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It has been proposed that any coupling constant in a covariant action can be treated as a conserved charge by promoting the coupling constant to auxiliary fields, typically realized by a scalar field paired with a higher-form gauge field.…
The notions of "motion" and "conserved quantities", if applied to extended objects, are already quite non-trivial in Special Relativity. This contribution is meant to remind us on all the relevant mathematical structures and constructions…
A mathematical proof is given that Maxwell's equations are an {\it artifact} of Hodge theory together with the laws of Gauss and Amp\`ere, taken as axioms. They are thus geometric in nature, independent of any specific physical mechanisms,…
Analysis of the original Feynman's formula for a moving point charge leads to the notion of a retarded time, which has to be treated as a field. The Lorentzian frame, the trajectory, and the retarded time field uniquely determine a system…
Maxwell's equations are modified to incorporate a scalar field to account for the London's superconductivity. Assuming the electromagnetic field is described by the Klein-Gordon equation, London's equations of superconductivity are then…
We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…
A new class of exact solutions of the Einstein-Maxwell system is found in closed form. This is achieved by choosing a generalised form for one of the gravitational potentials and a particular form for the electric field intensity. For…
Formal definition of the reference frame is given. This definition is valid for nonrelativistic and relativistic cases. Proposed definition allows using wide classes of reference frames without restriction to inertial, uniformly accelerated…
We derive the covariant equations of motion for Maxwell field theory and electrodynamics in multiscale spacetimes with weighted Laplacian. An effective spacetime-dependent electric charge of geometric origin naturally emerges from the…
Special relativity theory is well established and confirmed by experiments. This research establishes an operational measurement way to express the great theory in a geometrical form. This may be valuable for understanding the underlying…
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…
We introduce the Maxwell-invariant extension of D=4 relativistic free particle model into ten-dimensional Maxwell tensorial space. The new model after first quantization describes in particular Lorentz frame the planar dynamics providing…
All quantum gravity approaches lead to small modifications in the standard laws of physics which lead to violations of Lorentz invariance. One particular example is the extended standard model (SME). Here, a general phenomenological…
It has been said that Maxwell's theory of electromagnetic field is relativistic as Einstein showed that these axioms of Maxwell are all Lorentz invariant. We investigate some issues regarding these results.
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…
We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
Magnetostatic fields in accelerators are conventionally described in terms of multipoles. We show that in two dimensions, multipole fields do provide solutions of Maxwell's equations, and we consider the distributions of electric currents…
Emergent concepts from astroparticle physics are incorporated into a classical solution of the Einstein-Maxwell equations for a binary magnetohydrodynamic fluid, in order to describe the final equilibrium state of compact objects infused…
Recently, Feigel has predicted a new effect in magnetoelectric media. The theoretical evaluation of this effect requires a careful analysis of a dynamics of the moving magnetoelectric medium and, in particular, the derivation of the…