Related papers: Direct, analytic solution for the electromagnetic …
We derive analytic solutions for the longitudinal and the transverse components of the vector potential in the Lorenz gauge for an arbitrary time-dependent charge-current distribution.
Vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The rapid development in quantum optics calls for electromagnetic solutions that straddle quantum physics as well as classical physics. The…
On transformation to the Fourier space $({\bf k}, \omega)$, the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. There is no source besides the…
The instantaneous nature of the potentials of the Coulomb gauge is clarified and a concise derivation is given of the vector potential of the Coulomb gauge expressed in terms of the instantaneous magnetic field.
A procedure for solving the Maxwell equations in vacuum, under the additional requirement that both scalar invariants are equal to zero, is presented. Such a field is usually called a null electromagnetic field. Based on the complex Euler…
A recent suggestion that vector potentials in electrodynamics (ED) are nontensorial objects under 4D frame rotations is found to be both unnecessary and confusing. As traditionally used in ED, a vector potential $A$ always transforms…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
A fully relativistically covariant and manifestly gauge invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. We show that the…
The expression for the Coulomb-gauge vector potential in terms of the `instantaneous' magnetic field derived by Stewart [2003 Eur. J. Phys. 24, 519] by employing Jefimenko's equation for the magnetic field and Jackson's formula for the…
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
A solution is proposed for finding the vector potential and magnetic field of any distribution of currents with axial symmetry. In this approach, the magnetic field and the vector potential are looked for not by solving a differential…
We present an educational path on the magnetic vector potential A addressed to undergraduate students and to pre-service physics teachers. Starting from the generalized Ampere-Laplace law, in the framework of a slowly varying time-dependent…
We propose a reformulation of electrodynamics in terms of a {\it physical} vector potential entirely free of gauge ambiguities. Quantizing the theory leads to a propagator that is gauge invariant by construction in this reformulation, in…
The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford's method of algebraically solving for the vector potential is reviewed, with…
Very little previous literature has considered the *exact* solution to Maxwell's equations for an infinite ideal cylindrical solenoid with an arbitrary time-dependent azimuthal surface current $K(t) \hat{\bf \phi}$. Most of the previous…
We consider quantum gravitational corrections to Maxwell's equations on flat space background. Although the vacuum polarization is highly gauge dependent, we explicitly show that this gauge dependence is canceled by contributions from the…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
Are the electromagnetic scalar and vector potentials dispensable? Lev Vaidman has suggested that local interactions of gauge-invariant quantities, e.g. magnetic torques, suffice for the description of all quantum electromagnetic phenomena.…