arXiv subjects

R. Casana

Publications and source records attributed to R. Casana.

At least 19 recordsLinked to original sources

arXiv2026

Exact BPS double-kinks in generalized $ϕ^4$, $ϕ^6$ and sine-Gordon models

We consider a $(1+1)$-dimensional theory with a single real scalar field $ϕ$ whose kinematics is modified by a generalizing function $f(ϕ)$. After briefly reviewing its Bogomol'nyi-Prasad-Sommerfield (BPS) structure, we focus on a particular $f(ϕ)$ to obtain analytic BPS double-kink solutions in three different models governed by the $ϕ^4$, $ϕ^6$, and sine-Gordon superpotentials. In all cases, the resulting double-kinks approach the boundaries by following an exponential decay, with the generalizing function controlling its dependence on $x$ and mass. We also calculate the BPS bound explicitly and study how the double kinks behave near the origin. The energy distribution of the novel BPS states engenders symmetric two-lump profiles for the $ϕ^4$ and sine-Gordon superpotentials. Whereas, for the $ϕ^6$ superpotential, the BPS energy profiles form asymmetric two-lumps.

hep-th↗

arXiv2024

Kinks and double-kinks in generalized $ϕ^{4}$-and $ϕ^{8}$-models

Examining the $ϕ^{4}$ and $ϕ^{8}$ models within a two-dimensional framework in the flat spacetime and embracing a theory with unconventional kinetic terms, one investigates the emergence of kinks/antikinks and double-kinks/antikinks. We devote our study to obtaining the field configurations with minimal energy, i.e., solutions possessing a Bogomol'nyi-Prasad-Sommerfield's bound. Next, to accomplish our goal, we adopt non-polynomial generalizing functions, namely, hyperbolic sine and cosine functions: the first produce BPS potentials exhibiting a minimum at $ϕ=0$, facilitating the emergence of genuine double-kink-type configurations. Conversely, the second promotes the rise of kink-type solutions.

hep-th↗

arXiv2024

Restricted baby Skyrme-Maxwell theory in a magnetic medium: BPS configurations and some properties

We study the existence of BPS configurations in a restricted baby Skyrme-Maxwell enlarged via the inclusion of a nontrivial magnetic permeability. In order to attain such a goal, we use the Bogomol'nyi-Prasad-Sommerfield prescription, which allows us to obtain the lower bound for the energy and the BPS equations whose [electrically neutral] solutions saturate that bound. During the energy minimization procedure, we find a differential constraint which involves the self-dual potential, the superpotential itself and also the magnetic permeability. In order to solve the BPS system, we focus our attention on those solutions with rotational symmetry. For that, we fix the magnetic permeability and select two BPS potentials which exhibit a similar behavior near to the vacuum. We depict the resulting profiles and proceed to an analytical description of the properties of the BPS magnetic field. Furthermore, we consider some essential aspects of our model, such as the conditions for the overall existence of the BPS solutions, and how the permeability affects the magnetic flux. Finally, we present a family of exact BPS solutions.

hep-th↗

arXiv2022

BPS solitons with internal structures in a restricted baby Skyrme-Maxwell theory in a magnetic medium

We consider a restricted baby Skyrme-Maxwell scenario enlarged via the inclusion of a nontrivial magnetic permeability. We then proceed with the minimization of its total energy by means of the Bogomol'nyi-Prasad-Sommerfield (BPS) prescription, from which we get that the self-dual potential now depends on the magnetic permeability itself. As a result, we obtain not only the lower bound for the energy, but also the self-dual equations whose solutions saturate that bound. In such a context, we focus our attention on those time-independent gauged skyrmions with radial symmetry and no electric charge. We solve the effective self-dual equations numerically for different choices of the magnetic permeability, from which we obtain BPS magnetic fields whose internal structures form concentric rings. We also explain analytically the formation of these structures based on the values of a single real parameter which characterizes the respective magnetic permeabilities.

hep-th↗

arXiv2022

Self-dual $CP(2)$ vortex-like solitons in the presence of magnetic impurities

We investigate the existence of vortex configurations in two gauged-$CP(2)$ models extended via the inclusion of magnetic impurities. In particular, we consider both the Maxwell-$CP(2)$ and the Chern-Simons-$CP(2)$ enlarged scenarios, separately. We choose a $CP(2)$-field configuration with a null topological charge not only in the simplest (free) case, but also when coupled to an Abelian gauge field. The implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism shows that the effective models for such a configuration possess a self-dual structure which looks like those inherent to the gauged sigma models. Therefore, when the $CP(2)$ field is coupled to the Maxwell term, the corresponding total energy possesses both a well-defined Bogomol'nyi bound and a quantized magnetic flux. Further, when the $CP(2)$ scenario is gauged with the Chern-Simons action, the total electric charge is verified to be proportional to the quantized magnetic flux. In addition, the analysis verifies that the magnetic impurity contributes to the BPS potentials and appears in both the models' BPS equations. Next, we introduce a Gaussian type impurity and solve the self-dual equations via a finite-difference scheme. The resulting solutions present a nonmonotonic behavior that flips both the magnetic and electric fields. Finally, we discuss the topologically trivial solutions in the limit for which the impurity becomes a Dirac $δ$-function.

hep-th↗

arXiv2020

Exact Kerr-like solution and its shadow in a gravity model with spontaneous Lorentz symmetry breaking

We obtain an exact Kerr-like black hole solution by solving the corresponding gravitational field equations in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking. In order to study the effects of this breaking, we consider the black hole shadow and find that the radial of the unstable spherical orbit on the equatorial plane $r_c$ decreases with the Lorentz breaking constant $\ell>0$, and increases with $\ell<0$. These shifts are similar to those of Einstein-aether black hole. The effect of the LV parameter on the black hole shadow is that it accelerates the appearance of shadow distortion, and could be detected by the new generation of gravitational antennas.

gr-qc↗

arXiv2019

Topological first-order solitons in a gauged $CP(2)$ model with the Maxwell-Chern-Simons action

We verify the existence of radially symmetric first-order solitons in a gauged $CP(2)$ scenario in which the dynamics of the Abelian gauge field is controlled by the Maxwell-Chern-Simons action. We implement the standard Bogomol'nyi-Prasad-Sommerfield (BPS) formalism, from which we obtain a well-defined lower bound for the corresponding energy (i.e. the Bogomol'nyi bound) and the first-order equations saturating it. We solve these first-order equations numerically by means of the finite-difference scheme, therefore obtaining regular solutions of the effective model, their energy being quantized according the winding number rotulating the final configurations, as expected. We depict the numerical solutions, whilst commenting on the main properties they engender.

hep-th↗

arXiv2019

First-order solitons with internal structures in an extended Maxwell-$CP(2)$ model

We study a Maxwell-$CP(2)$ model coupled to a real scalar field through a dielectric function multiplying the Maxwell term. In such a context, we look for first-order rotationally symmetric solitons by means of the Bogomol'nyi algorithm, i.e. by minimizing the total energy of the effective model. We perform our investigation by choosing an explicit form of the dielectric function. The numerical solutions show regular vortices whose shapes dramatically differ from their canonical counterparts. We can understood such differences as characterizing the existence of an internal structure.

hep-th↗

arXiv2018

Nontopological first-order vortices in a gauged $CP(2)$ theory endowed with the Chern-Simons action

We study a gauged $CP(2)$ scenario model with the Chern-Simons term, focusing our attention on those time-independent radially symmetric configurations with nontopological profile. We proceed the minimization of the effective energy in order to introduce the corresponding first-order framework, from which we define a legitimate self-dual scenario. We solve the resulting first-order equations numerically by means of the finite-difference scheme, from which we depict the nontopological solutions. We also identify a special kind of solutions which can be partially described by an analytical treatment.

hep-th↗

arXiv2018

Lorentz-violating nonminimal coupling contributions in mesonic hydrogen atoms and generation of photon higher-order derivative terms

We have studied the contributions of Lorentz-violating CPT-odd and CPT-even nonminimal couplings to the energy spectrum of the mesonic hydrogen and the higher-order radiative corrections to the effective action of the photon sector of a Lorentz-violating version of the scalar electrodynamics. By considering the complex scalar field describes charged mesons (pion or kaon), the non-relativistic limit of the model allows to attain upper-bounds by analyzing its contribution to the mesonic hydrogen energy. By using the experimental data for the $1S$ strong correction shift and the pure QED transitions $4P \rightarrow 3P$, the best upper-bound for the CPT-odd coupling is $<10^{-12}\text{eV}^{-1}$ and for the CPT-even one is $<10^{-16}\text{eV}^{-2}$. Besides, the CPT-odd radiative correction to the photon action is a dimension-5 operator which looks like a higher-order Carroll-Field-Jackiw term. The CPT-even radiative contribution to the photon effective action is a dimension-6 operator which would be a higher-order derivative version of the minimal CPT-even term of the standard model extension.

hep-ph↗

arXiv2018

First-order vortices in a gauged $CP(2)$ model with a Chern-Simons term

We consider a gauged $CP(2)$ theory in the presence of the Chern-Simons action, focusing our attention on those time-independent solutions possessing radial symmetry. In this context, we develop a coherent first-order framework via the Bogomol'nyi prescription, from which we obtain the corresponding energy lower-bound and the first-order equations the model supports. We use these expressions to introduce effective BPS scenarios, solving the resulting first-order equations by means of the finite-difference scheme, this way attaining genuine field solutions engendering topological configurations. We depict the new profiles, commenting on the main properties they engender.

hep-th↗

arXiv2017

An exact Schwarzschild-like solution in a bumblebee gravity model

We have obtained an exact vacuum solution from a gravity sector contained in the minimal standard-model extension. The theoretical model assumes a Riemann spacetime coupled to the bumblebee field which is responsible for the spontaneous Lorentz symmetry breaking. The solution achieved in a static and spherically symmetric scenario establishes a Schwarzschild-like black hole. In order to study the effects of the spontaneous Lorentz symmetry breaking, we have investigated some classics tests including the advance of the perihelion, bending of light and Shapiro's time-delay. Furthermore, we have computed some upper-bounds from which the most stringent one attains a sensitivity at the $10^{-13}$ level.

gr-qc↗

arXiv2017

Nontopological first-order vortices in a gauged $CP(2)$ model with a dielectric function

We consider nontopological first-order solitons arising from a gauged $CP(2)$ model in the presence of the Maxwell term multiplied by a nontrivial dielectric function. We implement the corresponding first-order scenario by proceeding the minimization of the total energy, this way introducing the corresponding energy lower-bound, such a construction being only possible due to a differential constraint including the dielectric function itself and the self-interacting potential defining the model. We saturate the aforementioned bound by focusing our attention on those solutions fulfilling a particular set of two coupled first-order differential equations. In the sequel, in order to solve these equations, we choose the dielectric function explicitly, also calculating the corresponding self-interacting potential. We impose appropriate boundary conditions supporting nontopological solitons, from which we verify that the energy of final structures is proportional to the magnetic flux they engender, both quantities being not quantized, as expected. We depict the new numerical solutions, whilst commenting on the main properties they present.

hep-th↗

arXiv2017

Topological first-order vortices in a gauged CP(2) model

We study time-independent radially symmetric first-order solitons in a CP(2) model interacting with an Abelian gauge field whose dynamics is controlled by the usual Maxwell term. In this sense, we develop a consistent first-order framework verifying the existence of a well-defined lower bound for the corresponding energy. We saturate such a lower bound by focusing on those solutions satisfying a particular set of coupled first-order differential equations. We solve these equations numerically using appropriate boundary conditions giving rise to regular structures possessing finite-energy. We also comment the main features these configurations exhibit. Moreover, we highlight that, despite the different solutions we consider for an auxiliary function $β\left( r\right) $ labeling the model (therefore splitting our investigation in two a priori distinct branches), all resulting scenarios engender the very same phenomenology, being physically equivalent.

hep-th↗

arXiv2016

Self-dual configurations in Abelian Higgs models with $k$-generalized gauge field dynamics

We have shown the existence of self-dual solutions in new Maxwell-Higgs scenarios where the gauge field possesses a $k$-generalized dynamic, i.e., the kinetic term of gauge field is a highly nonlinear function of $F_{μν}F^{μν}$. We have implemented our proposal by means of a $k$-generalized model displaying the spontaneous symmetry breaking phenomenon. We implement consistently the Bogomol'nyi-Prasad-Sommerfield formalism providing highly nonlinear self-dual equations whose solutions are electrically neutral possessing total energy proportional to the magnetic flux. Among the infinite set of possible configurations, we have found families of $k$-generalized models whose self-dual equations have a form mathematically similar to the ones arising in the Maxwell-Higgs or Chern-Simons-Higgs models. Furthermore, we have verified that our proposal also supports infinite twinlike models with $|ϕ|^4$-potential or $|ϕ|^6$-potential. With the aim to show explicitly that the BPS equations are able to provide well-behaved configurations, we have considered a test model in order to study axially symmetric vortices. By depending of the self-dual potential, we have shown that the $k$-generalized model is able to produce solutions that for long distances have a exponential decay (as Abrikosov-Nielsen-Olesen vortices) or have a power-law decay (characterizing delocalized vortices). In all cases, we observe that the generalization modifies the vortex core size, the magnetic field amplitude and the bosonic masses but the total energy remains proportional to the quantized magnetic flux.

hep-th↗

arXiv2016

Gupta-Bleuler's quantization of a parity-odd CPT-even electrodynamics of the standard model extension

{Following a successfully quantization scheme previously }{{% developed {\ in Ref. \cite{GUPTAEVEN} for a}} parity-even {gauge sector} {of the SME, we}} have established the Gupta-Bleuler {% quantization {of a} {\ parity-odd} and CPT-even }electrodynamics of {the }standard model extension (SME) {without recoursing to a small photon mass regulator}. {Keeping the photons massless,} {% {we have adopted the gauge fixing condition:}} $G(A_{μ})=(\partial _{0}+κ^{0j}\partial _{j}) (A_{0}+κ^{0k}A_{k})+\partial _{i}A^{i}$% . The{\ four} polarization vectors of the gauge field are {% exactly} determined by solving an eigenvalue problem,{\ exhibiting birefringent second order contributions in the Lorentz-violating parameters}% . They allow to express the Hamiltonian in terms of annihilation and creation operators whose positivity is guaranteed by imposing a weak Gupta-Bleuler constraint, defining the physical states. Consequently, we compute the field commutation relation which has been expressed in terms of Pauli-Jordan functions modified by Lorentz violation whose light-cone structures have allowed to analyze the microcausality issue.

hep-th↗

arXiv2016

Self-dual solitons in a $CPT$-odd and Lorentz-violating gauged $O(3)$ sigma model

We have performed a complete study of self-dual configurations in a $CPT$-odd and Lorentz-violating gauged $O(3)$ nonlinear sigma model. We have consistently implemented the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism and obtained the correspondent differential first-order equations describing electrically charged self-dual configurations. The total energy and magnetic flux of the vortices, besides being proportional to the winding number, also depend explicitly on the Lorentz-violating coefficients belonging to the sigma sector. The total electrical charge is proportional to the magnetic flux such as it occurs in Chern-Simons models. The Lorentz violation in the sigma sector allows one to interpolate between Lorentz-violating versions of some sigma models: the gauged $O(3)$ sigma model and the Maxwell-Chern-Simons $O(3)$ sigma model. The Lorentz violation enhances the amplitude of the magnetic field and BPS energy density near the origin, augmenting the deviation in relation to the solutions deprived of Lorentz violation.

hep-th↗

arXiv2016

Electromagnetic Field in Lyra Manifold: A First Order Approach

We discuss the coupling of the electromagnetic field with a curved and torsioned Lyra manifold using the Duffin-Kemmer-Petiau theory. We will show how to obtain the equations of motion and energy-momentum and spin density tensors by means of the Schwinger Variational Principle.

gr-qc↗