arXiv subjects
Publications and source records attributed to G. Vaman.
Novel distributional Laplacians of an arsinh function and a related logarithm function are derived. The method used to establish the former result is employed in a calculation of the gauge transformation function for the case of a uniformly moving point charge.
There is a simple formula for the gauge function of the transformation from the Lorenz gauge to the Coulomb gauge, valid under a condition that is satisfied by some charge densities employed in the literature. An equation for the gauge function of this transformation that is alternative but equivalent to a formula of Jackson is derived also.
The fact that electromagnetic effects propagate at the speed of light suggests how the Lorenz-gauge scalar and vector potentials of a uniformly moving point charge must be modified when the charge was initially at rest and then set suddenly into uniform motion. The modified potentials are shown to satisfy the requisite inhomogeneous wave equations. The gauge function of the transformation of these potentials to the Coulomb gauge is calculated in closed form. It is validated by confirming that the Coulomb-gauge vector potential that is calculated using it yields together with the Coulomb-gauge scalar potential the same electric and magnetic fields as those calculated with the Lorenz-gauge potentials.
We write the electromagnetic self-force of a Lorentz-contractible spherical shell of radius $R$ in arbitrary rectilinear motion as a series expansion in powers of $R$, and calculate the first two terms of this series. The method we use, which is based on the description of the particle in terms of a velocity-dependent volume charge density, avoids some important difficulties of the previous approaches from the literature. We compare our results with the results obtained by other authors. The whole calculation is done in the laboratory frame of reference.
We calculate a double integral over a product of Legendre polynomials multiplied by a binomial raised to a power.
The electromagnetic self-force of a point charge moving arbitrarily on a rectilinear trajectory is calculated by averaging its retarded electric self-field over a sphere of infinitesimal radius centered on the charge's present position. The finite part of the self-force obtained is the well-established relativistic radiation reaction, while its divergent part implies the pre-relativistic longitudinal electromagnetic mass of Abraham.
We show that the "defective" terms in the expression that Dondera [Phys. Rev. D 98, 096008 (2018)] obtained for the momentum of the retarded field of an accelerating point charge are mathematically well justified. The repair should not be sought in assigning an accelerating "bare" charge ad hoc compensating attributes. We advance a conjecture, supported by published work, concerning the Hadamard finite part of the divergent integral for the retarded-field momentum in question.
We calculate the electromagnetic self-force of a uniformly charged spherical ball moving on a rectilinear trajectory, neglecting the Lorentz contraction.
The self-force of a point charge moving on a rectilinear trajectory is obtained, with no need of any explicit removal of infinities, as the negative of the time rate of change of the momentum of its retarded self-field.
We calculate the self-force of a point charge in rectilinear motion, using a local method and compare our results with those from the literature.
We use the multipole technique to derive four equivalent expressions for the bipolar expansion of the inverse distance, valid in all the regions of configuration space. Using the first-order perturbation theory, we calculate the overlap correction to the long-range electrostatic energy between two hydrogen atoms and between a hydrogen atom and a proton.
We calculate the electrostatic potential of a periodic lattice of arbitrary extended charges by using the Cartesian multipole formalism. This method allows the separation of the long-range potential from the contact potential (potential on the source). We write both the electrostatic potential and the interaction energy as convergent sums in the reciprocal space.
We derive van der Waals-London and Casimir forces by calculating the eigenmodes of the electromagnetic field interacting with two semi-infinite bodies (two halves of space) with parallel surfaces separated by distance d. We adopt simple models for metals and dielectrics, well-known in the elementary theory of dispersion. In the non-retarded (Coulomb) limit we get a d^{-3}-force (van der Waals-London force), arising from the zero-point energy (vacuum fluctuations) of the surface plasmon modes. When retardation is included we obtain a d^{-4}-(Casimir) force, arising from the zero-point energy of the surface plasmon-polariton modes (evanescent modes) for metals, and from propagating (polaritonic) modes for identical dielectrics. The same Casimir force is also obtained for "fixed surfaces" boundary conditions, irrespective of the pair of bodies. The approach is based on the equation of motion of the polarization and the electromagnetic potentials, which lead to coupled integral equations. These equations are solved, and their relevant eigenfrequencies branches are identified.
Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions. Known results are re-obtained in much a more direct manner and new ones are derived. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The dielectric response and the electron energy loss are computed. The surface contribution to the energy loss exhibits an oscillatory behaviour in the transient regime near the surfaces. The propagation of an electromagnetic wave in these plasmas is treated by using the retarded electromagnetic potentials. The resulting integral equations are solved and the reflected and refracted waves are computed, as well as the reflection coefficient. For the slab we compute also the transmitted wave and the transmission coefficient. Generalized Fresnel's relations are thereby obtained for any incidence angle and polarization. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient for a semi-infinite plasma exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection). Similarly, apart from characteristic oscillations, the reflection and transmission coefficients for a plasma slab exhibit an appreciable enhancement in the damped regime.