Related papers: The Stationary Maxwell-Dirac Equations
We derive the discretized Maxwell's equations using the discrete variational derivative method (DVDM), calculate the evolution equation of the constraint, and confirm that the equation is satisfied at the discrete level. Numerical…
It is pointed out that the usual derivation of the well-known Maxwell electromagnetic equations holds only for a medium at rest. A way in which the equations may be modified for the case when the mean flow of the medium is steady and…
A close examination of the Maxwell-Lorentz theory of electrodynamics reveals that polarization and magnetization of material media need not be treated as local averages over small volumes - volumes that nevertheless contain a large number…
Including torsion in the geometric framework of the Weyl-Dirac theory we build up an action integral, and obtain from it a gauge covariant (in the Weyl sense) general relativistic massive electrodynamics. Photons having an arbitrary mass,…
We show that a large class of null electromagnetic fields are immune to any modifications of Maxwell's equations in the form of arbitrary powers and derivatives of the field strength. These are thus exact solutions to virtually any…
A waveguide coincides with a three-dimensional domain G having finitely many cylindrical outlets to infinity; the boundary of G is smooth. In G, we consider the stationary Maxwell system with real spectral parameter k and identity matrices…
Detailed analysis of the coupled Dirac-Maxwell equations and the structure of their solutions is presented. Numerical solutions of the field equations in the case of spherical symmetry with negligible gravitational self-interaction reveal…
We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous,…
The Klein-Gordon and Dirac equations are considered in a semi-infinite lab ($x > 0$) in the presence of background metrics $ds^2 =u^2(x) \eta_{\mu\nu} dx^\mu dx^\nu$ and $ds^2=-dt^2+u^2(x)\eta_{ij}dx^i dx^j$ with $u(x)=e^{\pm gx}$. These…
Maxwell's four differential equations describing electromagnetism are amongst the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's…
We formulate an existence theorem that states that given localized scalar and vector time-dependent sources satisfying the continuity equation, there exist two retarded fields that satisfy a set of four field equations. If the theorem is…
We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the…
The Einstein-Maxwell equations in D-dimensions admitting (D-3) commuting Killing vector fields have been investigated. The existence of the electric, magnetic and twist potentials have been proved. The system is formulated as the harmonic…
The Maxwell-Dirac equations in one space dimension are proved to be well posed in the charge class, that is, with $L^2$ data for the spinor. We also prove that this result is sharp, in the sense that well-posedness fails for spinor data in…
In this article we have illustrated how is possible to formulate Maxwell's equations in vacuum in an independent form of the usual systems of units. Maxwell's equations, are then specialized to the most commonly used systems of units:…
Stationary circularly symmetric solutions of General Relativity with negative cosmological constant coupled to the Maxwell field are analyzed in three spacetime dimensions. Taking into account that the fall-off of the fields is slower than…
Expectation values of the electromagnetic field and the electric current are introduced at space-time resolution which belongs to the quantum domain. These allow us to approach some key features of classical electrodynamics from the…
At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also…
We study nonlinear bound states, or solitary waves, in the Dirac-Maxwell system proving the existence of solutions in which the Dirac wave function is of the form $\phi(x,\omega)e^{-i\omega t}$, $\omega\in(-m,\omega_*)$, with some…
According to Dirac's theory of the positron, an electromagnetic field tends to create pairs of particles which leads to a change of Maxwell's equations in the vacuum. These changes are calculated in the special case that no real electrons…