Related papers: Multipole charge conservation and implications on …
Though sufficient for local conservation of charge, Maxwells displacement current is not necessary. An alternative to the Ampere-Maxwell equation is exhibited and the alternatives electric and magnetic fields and scalar and vector…
Dynamical PDEs that have a spatial divergence form possess conservation laws that involve an arbitrary function of time. In one spatial dimension, such conservation laws are shown to describe the presence of an $x$-independent source/sink;…
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 electromagnetic interactions of particles there arises defect of masses, i.e. the energy is liberated since the particles of the different charges are attracted. It is shown that this change of the effective mass of a particle in the…
The extended BMS group includes supertranslation, dual supertranslation and Lorentz transformations. The generators of these symmetries can be classified according to their parity into "electric" and "magnetic" types. Using a multipole…
We begin with the time-dependent electric and magnetic dipole solution of Maxwell's equations in Minkowski space. This Maxwell field is then used to determine the behavior of the gravitational field (the Weyl tensor) as a second-order…
We discuss under what conditions the duality between electric and magnetic fields is a valid symmetry of macroscopic quantum electrodynamics. It is shown that Maxwell's equations in the absence of free charges satisfy duality invariance on…
Unlike a single Carroll particle, a multiparticle Carroll system can move under suitable conditions, as we demonstrate it explicitly for two particles with a momentum-dependent interaction: the center-of-mass remains fixed, however relative…
In this paper we review recent results on the existence of non-topological solitons in classical relativistic nonlinear field theories. We follow the Coleman approach, which is based on the existence of two conservation laws, energy and…
The duality relation between the electric and magnetic fields, in the presence of an additional axion-like field, is considered. We derive the new equations that describe the electrodynamics in this model, and we discuss the implications…
The electromagnetic field can be expressed in terms of two complex potentials $ \alpha, \beta ,$ which are related to the Debye potentials. The evolution equations for these potentials are derived, which are separable either in parabolic…
Electromagnetic waves carry an infinite number of conserved quantities. We give a simple explanation of this fact, which also shows how to write down conserved quantities at will and calculate their associated symmetry transformations. This…
We study the conserved quantity associated with the dual symmetry of the Maxwell equations, called the optical helicity, by means of transverse Hertz vectors. In the presence of charges, its evolution yields the integral of…
This study is grounded in the concept of spatial symmetry, which allows two co-phase RF sources to jointly radiate harmonic electromagnetic (EM) waves, even in presence of electromagnetic couplings between them. The superposition law is…
We develop the theory of momentum map for the Maxwell-Lorentz equations with spinning extended charged particle. This theory is indispensable for the study of long-time behaviour and radiation of the solitons of this system. The development…
In nonlinear electrodynamics, QED included, we find a static solution to the field equations with an electric charge as its source, which is comprised of homogeneous parallel magnetic and electric fields, and a radial…
We consider a model of topological solitons where charged particles have finite mass and the electric charge is quantised already at the classical level. In the electrodynamic limit, which physically corresponds to electrodynamics of…
This paper is devoted to presenting a rigorous mathematical derivation for the classical phenomenon in Maxwell's theory that a charged particle moves along a straight line in a constant electromagnetic field if the initial velocity is…
We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to…
Most nonabelian gauge theories admit the existence of conserved and quantized topological charges as generalizations of the Dirac monopole. Their interactions are dictated by topology. In this paper, previous work in deriving classical…