We consider the Dirac equation, written in polar formalism, presence of general Coulomb-like potentials, that is, potentials arising from time component vector potential and depending only on radial coordinate, order to study conditions integrability, given as some specific form for solution: we find angular dependence can always be integrated, while is reduced finding solution a Riccati equati...

Two results support the idea that the scalar and vector potentials in the Lorenz gauge can be considered to be physical quantities: (i) they separately satisfy the properties of causality and propagation at the speed of light and do not imply spurious terms and (ii) they can naturally be written in a manifestly covariant form. In this paper we introduce expressions for the Lorenz-gauge potentia...

In this note we study a minimization problem for a vector of measures subject to a prescribed interaction matrix in the presence of external potentials. The conductors are allowed to have zero distance from each other but the external potentials satisfy a growth condition near the common points. We then specialize the setting to a specific problem on the real line which arises in the study of c...

Current-carrying and superconducting systems can be treated within density-functional theory if suitable additional density variables ~the current density and the superconducting order parameter, respectively! are included in the density-functional formalism. Here we show that the corresponding conjugate potentials ~vector and pair potentials, respectively! are not uniquely determined by the de...

A modified system of equations of electrodynamics has been obtained. Beside the Lagrangian one an alternative gauge-like formalism has been developed to introduce the toroid moment contributions in the equations obtained. The two potential formalism that was worked out by us earlier has been developed further where along with the two vector potentials we introduce two scalar potentials thus tak...

The geometrical structure of electrodynamics is reviewed following the analogy with gravity. It is found that the vector potentials that represent magnetic fields can be identified as connections. As a consequence, these potentials should be assigned to the links of discretization grids. A ghost field is introduced to guarantee numerical stability in the solution scheme of solving electromagnet...

Angular potentials play an important role in the refinement of protein structures through angle-dependent restraints (e.g., those determined by cross-correlated relaxations, residual dipolar couplings, and hydrogen bonds). Analytic derivatives of such angular potentials with respect to the dihedral angles of proteins would be useful for optimizing such restraints and other types of angular pote...

Vector spherical harmonic analyses have been used successfully to solve laminar and mean-field magnetohydrodynamic dynamo problems with interactions, such as the laminar induction term, anisotropic alpha-effects and anisotropic diffusion, which are difficult to analyse spectrally in spherical geometries. Spectral forms of the non-linear rotating Boussinesq and anelastic momentum, magnetic field...

We consider incompressible Euler flows in terms of the stream function in two dimensions and the vector potential in three dimensions. We pay special attention to the case with singular distributions of the vorticity, e.g., point vortices in two dimensions. An explicit equation governing the velocity potentials is derived in two steps. (i) Starting from the equation for the stream function [Ohk...

A systematic analysis of the weak responses for charged-current quasielastic neutrino-nucleus reactions is presented within scheme a fully relativistic microscopic model considering momentum-dependent scalar and vector mean field potentials in both initial final nucleon states. The obtained are compared with ones corresponding to simpler approaches: energy-independent plane wave limit state, i....