates and obtain the energy spectrum. The minimal length scale of the theory introduces a natural cutoff for the momenta in the plane parallel to the plates and a maximum number of discrete modes between the plates. The zero-point energy is calculated by summing over the modes, and by assuming $λ\ll L$, we expressed it as an expansion in powers of $1/N$, being $N=L/ λ$ the number of points between the plates. Closed analytical expressions are obtained for the Casimir energy in the cases of small and large scalar mass limits.

hep-ph↗

arXiv2019

Gravitational Searches for Lorentz Violation with Ultracold Neutrons

We investigate the consequences of Lorentz violation (as expressed within the gravity sector of the Standard-Model Extension) for gravitational quantum states of ultracold neutrons (UCNs). Since our main aim is to compare our theoretical results with the recent high-sensitivity GRANIT experiment, we frame this work according to the laboratory conditions under which it was carried out. This offers the possibility of testing Lorentz invariance by experiments using UCNs. Thus we consider the nonrelativistic Hamiltonian describing the quantum mechanics of an unpolarized neutron's beam in presence of a weak-gravity field, and the latter is described by a post-Newtonian expansion of the metric up to order $O (2)$ and linear in the Lorentz-violating coefficients $\bar{s} ^{μν}$. Using a semi-classical wave packet, which is appropriate to describe an intense beam of UCNs, we derive the effective Hamiltonian describing the neutron's motion along the axis of free fall and then we compute the Lorentz-violating shifts on the energy levels. The comparison of our results with those obtained in the GRANIT experiment leads to an upper bound for a particular combination of the Lorentz-violating coefficients.

hep-ph↗