Related papers: First order Maxwell operator formalism for macrosc…
In this paper, we consider band-structure calculations governed by the Helmholtz or Maxwell equations in piecewise homogeneous periodic materials. Methods based on boundary integral equations are natural in this context, since they…
We consider the following first order systems of mathematical physics. 1.The Dirac equation with scalar potential. 2.The Dirac equation with electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The system describing…
Considerable work has been done on the one-loop effective action in combined electromagnetic and gravitational fields, particularly as a tool for determining the properties of light propagation in curved space. After a short review of…
The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
The main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical…
Motivated by the research on upper bounds on the rate of quantum transport for one-dimensional operators, particularly, the recent works of Jitomirskaya--Liu and Jitomirskaya--Powell and the earlier ones of Damanik--Tcheremchantsev, we…
We calculate the conductance of a circular constriction of radius $a$ in an insulating diaphragm which separates two conducting half-spaces characterized by the mean free path $\ell$. Our exact result interpolates between the Maxwell…
In the first part of this work, we consider second order supersymmetric differential operators in the semiclassical limit, including the Kramers-Fokker-Planck operator, such that the exponent of the associated Maxwellian $\phi$ is a Morse…
An axiomatic approach to electrodynamics reveals that Maxwell electrodynamics is just one instance of a variety of theories for which the name electrodynamics is justified. They all have in common that their fundamental input are Maxwell's…
In this work we extend the Kugo-Ojima-Nakanishi covariant operator formalism to quantize two higher derivative systems, considering their extended phase space structures. More specifically, the one describing spin-$0$ particles by a vector…
In an exact quantum-mechanical framework, we show that expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge, and in the presence of classical sources, automatically lead to causal and retarded…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
Pendry and MacKinnon meaningful discretization of Maxwell's equations was put forward specifically as part of a finite-element numerical algorithm. By contrast with a numerical approach, in the same spirit evoked by the relationships…
The goal of this article is to establish general principles for high frequency dispersive estimates for Maxwell's equation in the exterior of a perfectly conducting ball. We construct entirely new generalized eigenfunctions for the…
In the paper we give consecutive description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and appear in many problems of condensed matter physics, magnetism and…
At a surface between electromagnetic media the Maxwell equations allow either the usual boundary conditions, or exactly one alternative: continuity of E(perpendicular), H(perpendicular), D(parallel), B(parallel). These `flipped' conditions…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
We develop a general algebraic scheme to decompose fractional quantum Hall (FQH) wave functions based on the operator contraction multiplication. By introducing fermionic and bosonic operators and establishing three fundamental contraction…
In the recent paper [J.\ Phys.\ A 44 (2011) 065203], we have arrived at the closed-form expression for the Green's function for the partial differential operator describing propagation of a scalar wave in an $N$-dimensional ($N\geqslant2$)…