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We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, P\"oschl-Teller I and P\"oschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special…
These lectures start with an elementary introduction to the subject of magnetic monopoles which should be accesible from any physics background. In the Weinberg-Salam model of electroweak interactions, magnetic monopoles appear at the ends…
A method is presented which allows the exact construction of conserved (i.e. divergence-free) current vectors from appropriate sets of multipole moments. Physically, such objects may be taken to represent the flux of particles or electric…
Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires…
In this paper we investigate the vacuum energies of several models of quantum fields interacting with static external currents (linear couplings) concentrated along parallel branes with an arbitrary number of codimensions. We show that we…
The classical electron is presented as made up of an electric charge and two Dirac monopoles of opposite charge performing a magnetic dipole. It is discussed that a valid variational principle for this system can be defined. The Dirac…
A pointlike electric charge at rest is considered in the spacetime which is a wormhole connecting two otherwise Minkowskian spaces. The potential (i. e. a solution of the Maxwell equations) is split into two parts: one of them depends only…
Anomalous symmetries induce currents which can be parallel rather than orthogonal to the hypermagnetic field. Building on the analogy with charged liquids at high magnetic Reynolds numbers, the persistence of anomalous currents is…
Based on the derivation of the macroscopic Maxwell's equations by spatial averaging of the microscopic equations, we discuss the electrophysiology of living organs. Other methods of averaging (or homogenization) like the bidomain model are…
A new model of nonlinear electrodynamics with three parameters is suggested and investigated. It is shown that if the external constant magnetic field presents the phenomenon of vacuum birefringence takes place. The indexes of refraction…
In general relativity and electrodynamics fields are always generated from static monopoles (like mass or electric charge) or their corresponding currents by surrounding them in a spherical configuration. We investigate a generation of…
Although for the most part classical, the topic of electrostatics finds to this day new applications. In this review we highlight several theoretical results on electrostatics, chosen to both illustrate general principles, and for their…
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it…
Intrinsic EDMs in microscopic systems at a level of sensitivity achievable in experiments under way or foreseen are predicted in supersymmetric unified theories. I describe this and other sources of measurable EDMs and I show how these…
We present an analytical study, validated by numerical simulations, of electroosmotic flow in a Hele-Shaw cell with non-uniform surface charge patterning. Applying the lubrication approximation and assuming thin electric double layer, we…
We study symmetry properties of the Einstein-Maxwell theory nonminimaly coupled to the dilaton field. We consider a static case with pure electric (magnetic) Maxwell field and show that the resulting system becomes a nonlinear sigma-model…
Electrostatic theory preserves charges, but allows dipolar excitations. Elasticity theory preserves dipoles, but allows quadrupolar (Eshelby like) plastic events. Charged amorphous granular systems are interesting in their own right; here…
We introduce a formulation where individual line segments of a current loop have translationally non-invariant contributions to the electro-quasi-static magnetic scalar potential and magnetic field in source-free regions. While closed…
New exact solvable elliptic potentials with free constants for the spectral problems of the third order are found. A time dependence of such potentials gives their isospectral deformations and solutions of nonlinear integrable equations.
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…