Resonances and different recording times on electromagnetic scalar and vector potentials

We review the electromagnetic scalar and vector potentials from the point of view of the Generalized Fredholm Integral Equations. Then we revise two sensitive concepts as the retarded and advanced Green functions. Provided we have developed the appropriate desired equations; we go to the problem of left-hand materials conditions for optimized broadcasting. We give also an academic but simple example. Key Words — Electromagnetic potentials, Generalized Fredholm Integral Equations, left-hand materials conditions, Green functions, resonances.

This chapter expresses the fields E ( r, t) and B ( r, t) in terms of the electromagnetic potentials Ф( r, t) and A ( r, t), and shows that these potentials are defined only up to a gauge transformation. This leads the reader naturally to the Coulomb and Lorenz gauges which are usually encountered in textbooks. The inhomogeneous wave equations whose solutions are the retarded electromagnetic potentials are also considered, as well as the Lienard–Wiechert potentials for an arbitrarily moving point charge. A few questions are included in which the Lagrangian and Hamiltonian of a point charge are expressed in terms of Ф and A. The chapter concludes by deriving a multipole expansion for the dynamic vector potential which will provide the starting point in our treatment of electromagnetic radiation later on in Chapter 11

We give an exact solution of the gravitational and electromagnetic field equations with a charged rotating source in new general relativity. The solution has three parameters Q, h and a, and it gives a charged Kerr metric space-time. The parallel vector fields and the electromagnetic vector potential are axially symmetric. In this space-time, we cannot discriminate new general relativity from general relativity, so far as scalar, the Dirac and the Yang-Mills fields and macroscopic bodies are used as probes. The space-time does not have singularities at all, although it has an “effective singularity”. Two kinds of Reissner-Nordström metric solutions, one is our solution with h = 0 and the other is a solution given by Hayashi and Shirafuji, are physically equivalent with each other. Nevertheless, these are markedly different from each other with regard to the asymptotic behavior of the torsion tensor for r →∞ and the space-time singularities.

A new eight-dimensional conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl’s electromagnetic theory. We derive the Maurer–Cartan structure equations and find the zero curvature solutions for the conformal connection. By showing that every one-particle Hamiltonian generates the structure equations we establish a correspondence between phase space and the eight-dimensional base space, and between the action and the integral of the Weyl vector. Applying the correspondence to generic flat solutions yields the Lorentz force law, the form and gauge dependence of the electromagnetic vector potential and minimal coupling. The dynamics found for these flat solutions applies locally in generic spaces. We then provide necessary and sufficient curvature constraints for general curved eight-dimensional geometries to be in 1–1 correspondence with four-dimensional Einstein–Maxwell space–times, based on a vector space isomorphism between the extra four dimensions and the Riemannian tangent space. Despite part of the Weyl vector serving as the electromagnetic vector potential, the entire class of geometries has vanishing dilation, thereby providing a consistent unified geometric theory of gravitation and electromagnetism. In concluding, we give a concise discussion of observability of the extra dimensions.

We modify the Einstein-Schrodinger theory to include a cosmological constant $\Lambda_z$ which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant $\Lambda_z$ is assumed to be nearly cancelled by Schrodinger's cosmological constant $\Lambda_b$ which multiplies the nonsymmetric fundamental tensor, such that the total $\Lambda=\Lambda_z+\Lambda_b$ matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as $|\Lambda_z|\to\infty$. For $|\Lambda_z|\sim 1/(Planck length)^2$ the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are $<10^{-16}$ of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein-Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein-Schrodinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner-Nordstrom solution except for additional terms which are $\sim 10^{-66}$ of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory.

The interaction and the transformation of the electromagnetic and gravitational waves and the variation of those amplitudes are analyzed theoretically, where the Einstein-Maxwell field is assumed. Two waves are defined such that the electromagnetic vector potentials and the gravitational tensor potentials and their first derivatives are continuous while their second derivatives are discontinuous at a wave front. It is proved that the concomitant electromagnetic and gravitational waves can interact with each other if an external electromagnetic field exists. The global behaviors of interaction and transformation of the two concomitant waves are also investigated, where a Lorentz metric space-time is assumed. The variation formulas for amplitude are derived. The amplitudes may grow or decay according to a factor depending on the mean and Gaussian curvatures of an initial wave front and to a factor depending on the external electromagnetic field. When there is no external electromagnetic field, there is no interaction between the two waves and they propagate independently, while when an external field exists, the electromagnetic wave may transform into the gravitational wave and vice versa. In a case of a weak constant external electromagnetic field, where a flat space may be assumed, the amplitude of a wave varies sinusoidally with respect to the distance measured along its ray. The length of interchangeability is defined by the length in which a wave is completely transformed into its dual wave, and it is inversely proportional to the strength of an external electromagnetic field.

Starting from basic principles, we develop a description of the electromagnetic interactions of a molecular gas in terms of a set of correlation functions which we call the molecular-electromagnetic correlation functions (MECF's). First we use the energy eigenfunctions for an isolated molecule of the species of interest to define a set of molecular creation and annihilation operators. We then derive a closed set of operator equations for these molecular creation and annihilation operators and the electromagnetic vector potential. Explicit definitions of the lowest-order MECF's are given in terms of these operators, and it is shown how the operator equations which have been obtained can be used to derive equations of motion for the MECF's. Finally, we illustrate the use of the MECF's in describing physical properties of the molecular gas and the electromagnetic field. Brief indications are given of the application of the MECF formulation to the semiclassical approximation and to the description of quantum emission of radiation, topics which are treated in greater detail in subsequent papers. The basic MECF formulation described here contains three rather mild approximations: (1) Atomic nuclei are treated as elementary particles; (2) nuclei and electrons are treated nonrelativistically; and (3) the effect of molecular collisions with the container walls on the internal molecular state is neglected. Consequently, the physical description contained in the formulation is rather complete; and the MECF results can be used both to provide a sound basis for some aspects of the usual heuristic models, and to ascertain the ways in which those models are incomplete.

Parity nonconserving nuclear forces induce electromagnetic currents and nuclear moments of the wrong parity (e.g., anapole moment). The interaction between atomic electrons and these currents is considered taking into account finite nuclear size and relativistic effects. The formula has been derived which allows one to separate the atomic and nuclear problems. The result can be approximately expressed as the interaction of an electron with a pointlike nuclear anapole moment times a correction factor [1-0.3(Z\ensuremath{\alpha}${)}^{2}$]. As an illustration we use a simple model to calculate the distribution of the parity-violating electromagnetic current, magnetic field, and vector potential.

Iterative solution of global electromagnetic wavefields with finite elements

A thought experiment is reviewed which shows two things. First, in a region of a rotating frame that is not simply connected, the inertial forces can be canceled without completely canceling the inertial vector potential (whose curl determines the Coriolis force); second, the presence of this uncanceled potential can be detected in a quantum interference experiment. It is then argued that the thought experiment was realized in an earlier experiment involving a rotating superconductor, and that the experimental results confirm the theoretical prediction. In this way, the first experimental verification of a physical effect due to a nonelectromagnetic potential in a force-free region is established. An analogous experiment for the gravitational vector potential is also discussed. Finally, it is pointed out that the close connection between electromagnetic and inertial vector potentials provides an intuitive way to make predictions about rotating superconductors.

Using full-wave numerical simulations and analytical multipole expansions we\ninvestigated the properties of real-space polarization singularities that\nemerge in light scattering by subwavelength particles. We considered spherical\nand torus particles made of dielectric or perfect-electric-conductor material.\nWe determined the topological indices and the trajectories of electric-field\npolarization singularities in both the near-field and far-field regions. In the\nfar-field region, a total of four singularities are identified and the sum of\ntheir polarization topological indices is two, independent of the particle's\ngeometric shape. In the near-field region, the polarization singularities\nstrongly depend on the particle's shape and the polarization of incident light,\nand their index sum is not governed by the Poincar\\'e-Hopf theorem anymore due\nto the non-transverse nature of the fields. From near field to far field, a\nflipping of sign can happen to the polarization topological indices of the C\nlines. The far-field properties of the singularities can be well explained by\nthe interference of the excited multipoles, but their near-field properties can\nbe strongly affected by the evanescent fields that are not captured by the\nmultipole expansions. Our work uncovers the important relationship between\nparticles' geometric properties and the polarization singularities of their\nscattering field. The results can be applied to manipulate polarization\nsingularities in nanophotonic systems and could generate novel applications in\noptical sensing.\n

Tunneling of Electromagnetic Waves in All-Dielectric Gradient Metamaterials

Fresnel's theory of the evanescent wave in total reflection entails that the propagation vectork and the momentum quantaħk have an imaginary component and, thus, a projection on the reflecting plane that is larger (in units such thatc=1) than the angular frequencyω and the energy quantaħω. We discuss the ‘tachyon properties’ of these energy-momentum quanta and propose an experimental test using absorption or stimulated emission by an atomic or ionic beam. We then show that the Maxwell-Minkowski tensor (although certainly appropriate to discuss the macroscopic energy-momentum exchange between wave and diopter) does not describe adequately the energy-momentum density of the quanta in the evanescent wave, this stemming from its too remote connection with the generator ∂i of space-time displacements. On the other hand de Broglie's energy-momentum tensorAk[∂i]B jk is the density canonically associated with the generator of space-time displacements; we show that it describes quite satisfactorily both the energy fluxes (as measured through the longitudinal Goos-Hanchen and our new transverse shifts of the reflected beam in total reflection) and the momentum densities of the quanta inside the evanescent wave. Finally, we show that it is the gauge which is transverse in the diopter's rest frame that directly yields the physically measured energy fluxes. We take this fact as a new argument, strongly supported by experimental evidence, in favour of the physical reality of electromagnetic potentials.

Abstract: In this paper, we have studied the Bianchi type-III cosmological model interacting scalar and electromagnetic field in theory of gravitation. We assume the electromagnetic vector potential in the form , and by considering the general case. It is found that if the study is confined to the case of.It is observed that the convergent and isotropic solution of the function can be evolved with vector potential in the constant form. Keyword: Bianchi Type III, Electromagnetic Field,theory of gravity, isotropy, constant vector potential.

Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that the Schrödinger equation admits an analogous treatment. We present a Lagrangian theory of a real scalar field φ whose equation of motion turns out to be equivalent to the Schrödinger equation with time independent potential. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics. The field φ is in the same relation to the real and imaginary part of a wave function as the vector potential is in respect to electric and magnetic fields. Preservation of quantum-mechanics probability is just an energy conservation law of the field φ.