Related papers: Dimensional reduction of electromagnetism
We present a systematic geometric framework for the dimensional reduction of classical electromagnetism based on the concept of descent along vector fields of invariance. By exploring the interplay between the Lie derivative and the Hodge…
The reduction of the three-dimensional classical electromagnetism is performed in a twofold way. In the first case the ordinary two-dimensional electromagnetism is obtained with sources in the form of conserved electric currents flowing…
We perform a reduction from three to two spatial dimensions of the physics of a spin-1/2 fermion coupled to the electromagnetic field, by applying Hadamard's method of descent. We consider first the free case, in which motion is determined…
In absence of currents and charges the quantized electromagnetic field can be described by wave functions which for each individual wave vector are normalized to one. The resulting formalism involves reducible representations of the…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
We investigate the general properties of the dimensional reduction of the Dirac theory, formulated in a Minkowski spacetime with an arbitrary number of spatial dimensions. This is done by applying Hadamard's method of descent, which…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. We show that for higher orders, it is more efficient to have fields represented in…
Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the one-dimensional case, charge and current densities,…
A Hubbard-like model with SU(4) symmetry for electrons with two-fold orbital degeneracy is studied extensively. Exact solution in one dimension is derived by means of Bethe ansatz, where the sites are supposed to be occupied by at most two…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…
By modeling a dielectric medium with two independent reservoirs, i.e., electric and magnetic reservoirs, the electromagnetic field is quantized in a linear dielectric medium consistently. A Hamiltonian is proposed from which using the…
The groundstate configuration and the eigenmodes of two parallel two-dimensional classical atoms are obtained as function of the inter-atomic distance (d). The classical particles are confined by identical harmonic wells and repel each…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. It has in general case quaternion single structure, consisting of four independent field constituents, which differ with each other by…
Anisotropy of a space naturally leads to direction dependent electromagnetic tensors and electromagnetic potentials. Starting from this idea and using variational approaches and exterior derivative formalism, we extend some of the classical…
The classical two-dimensional problem of non-interacting electrons scattered by short-range impurity centers in the presence of magnetic field is investigated both analytically and numerically. A strong magnetoresistance exists in such a…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
Exact results for the classical and quantum system of two vertically coupled two-dimensional single electron quantum dots are obtained as a function of the interatomic distance (d) and with perpendicular magnetic field. The classical system…
The concept "Classical Electromagnetism" in the title of the paper here refers to a theory built on three foundations: relativity principles, the original Maxwell's equations, and the mathematics of exterior calculus. In this theory of…
We describe a novel approach to dimensional reduction in classical field theory. Inspired by ideas from noncommutative geometry, we introduce extended algebras of differential forms over space-time, generalized exterior derivatives and…
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…