Related papers: Multipole Expansion in Generalized Electrodynamics
In undergraduate classes, the potential flow that goes around a circular cylinder is designed for complemental understanding of mathematical technique to handle the Laplace equation with Neumann boundary conditions and the physical concept…
The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just…
We advocate for a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables; the…
Based on some previous results, one gives a general formula for introducing electromagnetic multipole expansions in terms of symmetric and traceless cartesian tensors.
Buckingham expansion is important for understanding molecular multipoles and (hyper)polarizabilities. In this study, we give a complete derivation of Buckingham expansion in the traced form using successive Taylor series. Based on such…
A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that…
In this work we study the so-called ModMax nonlinear electrodynamics, which is a novel model designed to preserve duality rotations and conformal transformations, such as the Maxwell's equations do. This model allows to study diverse…
We addressed the problem of generalizing the extensive postulates of the standard thermodynamics in order to extend it to the study of nonextensive systems. We did it in analogy with the traditional analysis, starting from the…
We discuss the construction of Maxwellian electrodynamics in 2+1 dimensions and some of its applications. Special emphasis is given to the problem of the retarded potentials and radiation, where substantial differences with respect to the…
We explore dynamical features of the maximally symmetric nonlinear extension of classical electromagnetism, recently proposed in the literature as ``ModMax'' electrodynamics. This family of theories is the only one that preserves all the…
An analysis of possible extension of the Painlev\'e test, to encompass the one-dimensional Vlasov equation, is performed. The extending requires a nontrivial generalization of the test. The proposed singularity analysis provides…
The quantum field theory of extended objects is employed to address the hitherto nonrenormalizable Pauli interaction. This is achieved by quantizing the Dirac field using the infinite dimensional generalization of the extended object…
This paper is devoted to the analysis of the divergence of the electron self-energy in classical electrodynamics. To do so, we appeal to the theory of distributions and a method for obtaining corresponding extensions. At first sight,…
Light-matter interaction models invariably rely on the multipole expansion of the electromagnetic potentials generated by complex charge distributions. These multipoles are typically taken to be traceless, however, for a correct evaluation…
Multipoles are paramount for describing electromagnetic fields in many areas of nanoscale optics, playing an essential role for the design of devices in plasmonics and all-dielectric nanophotonics. Challenging the traditional division into…
The inversion in the sphere or Kelvin transformation, which exchanges the radial coordinate for its inverse, is used as a guide to relate distinct electrostatic problems with dual features. The exact solution of some nontrivial problems are…
We give a brief review of some generalized continuum theories applied to the crystals with complicated microscopic structure. Three different ways of generalization of the classical elasticity theory are discussed. One is the high-gradient…
In this comment, we discuss some features of the multipolar expansion of the power radiated by a confined system of charges and currents, and the possibility of generalization to a higher arbitrary order of the multipolar expansion.
We study magnetic monopoles in a Lorentz- and CPT-odd electrodynamical framework in (3+1) dimensions. This is the standard Maxwell model extended by means of a Chern-Simons-like term, $b_\mu\tilde{F}^{\mu\nu}A_\nu$ ($b_\mu$ constant), which…
Electric and magnetic multipole densities in crystalline solids, including the familiar electric dipole density in ferroelectrics and the magnetic dipole density in ferromagnets, are of central importance for our understanding of ordered…