Narrow Results

It is shown how initial conditions can be appropriately defined for the integration of Lorentz–Dirac equations of motion. The integration is performed forward in time. The theory is applied to the case of the motion of an electron in an intense laser pulse, relevant to nonlinear Compton scattering.

Fractals are measurable metric sets with non-integer Hausdorff dimensions. If electric and magnetic fields are defined on fractal and do not exist outside of fractal in Euclidean space, then we can use the fractional generalization of the integral Maxwell equations. The fractional integrals are considered as approximations of integrals on fractals. We prove that fractal can be described as a specific medium.

We study an electrodynamics consistent with anisotropic transformations of spacetime with an arbitrary dynamic exponent z. The equations of motion and conserved quantities are explicitly obtained. We show that the propagator of this theory can be regarded as a quantum correction to the usual propagator. Moreover, we obtain that both the momentum and angular momentum are not modified, but their conservation laws do change. We also show that in this theory the speed of light and the electric charge are modified with z. The magnetic monopole in this electrodynamics and its duality transformations are also investigated. For that we found that there exists a dual electrodynamics, with higher derivatives in the electric field, invariant under the same anisotropic transformations.

In the presence of anisotropic cosmic expansions at global or local scale the equations of electrodynamics in expanding spacetime are modified and presented here. A new effect should arise in regions of local anisotropic expansion in a cosmologically isotropic background. These regions should naturally exist, being connected with scales decoupling from the Hubble flow. Possible observational consequences of this effect are suggested. In particular, we predict the appearance or variation of the polarization of electromagnetic radiation coming from or passing through these regions. This effect is observable and possibly already observed in the polarization of quasars.

Using the Dirac method, we study the Hamiltonian consistency for three field theories. First, we study the electrodynamics a la Hořava and we show that this system is consistent for an arbitrary dynamical exponent z. Second, we study a Lifshitz type electrodynamics, which was proposed by Alexandre and Mavromatos [Phys. Rev. D 84, 105013 (2011)]. For this latter system we found that the canonical momentum and the electrical field are related through a Proca type Green function, however this system is consistent. In addition, we show that the anisotropic Yang–Mills theory with dynamical exponent z = 2 is consistent. Finally, we study a generalized anisotropic Yang–Mills theory and we show that this system is consistent too.

Within the framework of generally covariant (pre-metric) electrodynamics, we specify a local vacuum spacetime relation between the excitation and the field strength F = (E,B). We study the propagation of electromagnetic waves in such a spacetime by Hadamard's method and arrive, with the constitutive tensor density κ ~ ∂H/∂F, at a Fresnel equation which is algebraic of 4th order in the wave covector. We determine how the different pieces of κ, in particular the axion and the skewon pieces, affect the propagation of light.

The asymmetry, between electric (E) and magnetic (H) fields of Maxwell's equation is here analyzed by using the concept of chirality. The chiral spinorial approach sets the stage for the construction of a more general theory of spin-1 particles than usual electrodynamics. Chiral components of a rank-2 spinor field are taken as the dynamic variables of the theory. A rank-2 spinor accommodates another particle (the magnetic photon). This new particle emerges naturally from chiral invariance arguments. The nonexistence, in nature, of such a particle is the reason for the nonexistence of monopoles and the asymmetry in Maxwell's equation. The existence of magnetic monopoles would restore the symmetry of Maxwell's equation. We establish, in this way, at a very formal level, the connection between magnetic monopoles and chiral asymmetry.

We show that the commonly known conductor boundary conditions E_‖ = B_⊥ = 0 can be realized in two ways which we call 'thick' and 'thin' conductor. The 'thick' conductor is the commonly known approach and includes a Neumann condition on the normal component E_⊥ of the electric field whereas for a 'thin' conductor E_⊥ remains without boundary condition. Both types describe different physics already on the classical level where a 'thin' conductor allows for an interaction between the normal components of currents on both sides. On quantum level different forces between a conductor and a single electron or a neutral atom result. For instance, the Casimir-Polder force for a 'thin' conductor is by about 13% smaller than for a 'thick' one.

In this paper, we have explored the effect of Fock–Lorentz linear fractional relativity on the electrodynamics laws, where the radius of universe $R$ emerges as a consequence in the new formulation of Fock’s transformation. By employing the Dirac Hamiltonian analysis scheme, we have studied the case of the free particle, as well as the charged particle in presence of an external electromagnetic field in the new deformed phase space “$R$-Minkowski.” The Lorentz force is obtained up to the first-order $O(R)$. Furthermore, we have discussed the modified form of Leinard–Wiechart potentials.

The observation of magnetic monopoles would lead to a symmetrization of Maxwell’s equations and provide explanations of fundamental properties such as the quantization of electric charge. Yet, in four dimensions, the covariant electromagnetic field tensor yields an action whose resulting field equations establish the absence of a magnetic charge. We here study the existence of magnetic monopoles in an extended space–time with a second time dimension, and construct the higher-dimensional gauge potential. This motivates the use of the Kalb–Ramond field, upon which a Kaluza–Klein-like reduction is performed under the assumption that the two time dimensions have no co-dependency. The resulting 5D electrodynamics contains a generalized version of Maxwell’s equations which contain magnetic charge densities whose source potential obeys a five-dimensional wave equation. As a second time dimension only acts on small length scales in the order of the Planck length, we provide a theory with symmetrized Maxwell’s equations including magnetic monopoles which do not violate current experimental evidence. We finally discuss the subsequent quantization of the electric charge as well as the weak interaction, equivalent to the violation of time reversal.

In this paper, we consider electric fields in media with power-law spatial dispersion (PLSD). Spatial dispersion means that the absolute permittivity of the media depends on the wave vector. Power-law type of this dispersion is described by derivatives and integrals of non-integer orders. We consider electric fields of point charge and dipole in media with PLSD, infinite charged wire, uniformly charged disk, capacitance of spherical capacitor and multipole expansion for PLSD-media.

A transient continuum model of the ODEP chip containing single circular particle inside is constructed based on multi-physical field coupling. The dielectrophoresis force and liquid viscous resistance acting on particle are calculated by employing the full Maxwell stress tensor. The coupled flow field, electric field and particle are solved by the arbitrary Lagrange–Euler (ALE) method simultaneously. The throughout dynamic process of particle in the ODEP chip is demonstrated, and the effect of several critical parameters on particle electrodynamics is illuminated. The additional disturbing effect of the photoconductive layer on the electric field as well as the micro-channel wall on the flow field is presented to clarify the particle motion in the vertical direction. The results in this study provide a detailed understanding of the particle dynamics in the ODEP chip.

The genesis of special relativity is intimately related to the development of the theory of light propagation. When optical phenomena were described, there are typically two kinds of theories: (i) One based on light rays and light particles and (ii) one considering the light as waves. When diffraction and refraction were experimentally discovered, light propagation became more often described in terms of waves. Nevertheless, when attempts were made to explain how light was propagated, it was nearly always in terms of a corpuscular theory combined with an ether, a subtle medium supporting the waves. Consequently, most of the theories from Newton's to those developed in the 19th century were dual and required the existence of an ether. We therefore used the ether as our Ariadne thread for explaining how the principle of relativity became generalized to the so-called Maxwell equations around the 1900's. Our aim is more to describe how the successive ideas were developed and interconnected than framing the context in which these ideas arose.

We take a quick look at the different possible universally coupled scalar fields in nature. Then, we discuss how the gauging of the group of scale transformations (dilations), together with the Poincaré group, leads to a Weyl–Cartan spacetime structure. There the dilaton field finds a natural surrounding. Moreover, we describe shortly the phenomenology of the hypothetical axion field. In the second part of our essay, we consider a spacetime, the structure of which is exclusively specified by the premetric Maxwell equations and a fourth rank electromagnetic response tensor density ${\chi }^{ijkl}=-{\chi }^{jikl}=-{\chi }^{ijlk}$ with 36 independent components. This tensor density incorporates the permittivities, permeabilities and the magneto-electric moduli of spacetime. No metric, no connection, no further property is prescribed. If we forbid birefringence (double-refraction) in this model of spacetime, we eventually end up with the fields of an axion, a dilaton and the 10 components of a metric tensor with Lorentz signature. If the dilaton becomes a constant (the vacuum admittance) and the axion field vanishes, we recover the Riemannian spacetime of general relativity theory. Thus, the metric is encapsulated in ${\chi }^{ijkl}$, it can be derived from it.

This research aims to develop a new approach towards a consistent coupling of electromagnetic and gravitational fields, by using an electron that couples with a weak gravitational potential by means of its electromagnetic field. To accomplish this, we must first build a new model which provides the electromagnetic nature of both the mass and the energy of the electron, and which is implemented with the idea of $\gamma$-photon decay into an electron–positron pair. After this, we place the electron (or positron) in the presence of a weak gravitational potential given in the intergalactic medium, so that its electromagnetic field undergoes a very small perturbation, thus leading to a slight increase in the field’s electromagnetic energy density. This perturbation takes place by means of a tiny coupling constant $\xi$ because gravity is a very weak interaction compared with the electromagnetic one. Thus, we realize that $\xi$ is a new dimensionless universal constant, which reminds us of the fine structure constant $\alpha$; however, $\xi$ is much smaller than $\alpha$ because $\xi$ takes into account gravity, i.e. $\xi \propto \sqrt{G}$. We find $\xi =V/c\cong 1.5302\times 10^{-22}$, where $c$ is the speed of light and $V\propto \sqrt{G}(\cong 4.5876\times 10^{-14}$m/s) is a universal minimum speed that represents the lowest limit of speed for any particle. Such a minimum speed, unattainable by particles, represents a preferred reference frame associated with a background field that breaks the Lorentz symmetry. The metric of the flat spacetime shall include the presence of a uniform vacuum energy density, which leads to a negative pressure at cosmological scales (cosmological anti-gravity). The tiny values of the cosmological constant and the vacuum energy density will be successfully obtained in agreement with the observational data.

It is well known that with an appropriate combination of three Liouville-type dilaton potentials, one can construct charged dilaton black holes in an (anti)-de Sitter [(A)dS] spaces in the presence of linear Maxwell field. However, asymptotically (A)dS dilaton black holes coupled to nonlinear gauge field have not been found. In this paper, we construct, for the first time, three new classes of dilaton black hole solutions in the presence of three types of nonlinear electrodynamics, namely Born–Infeld (BI), Logarithmic (LN) and Exponential nonlinear (EN) electrodynamics. All these solutions are asymptotically (A)dS and in the linear regime reduce to the Einstein–Maxwell-dilaton (EMd) black holes in (A)dS spaces. We investigate physical properties and the causal structure, as well as asymptotic behavior of the obtained solutions, and show that depending on the values of the metric parameters, the singularity can be covered by various horizons. We also calculate conserved and thermodynamic quantities of the obtained solutions. Interestingly enough, we find that the coupling of dilaton field and nonlinear gauge field in the background of (A)dS spaces leads to a strange behavior for the electric field. We observe that the electric field is zero at singularity and increases smoothly until reaches a maximum value, then it decreases smoothly until goes to zero as $r\to \infty$. The maximum value of the electric field increases with increasing the nonlinear parameter $\beta$ or decreasing the dilaton coupling $\alpha$ and is shifted to the singularity in the absence of either dilaton field ($\alpha =0$) or nonlinear gauge field ($\beta \to \infty$).

We report on recent developments toward a relativistic quantum-mechanical theory of motion for a fixed, finite number of electrons, photons and their anti-particles, as well as its possible generalizations to other particles and interactions.

The paper proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress–energy tensor for a system with an electromagnetic field leads to the solution of Einstein Field Equations indicating a relationship between the electromagnetic field tensor and the metric tensor. In this EFE solution, the cosmological constant is related to the invariant of the electromagnetic field tensor, and additional pulls appear, dependent on the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of the proposed stress–energy tensor expresses relativistic Cauchy’s momentum equation, leading to the emergence of force densities which can be developed and parameterized to obtain known interactions. Transformation equations were also obtained between spacetime with fields and forces, and a curved spacetime reproducing the motion resulting from the fields under consideration, which allows for the extension of the solution with new fields.

We present a variational formulation of electrodynamics using de Rham even and odd differential forms. Our formulation relies on a variational principle more complete than the Hamilton principle and thus leads to field equations with external sources and permits the derivation of the constitutive relations. We interpret a domain in space-time as an odd de Rham 4-current. This permits a treatment of different types of boundary problems in an unified way. In particular we obtain a smooth transition to the infinitesimal version by using a current with a one point support.

In this paper the Seiberg–Witten map is first analyzed for non-commutative Yang–Mills theories with the related methods, developed in the literature, for its explicit construction, that hold for any gauge group. These are exploited to write down the second-order Seiberg–Witten map for pure gravity with a constant non-commutativity tensor. In the analysis of pure gravity when the classical space–time solves the vacuum Einstein equations, we find for three distinct vacuum solutions that the corresponding non-commutative field equations do not have solution to first order in non-commutativity, when the Seiberg–Witten map is eventually inserted. In the attempt of understanding whether or not this is a peculiar property of gravity, in the second part of the paper, the Seiberg–Witten map is considered in the simpler case of Maxwell theory in vacuum in the absence of charges and currents. Once more, no obvious solution of the non-commutative field equations is found, unless the electromagnetic potential depends in a very special way on the wave vector.