Related papers: Can Maxwell's equations be obtained from the conti…
We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles, relaxing an unnecessary assumption on the structure of the four-potential inherent to the standard approach and thus restoring the full…
This letter reports on a metriplectic formulation of collisional, nonlinear full-$f$ electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy production. In an axisymmetric background magnetic field, the…
We discuss a signal theorem for charged particle detectors where the finite propagation time of the electromagnetic waves produced by a moving charge cannot be neglected. While the original Ramo-Shockley theorem and related extensions are…
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…
The problems of Classical Electrodynamics with the electron equation of motion and with non-integrable singularity of its self-field stress tensor are well known. They are consequences, we show, of neglecting terms that are null off the…
The existing field theories are based on the properties of closed exterior forms, which correspond to conservation laws for physical fields. In the present paper it is shown that closed exterior forms corresponding to field theories are…
In the framework of the field theory it is shown that a time (viewed as a scalar temporal field) is an internal property of the physical system, which defines its causal structure and evolution. A new concept of internal time allows to…
Close insight into mathematical and conceptual structure of classical field theories shows serious inconsistencies in their common basis. In other words, we claim in this work to have come across two severe mathematical blunders in the very…
A dielectric dilemma faces scientists because Maxwell's equations are poor approximations as usually written, with a single dielectric constant. Maxwell's equations are then not accurate enough to be useful in many applications involving…
We develop a quantization scheme for Maxwell's equations without source on an arbitrary four dimensional globally hyperbolic spacetime. The field strength tensor is the key dynamical object and it is not assumed a priori that it descends…
We consider the Maxwell field coupled to a single rotating charge. This Hamiltonian system admits soliton-type solutions, where the field is static, while the charge rotates with constant angular velocity. We prove that any solution of…
The complete charge-current density and field strength of an arbitrarily accelerated relativistic point-charge are explicitly calculated. The current density includes, apart from the well-established three-dimensional delta-function which…
The conventional decomposition of a vector field into longitudinal (potential) and transverse (vortex) components (Helmholtz's theorem) is claimed in [1] to be inapplicable to the time-dependent vector fields and, in particular, to the…
A framework based on an extension of Kaluza's original idea of using a five dimensional space to unify gravity with electromagnetism is used to analyze Maxwell\'{}s field equations. The extension consists in the use of a six dimensional…
Historically and to date, the continuity equation has served as a consistency criterion for the development of physical theories. Employing Clifford's geometric algebras, a system of continuity equations for a generalised multivector of the…
We consider the well-posedness of the initial value problem for Einstein-Maxwell theory modified by higher derivative effective field theory corrections. Field redefinitions can be used to bring the leading parity-symmetric 4-derivative…
We study Maxwell's equations in conducting media with perfectly conducting boundary conditions on Lipschitz domains, allowing rough material coefficients and $L^2$-data. Our first contribution is a direct proof of well-posedness of the…
We present a scenario for deriving Maxwell theory from IIB matrix model. Four dimensional spacetime and theories on it relate different dimensional ones by applying appropriate limits of the backgrounds of matrix model. It is understood by…
This work, that is devoted to the memory of Dr. Andrew Chubykalo and his legacy, is the improved version of the paper published in Annales de la Fondation Louis de Broglie journal. In this article, methods for solving the Maxwell equations…
We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B. This is a physically relevant, but difficult dynamical problem, to which contributions range over…