Point-like Charge Research Articles

On generalized ModMax model of nonlinear electrodynamics

A new generalized ModMax model of nonlinear electrodynamics with four parameters is proposed. The ModMax model and Born–Infeld-type electrodynamics are particular cases of the present model. It is shown that a singularity of the electric field at the center of point-like charged particles is absent. We found corrections to Coulomb's law at r→∞ and obtained the total electrostatic and magnetic energies of point-like charges. Free electric and magnetic charges and their densities are obtained.

Magnetoelectric boundary simulated by a Chern\u2013Simons-like model

In this work we study some physical phenomena that emerge in the vicinity of a magnetoelectric boundary. For simplicity, we restrict to the case of a planar boundary described by a coupling between the gauge field with a planar external Chern–Simons-like potential. The results are obtained exactly. We compute the correction undergone by the photon propagator due to the presence of the Chern–Simons coupling and we investigate the interaction between a stationary point-like charge and the magnetoelectric boundary. In the limit of a perfect mirror, where the coupling constant between the field and the potential diverges, we recover the image method. For a non perfect mirror, we show that we have an attenuated image charge and, in addition, an image magnetic monopole whose field strength does not exhibit the presence of the undesirable and artificial divergences introduced by Dirac strings. We also study the interaction between the plate and a quantum particle with spin. In this case we have a kind of charge-magnetic dipole interaction due to the magnetoelectric properties of the plate.

Magnetic dominance of axion electrodynamics: photon capture effect and anisotropy of Coulomb potential

For magnetic fields larger than the characteristic scale linked to axion-electrodynamics, quantum vacuum fluctuations due to axion-like fields can dominate over those associated with the electron-positron fields. This conjecture is explored by investigating both the axion-modified photon capture by a strong magnetic field and the Coulomb potential of a static pointlike charge. We show that in magnetic fields characteristic of neutron stars sim 10^{13}–10^{15};mathrm{G}, the capture of gamma photons prior to the production of a pair can prevent the existence of an electron-positron plasma, essential for explaining the pulsar radiation mechanism. This incompatibility is used to limit the axion parameter space. Our bounds improve existing outcomes in the region of mass msim 10^{-10}–10^{-5};{mathrm{eV}}. The effect of capture, known in QED as relating to gamma-quanta, is extended in axion electrodynamics to include X-ray photons with the result that a specially polarized part of the heat radiation from the surface is canalized along the magnetic field. Besides, we find that in the regime in which the dominance takes place, the running QED coupling depends on the field strength and the modified Coulomb potential is of Yukawa-type in the direction perpendicular to the magnetic field at distances much smaller than the axion Compton wavelength, while along the field it follows approximately the Coulomb law at any length scale. Despite the Coulomb singularity manifested in the latter case, we argue that the ground-state energy of a non-relativistic hydrogen atom placed in a strong magnetic field turns out to be bounded due to the nonrenormalizable feature of axion-electrodynamics.

Can the power Maxwell nonlinear electrodynamics theory remove the singularity of electric field of point-like charges at their locations?

We introduce a variable power Maxwell nonlinear electrodynamics theory which can remove the singularity of electric field of point-like charges at their locations. One of the main problems of Maxwell's electromagnetic field theory is related to the existence of singularity for the electric field of point-like charges at their locations. In other words, the electric field of a point-like charge diverges at the charge location which leads to an infinite self-energy. In order to remove this singularity a few nonlinear electrodynamics (NED) theories have been introduced. The Born-Infeld (BI) NED theory is one of the most famous among them. However the power Maxwell (PM) NED cannot remove this singularity. In this paper, we show that the PM NED theory can remove this singularity, when the power of PM NED is less than .

Novel summation formulas for Jacobi and Gegenbauer polynomials

Thermal equilibrium of a two-dimensional model of mobile point-like charges with pair logarithmic interactions, immersed in a fixed neutralising background, is exactly solvable at a special coupling constant. Assuming gauge invariance of the statistical mechanics and the requirement of local charge neutrality in the bulk regime of the system, the exact solution implies explicit expressions for inverse elements of an infinite interaction matrix. This result is equivalent to new summation formulas over upper index for bilinear products of Jacobi and Gegenbauer polynomials which are complementary to standard completeness relations involving lower indices for these polynomials. We go beyond the physical input and derive multi-variable generalizations of the summation formulas.

Double-logarithmic nonlinear electrodynamics

A new model of nonlinear electrodynamics is introduced and investigated. The theory carries one dimensionful parameter β as in Born-Infeld electrodynamics. It is shown that the dual symmetry and dilatation (scale) symmetry are broken in the proposed model. The electric field of a point-like charge is derived for this model, showing that it is non-singular at the origin. Using this electric field, the static electric energy of a point-like charge is calculated. In the presence of an external magnetic field, the theory shows a phenomenon known as vacuum birefringence. The refraction index of two polarizations, parallel and perpendicular to the external magnetic induction field, are calculated. The canonical and symmetrical Belinfante energy-momentum tensors are obtained. Using the causality and unitarity principles, the regions where the theory becomes causal and unitary are found.

Quantum phases for electric charges and electric (magnetic) dipoles: physical meaning and implication

We analyse the physical meaning of quantum phase effects for point-like charges and electric (magnetic) dipoles in an electromagnetic (EM) field. At present, there are known eight effects of such a kind: four of them (the magnetic and electric Aharonov – Bohm phases for electrons, the Aharonov – Casher phase for a moving magnetic dipole and the He – McKellar – Wilkens phase for a moving electric dipole) had been disclosed in 20th century, while four new quantum phases had recently been found by our team (A. L. Kholmetskii, O. V. Missevitch, T. Yarman). In our analysis of physical meaning of these phases, we adopt that a quantum phase for a dipole represents a superposition of quantum phases for each charge, composing the dipole. In this way, we demonstrate the failure of the Schrödinger equation for a charged particle in an EM field to describe new quantum phase effects, when the standard definition of the momentum operator is used. We further show that a consistent description of quantum phase effects for moving particles is achieved under appropriate re-definition of this operator, where the canonical momentum of particle in EM field is replaced by the interactional EM field momentum. Some implications of this result are discussed.

Quantum corrections to the accretion onto a Schwarzschild black hole in the background of quintessence

It is well known that quantum effects may lead to removal of the intrinsic singularity point of back holes. Also, the quintessence scalar field is a candidate model for describing late-time acceleration expansion. Accordingly, Kazakov and Solodukhin considered the existence of back-reaction of the spacetime due to the quantum fluctuations of the background metric to deform a Schwarzschild black hole, which led to a change of the intrinsic singularity of the black hole to a 2-sphere with a radius of the order of the Planck length. Also, Kiselev rewrote the Schwarzschild metric by taking into account the quintessence field in the background. In this study, we consider the quantum-corrected Schwarzschild black hole inspired by Kazakov–Solodukhin’s work, and the Schwarzschild black hole surrounded by quintessence deduced by Kiselev to study the mutual effects of quantum fluctuations and quintessence on the accretion onto the black hole. Consequently, the radial component of the 4-velocity and the proper energy density of the accreting fluid have a finite value on the surface of its central 2-sphere due to the presence of quantum corrections. Also, by comparing the accretion parameters in different kinds of black holes, we infer that the presence of a point-like electric charge in the spacetime is somewhat similar to some quantum fluctuations in the background metric.

Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence

We analyze the stability of time-reversal (${\mathcal T}$) and lattice four-fold ($C_4$) symmetry breaking three-dimensional higher-order topological (HOT) Dirac semimetals (DSMs) and the associated one-dimensional hinge modes in the presence of random pointlike charge impurities. Complementary real space numerical and momentum space renormalization group (RG) analyses suggest that a HOTDSM, while being a stable phase of matter for sufficiently weak disorder, undergoes a continuous quantum phase transition into a trivial metal at finite disorder. However, the corresponding critical exponents (numerically obtained from the scaling of the density of states) are extremely close to the ones found in a dirty, but first-order DSM that on the other hand preserves ${\mathcal T}$ and $C_4$ symmetries, and support two Fermi arc surface states. This observation suggests an emergent \emph{superuniversality} (insensitive to symmetries) in the entire family of dirty DSMs, as also predicted by a leading-order RG analysis. As a direct consequence of the bulk-boundary correspondence, the hinge modes in a system with open boundaries gradually fade away with increasing randomness, and completely dissolve in the trivial metallic phase at strong disorder.

Saturation of Energy Levels of the Hydrogen Atom in Strong Magnetic Field

We demonstrate that the finiteness of the limiting values of the lower energy levels of a hydrogen atom under an unrestricted growth of the magnetic field, into which this atom is embedded, is achieved already when the vacuum polarization (VP) is calculated in the magnetic field within the approximation of the local action of Euler–Heisenberg. We find that the mechanism for this saturation is different from the one acting, when VP is calculated via the Feynman diagram in the Furry picture. We study the effective potential that appears when the adiabatic (diagonal) approximation is exploited for solving the Schrödinger equation for the longitudinal degree of freedom of the electron on the lowest Landau level in the atom. We find that the (effective) potential of a point-like charge remains nonsingular thanks to the growing screening provided by VP. The regularizing length turns out to be α/3π¯λC, where ¯λC is the electron Compton length. The family of effective potentials, labeled by growing values of the magnetic field condenses towards a certain limiting, magnetic-field-independent potential-distance curve. The limiting values of even ground-state energies are determined for four magnetic quantum numbers using the Karnakov–Popov method.

Dirichlet boundary condition for the Lee\u2013Wick-like scalar model

Lee–Wick-like scalar model near a Dirichlet plate is considered in this work. The modified propagator for the scalar field due to the presence of a Dirichlet boundary is computed, and the interaction between the plate and a point-like scalar charge is analysed. The non-validity of the image method is investigated and the results are compared with the corresponding ones obtained for the Lee–Wick gauge field and for the standard Klein–Gordon field.

New Effects in the Vicinity of a Perfectly Conducting Plate in a Non-minimal Lorentz Violation Scenario

In this paper we consider some physical phenomena in the vicinity of a conducting plate in a non-minimal Lorentz-violating scenario in 3 + 1 dimensions. We consider a model where the dynamics of the abelian gauge field is given by the standard Maxwell Lagrangian added by a Lorentz symmetry breaking term with the presence of higher order derivatives in the gauge field. The Lorentz symmetry breaking is due to the presence of a single background vector dλ and we perform the calculations perturbatively up to first order in dλ. We obtain the propagator for the gauge field in the presence of a mirror and the interaction force between the mirror and a point-like electric charge, as well as the interaction force between the mirror and an electric dipole. We show that, on the contrary to what happens in a minimal Lorentz-violating scenario with one single background field (L.H.C. Borges, F.A. Barone, Eur. Phys. J. C 693, 77, 2017), the image method is not valid in the model that we consider in this paper. As a consequence, the symmetry of spatial reflection on the mirror is broken. We also investigate the emergence of a torque in a system composed by a mirror and a point-like electric charge, placed at a fixed distance apart each other. The results obtained in this work have no counterpart in the Maxwell electrodynamics and were not verified in any Lorentz-violating scenario previously.

Generalised Schwarzschild metric from double copy of point-like charge solution in Born-Infeld theory

We discuss possible application of the classical double copy procedure to construction of a generalisation of the Schwarzschild metric starting from an α′-corrected open string analogue of the Coulomb solution. The latter is approximated by a point-like charge solution of the Born-Infeld action, which represents the open string effective action for an abelian vector field in the limit when derivatives of the field strength are small. The Born-Infeld solution has a regular electric field which is constant near the origin suggesting that corrections from the derivative terms in the open string effective action may be small there. The generalization of the Schwarschild metric obtained by the double copy construction from the Born-Infeld solution looks non-singular but the corresponding curvature invariants still blow up at r=0. We discuss the origin of this singularity and comment on possible generalizations.

Magnetic Pole as Produced by a Point-like Electric Charge Embedded in Constant-Field Background

We consider a linear magnetic response to a point electric charge embedded in the background of parallel constant electric and magnetic fields in the framework of nonlinear electrodynamics. We find two types of responses. One is given by a vector potential free of any string singularity. The corresponding magnetic field may be thought of as two magnetic poles of opposite polarity coexisting at one point. The other response is given by a vector potential singular on a half-axis directed along the background fields. Its magnetic field is a magnetic monopole plus a field confined to an infinitely thin solenoid, whose role is the same as that of the Dirac string. The value of the magnetic charge is determined by the electric charge and the background fields and is expressed in terms of derivatives of the nonlinear local Lagrangian. Once the potential is singular, the nonlinear Maxwell equations written for potentials and field intensities are not equivalent. We argue why the preference should be given to potentials.

Magnetic response from constant backgrounds to Coulomb sources

Within general nonlinear electrodynamics given by a local action, very special magnetic field configuration carrying no magnetic charge is found as a linear response of the vacuum, filled with constant electric and magnetic fields, to an embedded static electric charge. When the electric charge is point-like and external fields are parallel, the response found may be interpreted as a field of two point-like magnetic charges of opposite polarities in one point. Coefficients characterizing the magnetic response and induced current are specialized to quantum electrodynamics (QED), where the nonlinearity is taken as that determined by the local Heisenberg–Euler effective action. It is demonstrated how the same response is reproduced in the (nonisotropic) region remote from the charge by considering the polarization operator of QED.

Dyonic and magnetized black holes based on nonlinear electrodynamics

We propose a new model of nonlinear electrodynamics with two dimensional parameters. The phenomenon of vacuum birefringence, the principles of causality and unitarity were studied. It was shown that there is no a singularity of the electric field in the center of point-like charges. Corrections to the Coulomb law as rrightarrow infty were obtained. Dyonic and magnetized black holes are considered. We show that in the self-dual case, when the electric charge equals the magnetic charge, corrections to Coulomb’s law and Reissner–Nordström solutions are absent. The metric function and its asymptotic limit as rrightarrow infty for magnetic black holes were evaluated. We calculate the magnetic mass of the black hole, which is finite. The thermodynamic properties and thermal stability of black holes were investigated. We calculated the Hawking temperature, the heat capacity and the Helmholtz free energy of black holes and showed that for some parameter values there are second-order phase transitions. It was demonstrated that at some range of the parameters the black holes are stable.

New point-like sources and a conducting surface in Maxwell\u2013Chern\u2013Simons electrodynamics

We investigate some aspects of the Maxwell–Chern–Simons electrodynamics focusing on physical effects produced by the presence of stationary sources and a perfectly conducting plate (mirror). Specifically, in addition to point charges, we propose two new types of point-like sources called topological source and Dirac point, and we also consider physical effects in various configurations that involve them. We show that the Dirac point is the source of the vortex field configurations. The propagator of the gauge field due to the presence of a conducting plate and the interaction forces between the plate and point-like sources are computed. It is shown that the image method is valid for the point-like charges as well as for Dirac points. For the topological source we show that the image method is not valid and the symmetry of spatial refection on the mirror is broken. In all setups considered, it is shown that the topological source leads to the emergence of torques.

Impact of Eccentricity on Nonlinear Oscillations of a Point-Like Charge in the Electric Field of a Curvature-Dependent Elliptic Charged Ellipse

Calculation of the interactive force between two horizontally stacked circular uniformly charged rings placed along the common vertical axis conducive to nonlinear oscillations under gravity has been addressed [1]. Although challenging, nonetheless the scope of the study limited to uniform charge distributions of the rings. Here we extend the analysis considering a charged ellipse with a nonuniform, curvature-dependent elliptic charge distribution exerting a force on a point-like charge placed on the vertical symmetry axis. Nonuniform charge distribution and its impact on various practical scenarios are not a common theme addressed in literature. Applying Computer Algebra System (CAS) particularly Mathematica [2], we analyze the issue on hand augmenting the traditional scope of interest. We overcome the CPU expensive symbolic computation following our newly developed numeric/symbolic method [1]. For comprehensive understanding, we simulate the nonlinear oscillations.

Modification of relativistic beam fields under the influence of external conducting and ferromagnetic flat boundaries

AbstractWe derive analytical expressions for external fields of a relativistic bunch of charged particles with a circular and an elliptical cross section under different boundary conditions and interaction of the fields with an accelerator structural elements. The particle density in the bunch is assumed to be uniform as well as non-uniform. At distances far apart from the bunch, in free space the field reduces to the relativistic modified Coulomb form for a pointlike charge and at small distances the expressions reproduce the external fields of a continuous beam. In an ultra-relativistic limit the longitudinal components of the internal and external electric fields of the bunch are strongly suppressed by the Lorentz factor. If the bunch is surrounded by conducting surfaces, the bunch self-fields are modified. Image fields generated by a bunch between two parallel conducting plates are studied in detail. Exact summation of the electric, $E_y$, and magnetic, $B_x$, image field components allows the infinite series to be represented in terms of elementary trigonometric functions. The new expressions for modified fields are applied to study image forces acting on the bunch constituents and the bunch as a whole. The coherent and incoherent tune shifts for an arbitrary bunch displacement from the midplane are calculated in the framework of an improved linear theory, for both infinite and finite parallel flat surfaces. Moreover, the developed method allows us to generalize the Laslett image coefficients $\epsilon_1$, $\epsilon_2$, $\xi_1$, $\xi_2$ to the case of an arbitrary bunch offset and reveal relationships between these coefficients. Appendix C provides a brief historical background of the development of the method of electrical images.

Magnetoelectric effect of a conducting sphere near a planar topological insulator

When time-reversal symmetry is broken on its surface, topological insulators exhibit a magnetoelectric response which is described by axion electrodynamics. A direct consequence of this theory is the appearance of a magnetic field that resembles the one produced by a magnetic image monopole when a point-like electric charge is located near the surface of the material. In this paper we investigate the more realistic problem when the point-like charge is replaced by a finite size sphere at constant potential. We calculate the electromagnetic fields using the potential formulation in a particular bispherical coordinate system. We find that the electromagnetic fields can be interpreted in terms of point electric and image magnetic charges as if the medium were the vacuum. As a manifestation of the magnetoelectric effect, we highlight the resulting magnetic field, which we analyze in detail along the symmetry axis, since such estimates could be useful in evaluating the experimental possibility of its measurement via sensible magnetometers. Our numerical estimates show that the proposed setup provides a magnetic field strength in the range of 10-100 mG, which is attainable with present day sensitivities in NV center-diamond magnetometers, for example.