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We explore how higher-order derivative terms impact a physical observable within a Lorentz-Symmetry Violating (LSV) framework. We specifically examine Podolsky electrodynamics coupled with the Carroll-Field-Jackiw model (CFJ). Our analysis shows how vacuum and wave propagation are affected by the interaction of LSV parameters with properties of Podolsky electrodynamics. In this scenario, our results indicate that the new electromagnetic vacuum is birefringent, dichroic, and dispersive. We also point out that the higher-derivative term in the presence of the CFJ space-time anisotropy induces an oscillation mechanism between the photon, which acquires a non-vanishing mass, and the massive vector mode carried by the higher derivative. We then investigate the electromagnetic radiation emitted by a moving charged particle interacting with this new medium. Our analysis reveals that the refractive vacuum through which the charged particle travels influences the electromagnetic radiation, leading to a profile similar to the Cherenkov effect., Comment: 13 pages

In this paper, we endeavour to build up a non-Abelian formulation to describe the self-interactions of massless vector bosons in the context of Loop Quantum Gravity (LQG). To accomplish this task, we start off from the modified Maxwell equations with the inclusion of LQG corrections and its corresponding local $U(1)$ gauge invariance. LQG effects in the electromagnetic interactions have significant importance, as they might be adopted to describe the flight time of cosmic photons coming from very high-energy explosions in the Universe, such as events of Gamma-Ray Bursts (GRBs). These photons have energy-dependent speeds, indicating that the velocity of light in the vacuum is not constant. To carry out the extension from the Abelian to the non-Abelian scenario, we shall follow the so-called Noether current procedure, which consists in recurrently introducing self-interactions into an initially free action for vector bosons by coupling the latter to the conserved currents of a global symmetry present in the action of departure. In the end of the non-Abelianization process, the initial global symmetry naturally becomes local. Once the Yang-Mills system includes LQG correction terms, it becomes possible to analyze how quantum-gravity induced contributions show up in both the electroweak and the QCD sectors of the Standard Model, providing a set-up for phenomenological investigations that may bring about new elements to discuss Physics beyond the Standard-Model., Comment: 7 pages

We set a generalised non-linear Lagrangian, encompassing Born-Infeld and Heisenberg-Euler theories among others. The Lagrangian reduces to the Maxwell Lagrangian at lowest order. The field is composed by a propagating light-wave in an electro-magnetic background. The wave exhibits energy variation when the background is space-time dependent. In the photon description, this implies a red or a blue shift, like what we obtained in massive theories, as the de Broglie-Proca or effective mass theories as the Standard-Model Extension under Lorentz symmetry violation. The two results, photon energy-conservation and the frequency shift are instead new for non-linear electro-magnetism. We conclude by discussing how these static frequency shifts when added to the expansion red shift allow new interpretations in cosmology or for atomic spectra. We finally consider the consequences on the Poincar\'e symmetry.

This paper focuses on additional inspections concerning the fermionic sector of the Standard Model Extension (SME). In this context, our main effort in this contribution is to investigate effects of Lorentz-symmetry violation (LSV) on the Klein Paradox, the Zitterbewegung and its phenomenology in connection to Condensed Matter Physics, Atomic Physics, and Astrophysics. Finally, we discuss a particular realization of LSV in the Dirac equation, considering an asymmetry between space and time due to a scale factor present in the linear momentum of the fermion, but which does not touch its time derivative. We go further and extend the implications of this asymmetry in the situation the scale factor becomes space-time dependent to compute its influence on the kinematics of the Compton effect with the extended dispersion relation for the fermion that scatters the photon., Comment: 15 pages, 2 figures

The efforts in this contribution consist in reassessing a modified Dirac equation that incorporates a $\gamma^0 \gamma_5$-Lorentz-symmetry violating (LSV) term induced as a Loop Quantum Gravity (LQG) effect. Originally, this equation has been applied and considered as a good scenario for describing a number of investigations on the flight time of cosmic neutrinos, which suggests that the speed, in vacuum, in connection with the geometry that describes a granular space-time, takes the energy-dependent form, e.g., $v(E) =1 \pm E/E_{\textrm{LSV}}$, with $E_{\textrm{LSV}} \approx 6,5 \times 10^{17}$ GeV for neutrinos. Once LQG provides a viable way to understand this picture consistently, we pursue an analysis of this effective Dirac equation to inspect some of its properties. These include: the derivation of the modified fermionic propagator, attainment of the Gordon decomposition of the vector current with minimal electromagnetic coupling to obtain information on the form factors, examination of the non-relativistic limit of the equation, evaluation of the spin- and velocity-dependent corrections to the Coulomb potential due to LQG effects, and the modified Hamiltonian in the low-relativistic regime. The study of the form factors may open up paths to set up bounds on the LQG parameters from the precision measurements of electromagnetic attributes of the charged leptons, such as their respective electric and magnetic dipole moments., Comment: 12 pages, 2 figures

This contribution sets out to pursue the investigation of a supersymmetric electrodynamics model with Lorentz-symmetry violation (LSV) manifested by a space-time unbalance in the propagation of the fermionic charged matter. Despite violation of Lorentz symmetry, the supersymmetry algebra is kept untouched. A superspace approach is then adopted to build up an $\mathcal{N}=1$-supersymmetric Abelian gauge theory in presence of a Lorentz-violating background supermultiplet that accommodates the space-time asymmetry parameter of the charged matter. It is described, in this scenario, how the particular Lorentz-symmetry breaking, brought about by the fermionic matter, affects its (matter) scalar partners and the photon/photino that minimally couple to charged matter. From the (modified) Dirac, Klein-Gordon and Maxwell field equations, the corresponding dispersion relations are worked out to inspect and discuss the physical effects of the LSV Majorana fermion condensates that naturally emerge from the background supermultiplet. Finally, efforts are targeted to investigate the Gordon decomposition of the charged lepton electromagnetic current. This is carried out by iterating the (fermion and scalar) matter field equations, which points to an effective contribution to the electron's electric dipole moment. This result allows us to attain an estimate of the pseudo-vector condensate of the (LSV) Majorana background fermion., Comment: 33 pages, 1 figure. Several detailed explanations, discussions and references added to improve presentation. Fits the published version

We investigate physical consequences of non-linear electrodynamic coupled to parameters that signal violation Lorentz-symmetry breaking (LSV). Our undertaking is done by considering a general non-linear photonic Lagrangian which coupled to the Carroll-Field-Jackiw's model (CFJ). Our endeavor reveals how the (meta) material constitutive properties of the vacuum and wave propagation are affected by the interference of the LSV parameters LSV with the specific non-linear electrodynamic model under consideration. We also discuss the refractive indices for this new medium characterized by the coupling between non-linearities and the operators that carry the LSV message. Our results show that the QED-vacuum responds with birefringence and a dispersive propagation of waves. Subsequently, we consider the electromagnetic radiation produced by a moving charged particle interacting with this new medium. Our inspection illustrates that the emitted radiation reproduces the features of the Cherenkov effect for certain intensities of background magnetic fields . Finally, we compute the static potential profile within the framework of the gauge-invariant, but path-dependent, variables formalism. A logarithmic correction to the usual static Coulomb potential emerges driven by the LSV parameter and there also appear corrections due to the non-linearity; nevertheless, the logarithm behavior drops out whenever the LSV parameter is switched off., Comment: 22 pages

Based on the Caldirola-Canai approach, we endeavor to propose a dissipative scalar field theory in Minkowski space-time. We present its free particle solutions for complex $\omega^\mu$ components, and we find three profiles of dispersion relations, two of them support gapped momentum states. We also present an alternative view of this model, where dissipation acts as a geometric effect, and an effective negative scalar curvature space-time emerges. Finally, we illustrate how the present model could be adapted to describe shear waves in Frenkel liquids.

We investigate possible evidence from Extended Theories of Electro-Magnetism by looking for deviations from the Amp\`ere-Maxwell law. The photon, main messenger for interpreting the universe, is the only free massless particle in the Standard-Model (SM). Indeed, the deviations may be due to a photon mass for the de Broglie-Proca (dBP) theory or the Lorentz Symmetry Violation (LSV) in the SM Extension (SME), but also to non-linearities from theories as of Born-Infeld, Heisenberg-Euler. With this aim, we have analysed six years of data of the Magnetospheric Multi-Scale mission, which is a four-satellite constellation, crossing mostly turbulent regions of magnetic reconnection and collecting about $95\%$ of the downloaded data, outside the solar wind. We examined 3.8 million data points from the solar wind, magnetosheath, and magnetosphere regions. In a minority of cases, for the highest time resolution burst data and optimal tetrahedron configurations drawn by the four spacecraft, deviations have been found ($2.2\%$ in modulus and $4.8\%$ in Cartesian components for all regions, but raising up in the solar wind alone to $20.8\%$ in modulus and $29.7\%$ in Cartesian components and up to 45.2\% in the extreme low-mass range). The deviations might be due to unaccounted experimental errors or, less likely, to non-Maxwellian contributions, for which we have inferred the related parameters for the dBP and SME cases. Possibly, we are at the boundaries of measurability for non-dedicated missions. We discuss our experimental results (upper limit of photon mass of $2.1 \times 10^{-51}$ kg, and of the LSV parameter $|\vec{k}^{\rm AF}|$ of $6 \times 10^{-9}$ m$^{-1}$), as the deviations in the solar wind, versus more stringent but model-dependent limits., Comment: Accepted by Eur. Phys. J. Plus. The combination of plasma and fundamental physics opens a new field. Results: A) An upper limit very close to last FRB observations; B) Many deviations from the Amp\`ere-Maxwell law in the solar wind due to experimental errors or to non-Maxwellian terms. Deviations question the model based upper limits by Ryutov (1997, 2007) adopted by the Particle Data Group

We study physical aspects for a new nonlinear electrodynamics (inverse electrodynamics). It is shown that this new electrodynamics displays the vacuum birefringence phenomenon in the presence of external magnetic field, hence we compute the bending of light. Afterwards we compute the lowest-order modification to the interaction energy within the framework of the gauge-invariant but path-dependent variables formalism. Our calculations show that the interaction energy contains a long-range (${1 \mathord{\left/ {\vphantom {1 {{r^5}}}} \right.\kern-\nulldelimiterspace} {{r^5}}}$-type) correction to the Coulomb potential., Comment: 10 pages

The total red shift $z$ might be recast as a combination of the expansion red shift and a static shift due to the energy-momentum tensor non-conservation of a photon propagating through Electro-Magnetic (EM) fields. If massive, the photon may be described by the de Broglie-Proca (dBP) theory which satisfies the Lorentz(-Poincar\'e) Symmetry (LoSy) but not gauge-invariance. The latter is regained in the Standard-Model Extension (SME), associated with LoSy Violation (LSV) that naturally dresses photons of a mass. The non-conservation stems from the vacuum expectation value of the vector and tensor LSV fields. The final colour (red or blue) and size of the static shift depend on the orientations and strength of the LSV and EM multiple fields encountered along the path of the photon. Turning to cosmology, for a zero $\Omega_{\Lambda}$ energy density, the discrepancy between luminosity and red shift distances of SNeIa disappears thanks to the recasting of $z$. Massive photons induce an effective dark energy acting `optically' but not dynamically., Comment: Version accepted by Eur. Phys. J. C

Bidimensional muonic and electronic atoms, with nuclei composed of a proton, deuteron, and triton, and governed by Chern-Simons potential, are numerically solved. Their eigenvalues and eigenfunctions are determined with a slightly modified Numerov method. Results are compared with those assuming that the same atoms are governed by the usual $1/r$ potential even in a two-dimensional space, as well as with its three-dimensional analogs., Comment: 17 pages, 7 figures

In this work we focus on the Carroll-Field-Jackiw (CFJ) modified electrodynamics in combination with a CPT-even Lorentz-violating contribution. We add a photon mass term to the Lagrange density and study the question whether this contribution can render the theory unitary. The analysis is based on the pole structure of the modified photon propagator as well as the validity of the optical theorem. We find, indeed, that the massive CFJ-type modification is unitary at tree-level. This result provides a further example for how a photon mass can mitigate malign behaviors., Comment: 6 pages, 1 figure

Aspects of screening and confinement are re-examined for a recently proposed compact Abelian Higgs model with a $\theta$-term. Our discussion is accomplished using the gauge-invariant but path-dependent variables formalism, which is an alternative to the Wilson loop approach. We explicitly show that the static potential profile is the sum of an effective-Yukawa and a linear potential, leading to the confinement of static external charges. We point out the central r\^ole of the parameter measuring the stiffness of the vortex lines present in the model in both the Yukawa-like and the confining sectors of the effective inter-particle potential we have computed., Comment: 5 pages

We revisit for 714 SNeIa the discrepancy between the red-shift associated to the distance modulus $\mu$ and the spectroscopic red-shift. Previous work has shown that the total red-shift $z$ might be a combination of the expansion red-shift $z_{\rm C}$ and of a static, blue or red shift $z_{\rm LSV}(r)$, $r$ being the comoving distance. The latter is due to the energy non-conservation of the photon propagating through Electro-Magnetic (EM) background fields (host galaxy, intergalactic and Milky Way), under Lorentz(-Poincar\'e) Symmetry Violation (LSV), associated to the Standard-Model Extension (SME). The non-conservation stems from the vacuum expectation value of the vector and tensor LSV fields. For zero radiation $\Omega_{\rm rad}$ and curvature $\Omega_{\rm k}$ densities, and matter density $\Omega_m = 0.28$, the SN1a positions in the ($\mu$, z) plan are recovered according to the different strengths, orientations, alignments and space-time dependencies of the EM fields and LSV components. The LSV vacuum energy may be thus tantamount to $\Omega_\Lambda \simeq 0.7$, but unrelated to an accelerated expansion. We present models with red or blue-shifts $z_{\rm LSV}$, below $10\%$ of $z$. The $\nu$ frequency variation is below $10^{-19} \Delta \nu/\nu$ per m., Comment: 5 pages, 2 figures, letter format

We study the dimensional reduction for a $(3+1)$-dimensional Lorentz Violating Lagrangian in the matter and gauge sectors in a Supersymmetric scenario. We thus obtain an effective model for photons induced by the effects of supersymmetry in our framework with Lorentz-symmetry violating. This model is discussed in connection with the attainment of a static potential between charged particles. Our calculation is done within the framework of the gauge-invariant, but path-dependent variable formalism. We thus find that the interaction energy displays a screening part, encoded by Bessel functions, and a linear confining potential., Comment: 7 pages

In this contribution, we start off from a fully relativistic description of a single electron non-minimally coupled to an external electromagnetic field. Making direct use of the field equation, instead of canonically deriving from the Lagrangian density, the relativistic total angular momentum is attained, where the effect of the relativistic torque due to the external sources is also taken into account. Both the spin density and the orbital angular momentum tensors are identified in the relativistic-covariant approach. Furthermore, the symmetric and gauge invariant energy-momentum tensor is derived as well. In addition, to inspect the non-relativistic regime, a perturbative expansion of the field equation up to the leading order in $\left(v/c\right)$ is carried out, where spin-orbit interaction terms naturally emerge in the non-relativistic Hamiltonian as a consequence of the non-minimal coupling. Features related to the spin currents, the spin-transfer torque and their dependence on both magnetic and electric external fields are then calculated and discussed. Considering that spin-orbit coupled systems are of particular interest in the study of spin Hall effect, a two-dimensional (planar) scenario of the system is contemplated, where the contributions to the Landau levels are re-assessed. As a consequence of the planar regime and the non-minimal coupling, a peculiar sort of fractionalization of the spin-up and -down components emerges with the different spin components localized in distinct positions., Comment: 9 pages

In this work, we re-assess a class of black hole solutions in a global monopole spacetime in the framework of an $f(R)$-gravity model. Our main line of investigation consists in considering a region close enough to the black hole, but such that the weak field approximation is still valid. The stability of the black hole is studied in terms of its thermodynamical properties, with the radial coordinate written as a power law function with the status of the main factor underneath the stability of the model. We obtain the explicit expressions for the thermodynamical quantities of the black hole as functions of the event horizon, by considering both the Hawking and the local temperatures. The phase transitions that may occur in this system, including the Hawking-Page phase transition, are inspected with particular attention. We work out and contemplate a solution of special interest in which one of the parameters is related to the cosmological constant. Our main result sets out to establish a comparison between both the Hawking and the local formalisms for the black hole in the framework of the $f(R)$-gravity in the particular space-time adopted here., Comment: arXiv admin note: text overlap with arXiv:1510.08176

We explore the properties of a new Maxwell electrodynamics coupled to a Lorentz-violating background through the presence of higher-derivative terms. Physical implications of this alternative effective theory modified by Lorentz-violating operators of mass dimension-$5$ are considered, such as modified dispersion relations which exhibit the vacuum birefringence phenomenon. Subsequently, we analyze the energy-momentum tensor in the case we reproduce the Gambini-Pullin electrodynamics. We explicitly show that for a background time-like four-vector, $n^{\mu}$, the equations of motion indeed reproduce those encountered by Gambini and Pullin in the framework of loop quantum gravity . Finally, extended expressions for Maxwell-type equations are written down in the case the external Lorentz-violating four-vector is space-like., Comment: 14 pages. Contribution to the Touring the Planck Scale - Antonio Aurilia Memorial Volume

In the presence of Lorentz Symmetry Violation (LSV) associated with the Standard-Model Extension (SME), we have recently shown the non-conservation of the energy-momentum tensor of a light-wave crossing an Electro-Magnetic (EM) background field even when the latter and the LSV are constant. Incidentally, for a space-time dependent LSV, the presence of an EM field is not necessary. Herein, we infer that in a particle description, the energy non-conservation for a photon implies violation of frequency invariance in vacuo giving rise to a red or blue shift. We discuss the potential consequences on cosmology., Comment: To appear as a letter in Eur. Phys. J. C. The paper proposes a new shift to be superposed to the cosmological redshift

The propagation of plasma waves in a new non-linear, logarithmic electrodynamics model is performed. A cold, uniform, collisionless fluid plasma model is applied. Electrostatic waves in magnetized plasma are shown to correspond to modified Trivelpiece-Gould modes, together with changes of the plasma and upper-hybrid frequencies, driven by the logarithmic electrodynamics effects. Electromagnetic waves are described by a generalized Appleton-Hartree dispersion relation. The cases of propagation parallel or perpendicular to the equilibrium magnetic field are analyzed in detail. In particular, generalized ordinary and extraordinary modes are obtained. We determine the changes, due to logarithmic electrodynamics, in the allowable and forbidden frequency bands of the new extraordinary mode. Estimates are provided about the strength of the ambient magnetic field, so that the non-linear electrodynamics effects become decisive.

We examine physical aspects for the electric version of a recently proposed logarithmic electrodynamics, for which the electric field of a point-like charge is finite at the origin. It is shown that this electrodynamics displays the vacuum birefringence phenomenon in the presence of external magnetic field. Afterwards we compute the lowest-order modification to the interaction energy by means of the gauge-invariant but path-dependent variables formalism. These are shown to result in a long-range ($1/r^3$-type) correction, in addition to a linear and another logarithmic correction, to the Coulomb potential., Comment: 4 pages. arXiv admin note: text overlap with arXiv:1709.03869

We study the impact of Lorentz violating terms on a physical observable for both electrodynamics of chiral matter and an Abelian Higgs-like model in $3+1$ dimensions. Our calculation is done within the framework of the gauge-invariant, but path-dependent, variables formalism. Interestingly enough, for electrodynamics of chiral matter we obtain a logarithmic correction to the usual static Coulomb potential. Whereas for a Abelian Higgs model with a Lorentz-breaking term, our result displays new corrections to the Yukawa potential., Comment: 7 pages

Within the Standard Model Extension (SME), we expand our previous findings on four classes of violations of Super-Symmetry (SuSy) and Lorentz Symmetry (LoSy), differing in the handedness of the Charge conjugation-Parity-Time reversal (CPT) symmetry and in whether considering the impact of photinos on photon propagation. The violations, occurring at the early universe high energies, show visible traces at present in the Dispersion Relations (DRs). For the CPT-odd classes ($V_{\mu}$ breaking vector) associated with the Carroll-Field-Jackiw (CFJ) model, the DRs and the Lagrangian show for the photon an effective mass, gauge invariant, proportional to $|{\vec V}|$. The group velocity exhibits a classic dependency on the inverse of the frequency squared. For the CPT-even classes ($k_{F}$ breaking tensor), when the photino is considered, the DRs display also a massive behaviour inversely proportional to a coefficient in the Lagrangian and to a term linearly dependent on $k_{F}$. All DRs display an angular dependence and lack LoSy invariance. In describing our results, we also point out the following properties: i) the appearance of complex or simply imaginary frequencies and super-luminal speeds and ii) the emergence of bi-refringence. Finally, we point out the circumstances for which SuSy and LoSy breakings, possibly in presence of an external field, lead to the non-conservation of the photon energy-momentum tensor. We do so for both CPT sectors., Comment: To appear in Eur. Phys. J. C. We extend our previuous findings in arXiv:1607.08786 [hep-ph] and determine an effective mass for the photon also in the even CPT sector. Furthermore, the light-wave dissipation in vacuum, interpreted from the particle view point, might be seen as loss of frequency, and thereby 'tired light'

We explore the physical consequences of a new nonlinear electrodynamics, for which the electric field of a point-like charge is finite at the origin, as in the well-known Born-Infeld electrodynamics. However, contrary to the latter, in this new electrodynamics the phenomenon of birefringence and dichroism take place in the presence of external magnetic fields. Subsequently we study the interaction energy, within the framework of the gauge-invariant but path-dependent variables formalism. Interestingly enough, the static potential profile contains a linear potential leading to the confinement of static charges., Comment: 5 pages. arXiv admin note: substantial text overlap with arXiv:1607.02997

Aspects of screening and confinement are reassessed for a $B \wedge F$ model with topological mass with the gauging of spin. Our discussion is carried out using the gauge-invariant, but path-dependent, variables formalism. We explicitly show that the static potential profile is the sum of a Yukawa and a linear potential, leading to the confinement of static external charges. Interestingly enough, similar results are obtained in a theory of antisymmetric tensor fields that results from the condensation of topological defects as a consequence of the Julia-Toulouse mechanism., Comment: 5 pages

For a $(3+1)$-dimensional generalization of the Schwinger model, we compute the interaction energy between two test charges. The result shows that the static potential profile contains a linear term leading to the confinement of probe charges, exactly as in the original model in two dimensions. We further show that the same 4-dimensional model also appears as one version of the $ B \wedge F$ models in $(3+1)$ dimensions under dualization of Stueckelberg-like massive gauge theories. Interestingly, this particular model is characterized by the mixing between a $U(1)$ potential and an Abelian $3$-form field of the type that appears in the topological sector of QCD., Comment: 5 pages. arXiv admin note: text overlap with arXiv:1504.05810

In the present contribution, we study the Landau-Lifshitz-Gilbert equation with two versions of structural derivatives recently proposed: the scale $q-$derivative in the non-extensive statistical mechanics and the axiomatic metric derivative, which presents Mittag-Leffler functions as eigenfunctions. The use of structural derivatives aims to take into account long-range forces, possible non-manifest or hidden interactions and the dimensionality of space. Having this purpose in mind, we build up an evolution operator and a deformed version of the LLG equation. Damping in the oscillations naturally show up without an explicit Gilbert damping term., Comment: 10 pages, 3 figures

Adopting the gauge-invariant and path-dependent variables formalism, we compute the interaction energy for a topological field theory describing $(1+3)$D topological superconductors in presence of external fields. As a result, in the case of a constant electric field- strength expectation value, we show that the interaction energy describes a purely screening phase, encoded in a Yukawa potential. On the other hand, in the case of a constant magnetic field-strength and for a very small Josephson coupling constant, the particle-antiparticle binding potential displays a linear term leading to the confinement of static charge probes along with a screening contribution., Comment: 6 pages

The dynamics of a radiating charge is one of the oldest unsettled problems in classical physics. The standard Lorentz-Abraham-Dirac (LAD) equation of motion is known to suffer from several pathologies and ambiguities. This paper briefly reviews these issues, and reports on a new model that fixes these difficulties in a natural way. This model is based on a hypothesis that there is an infinitesimal time delay between action and reaction. This can be related to Feynman's regularization scheme, leading to a quasi-local QED with a natural UV cutoff, hence without the need for renormalization as the divergences are absent. Besides leading to a pathology-free equation of motion, the new model predicts a modification of the Larmor formula that is testable with current and near future ultra-intense lasers., Comment: 6 pages. The title and Eq. 4 were slightly modified in this version. To appear in the Proceedings of Group-31 (The 31st International Colloquium on Group Theoretical Methods in Physics)

The power radiated by a moving charge is given by Larmor's formula which can be derived by integrating the Li\'enard-Wiechert potential over the whole past history of the charge. However, extracting the same result from the Lorent-Abraham-Dirac (LAD) equation of motion is problematic. This is well known for uniform proper acceleration for which case the radiation force vanishes and hence the very origin of the radiated energy is not clear, leading to an energy balance paradox. The purpose of this letter is first to evince that this problem occurs in the general case and not only for uniform acceleration. Second we show that the widely accepted treatment based on the bound field technique cannot fix the energy balance discrepancy. Indeed the related Schott term is not a legitimate four-momentum for being indefinite and not conserved., Comment: Version submitted for publication, important changes, new Refs. added, 5 pages and 1 figure

In the context of Standard Model Extensions (SMEs), we analyse four general classes of Super Symmetry (SuSy) and Lorentz Symmetry (LoSy) breaking, leading to {observable} imprints at our energy scales. The photon dispersion relations show a non-Maxwellian behaviour for the CPT (Charge-Parity-Time reversal symmetry) odd and even sectors. The group velocities exhibit also a directional dependence with respect to the breaking background vector (odd CPT) or tensor (even CPT). In the former sector, the group velocity may decay following an inverse squared frequency behaviour. Thus, we extract a massive and gauge invariant Carroll-Field-Jackiw photon term in the Lagrangian and show that the mass is proportional to the breaking vector. The latter is estimated by ground measurements and leads to a photon mass upper limit of $10^{-19}$ eV or $2 \times 10^{-55}$ kg and thereby to a potentially measurable delay at low radio frequencies.

Magnetic and thermodynamical properties of a system of spins in a honeycomb lattice, such as magnetization, magnetic susceptibility and specific heat, in a low-temperature regime are investigated by considering the effects of a Kekul\'e scalar exchange and QED vacuum polarization corrections to the interparticle potential. The spin lattice calculations are carried out by means of Monte Carlo simulations. We present a number of comparative plots of all the physical quantities we have considered and a detailed analysis is presented to illustrate the main features and the variation profiles of the properties with the applied external magnetic field and temperature., Comment: 15 figures

Within the framework of the gauge-invariant, but path-dependent, variables formalism, we study the manifestations of vacuum electromagnetic nonlinearities in $D=3$ models. For this we consider both generalized Born-Infeld and Pagels-Tomboulis-like electrodynamics, as well as, an Euler-Heisenberg-like electrodynamics. We explicitly show that generalized Born-Infeld and Pagels-Tomboulis-like electrodynamics are equivalent, where the static potential profile contains a long-range (${\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle {{r^2}}$}}$-type) correction to the Coulomb potential. Interestingly enough, for an Euler-Heisenberg-like electrodynamics the interaction energy contains a linear potential, leading to the confinement of static charges., Comment: 9 pages

Using a method based on the generating functional plus a kind of "correspondence principle" --- which acts as a bridge between the electromagnetic and scalar fields --- it is shown that the interparticle potential energy concerning a given $D$-dimensional electromagnetic model can be obtained in a simple way from that related to the corresponding scalar system. The $D$-dimensional electromagnetic potential for a general model containing higher derivatives is then found from the corresponding scalar one and the behavior of the former is analyzed at large as well as small distances. In addition, we investigate the presence of ghosts in the four-dimensional version of the potential associated with the model above and analyze the reason why the Coulomb singularity is absent from this system. The no-go theorem by Ostrogradski is demystified as well.

The effect of Lorentz symmetry violation in the phenomenon of photon gravitational bending, is investigated. Using a semiclassical approach, where the photon is described by the Carrol-Field-Jackiw (CFJ) electrodynamics which is responsible for implementing the Lorentz symmetry violation, the gravitational deflection angle related to the CFJ photon is computed. As expected, this bending angle experiences a deviation from the usual Einstein result and the latter is recovered in the appropriate limit. A comparison between the theoretical prediction and the experimental results allows to conclude that no trace of Lorentz symmetry breaking is found provided the components of the background vector field are $\lesssim 10^{-8}$ eV., Comment: We have found some basic mistakes that invalidate the results we have obtained

By using the gauge-invariant but path-dependent, variables formalism, we consider a recently proposed topologically massive $U{\left( 1 \right)_{\cal W}} \times U{(1)_{\cal Y}}$ Chern-Simons-Higgs theory in $2+1$ dimensions. In particular, we inspect the impact of a Chern-Simons mixing term between two Abelian gauge fields on physical observables. We pursue our investigation by analysing the model in two different situations. In the first case, where we integrate out the massive excitation and consider an effective model for the massless field, we show that the interaction energy contains a linear term leading to the confinement of static charge probes along with a screening contribution. The second situation, where the massless field can be exactly integrated over with its constraint duly taken into account, the interesting feature is that the resulting effective model describes a purely screening phase, without any trace of a confining regime., Comment: 11 pages, to appear in AHEP

Recently, we have demonstrated that there exists a possible relationship between q-deformed algebras in two different contexts of Statistical Mechanics, namely, the Tsallis' framework and the Kaniadakis' scenario, with a local form of fractional-derivative operators for fractal media, the so-called Hausdorff derivatives, mapped into a continuous medium with a fractal measure. Here, in this paper, we present an extension of the traditional calculus of variations for systems containing deformed-derivatives embedded into the Lagrangian and the Lagrangian densities for classical and field systems. The results extend the classical Euler-Lagrange equations and the Hamiltonian formalism. The resulting dynamical equations seem to be compatible with those found in the literature, specially with mass-dependent and with nonlinear equations for systems in classical and quantum mechanics. Examples are presented to illustrate applications of the formulation. Also, the conserved Nether current, are worked out., Comment: 13 pages. arXiv admin note: text overlap with arXiv:1502.07606

Among the so-called classical tests of general relativity (GR), light bending has been confirmed with an accuracy that increases as times goes by. Here we study the gravitational deflection of photons within the framework of classical and semiclassical higher-derivative gravity (HDG) -- the only version of GR that is known up to now to be renormalizable along with its matter couplings. Since our computations are restricted to scales much below the Planck cut-off we need not be afraid of the massive spin-2 ghost that haunts HDG. An upper bound on the constant related to the $R^2_{\mu \nu}$-sector of the theory is then found by analyzing -- from a classical and semiclassical viewpoint -- the deflection angle of a photon passing by the Sun. This upper limit greatly improves that available in the literature., Comment: 9 pages, 7 figures. Accepted for publication in PRD

By means of numerical simulations, we explore possible effects of a special interparticle interaction potential which is a function of external and internal conditions of graphene-like systems. In addition to the electromagnetic interaction, we introduce a new potential due to the exchange of a massive scalar, associated to the so-called Kekul\'e deformations; this interaction displays a spin-dependent profile. It turns out that the magnitude of Kekul\'e deformation may significantly affect physical properties of graphene. A Monte Carlo analysis enables one to analyze the behavior of the system under variation of the applied external field, temperature, and the particular type of the exchanged excitation that induces the potential. We pursue an investigation of the spin configurations, we analyze differences in thermal equilibrium magnetization and we carry out calculations of the magnetic susceptibility and the specific heat in the presence of the Kekul\'e-induced new potential., Comment: 8 pages, fits published version

We consider both generalized Born-Infeld and Exponential Electrodynamics. The field-energy of a point-like charge is finite only for Born-Infeld-like Electrodynamics. However, both Born-Infeld-type and Exponential Electrodynamics display the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy for both classes of Electrodynamics, within the framework of the gauge-invariant path-dependent variables formalism. These are shown to result in long-range ($1/r^5$- type) corrections to the Coulomb potential. Once again, for their non-commutative versions, the interaction energy is ultraviolet finite., Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1312.5157

In the present contribution, by studying a fractional version of Dirac's equation for the electron, we show that the phenomenon of Zitterbewegung in a coarse-grained medium exhibits a transient oscillatory behavior, rather than a purely oscillatory regime, as it occurs in the integer case, $\alpha=1$. Our result suggests that, in such systems, the Zitterbewegung-type term related to a trembling motion of a quasiparticle is tamed by its complex interactions with other particles and the medium. This can justify the difficulties in the observation of this interesting phenomenon. The possibility that the Zitterbewegung be accompanied by a damping factor supports the viewpoint of particle substructures in Quantum Mechanics., Comment: 11 pages, 1 figure. This paper has been published in J. Adv. Phys. 7 (2015) 1440

In this paper, we analyse a curvature- and torsion-square quantum gravity action with an additional Holst term minimally coupled to a massive Dirac field in four dimensions. The main purpose here is to try to estimate and compare the value of the Barbero-Immirzi (BI) parameter with its currently known results. To do that, we work out the physical mass of the fermion as a function of this parameter in a perturbative one-loop calculation, assuming the scenario of a physics at the TeV-scale., Comment: Seven pages, 1 figure. Accepted to be plublished in Physica Review D

We pursue an investigation of Logarithmic Electrodynamics, for which the field-energy of a point-like charge is finite, as it happens in the case of the usual Born-Infeld electrodynamics. We also show that, contrary to the latter, Logarithmic Electrodynamics exhibits the feature of birefringence. Next, we analyze the lowest-order modifications for both Logarithmic Electrodynamics and for its non-commutative version, within the framework of the gauge-invariant path-dependent variables formalism. The calculation shows a long-range correction ($1/r^5$- type) to the Coulomb potential for Logarithmic Electrodynamics. Interestingly enough, for its non-commutative version, the interaction energy is ultraviolet finite. We highlight the role played by the new quantum of length in our analysis., Comment: 11 pages, 2 figures

In a previous work, we have been able to settle Jackiw's et al. chiral gauge theory for Dirac fermions in graphene in an N=1 supersymmetric framework, using a tau3-QED prescription, defined by means of a single pair of gauge charged superfields, but without preserving a global phase symmetry associated to the electric charge. In the present work, we propose another N=1-generalisation which indeed preserves this symmetry, namely, a straightforward extension built upon a set of two pairs of (chiral) gauge-charged superfields plus an extra pair of electrically neutral superfields. We then further proceed to establish, via a dimensional reduction procedure, an N=2 extension, allowing for the identification of non-perturbative features, as we put forward Bogomol'nyi equations and obtain vortex-like solutions saturating a topologically non-trivial bound. Remarkably, the bosonic projection of the N=2 functional space onto the saturated regime analysed herewith reveals to be free from extra scalar degrees of freedom that would otherwise demand a phenomenological interpretation. The investigation of Jackiw's model within an N=2 complex superspace is also motivated by the assumption that an R-parity-like symmetry could provide a route to incorporate the global phase-fermion number invariance as an external-like symmetry of the theory, thus associating the electric charge in graphene to the complex covariance (super-)space for the N=2-D=3 setup. We prove such a hypothesis to be realisable, as we build up the model endowed with all the symmetries required to further extend Jackiw's chiral gauge theory., Comment: 21 pages, 2 figures (with corrections in v2), added references, new commentaries added (but results remain unchanged). v3: just minor changes in acknowledgements

We propose a macroscopic description of the superconducting state in presence of an applied external magnetic field in terms of first order differential equations. They describe a corrugated two-component order parameter intertwined with a spin-charged background, caused by spin correlations and charged dislocations. The first order differential equations are a consequence of a Weitzenb\"ock-Liechnorowitz identity which renders a SUL(2) \otimes UL(1) invariant ground state, based on (L) local rotational and electromagnetic gauge symmetry. The proposal is based on a long ago developed formalism by \'Elie Cartan to investigate curved spaces, viewed as a collection of small Euclidean granules that are translated and rotated with respect to each other. \'Elie Cartan's formalism unveils the principle of local rotational invariance as a gauge symmetry because the global SU(2) invariance of the order parameter is turned local by the interlacement of spin and charge to pairing., Comment: 19 pages, 3 figures