Related papers: Electrostatics and Riemann Surfaces
Special Bohr - Sommerfeld geometry, first formulated for simply connected symplectic manifolds (or for simple connected algebraic varieties), gives rise to some natural problems for the simplest example in non simply connected case. Namely…
When dealing with certain kind of complex phenomena the theoretician may face some difficulties -- typically a failure to have access to information for properly characterize the system -- for applying the full power of the standard…
We evaluate the electrostatic potential and the electrostatic field created by a point charge and an arbitrarly oriented electrical dipole placed near a grounded perfectly conducting sphere. Induced surface charge distributions as well as…
An increasingly important area of interest for mathematicians is the study of Abelian differentials. This growing interest can be attributed to the interdisciplinary role this subject plays in modern mathematics, as various problems of…
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
We show that for an infinite, uniformly charged plate no well defined electric field exists in the framework of electrostatics, because it cannot be defined as a mathematically consistent limit of a solution for a finite plate. We discuss…
We outline here a simple mathematical introduction to the notions of multipoles for a general extensive property $\Pi$ from the point of view of continuum mechanics. Classically, $\Pi$ is the electric charge, but the theory is not limited…
We derive new general expressions for the fluctuating electromagnetic field outside a homogeneous material surface. The analysis is based on general results from the thermodynamics of irreversible processes, and requires no consideration of…
In the paper [4] is presented a theory which unifies the gravitation theory and the mechanical effects, which is different from the Riemannian theories like GTR. Moreover it is built in the style of the electomagnetic field theory. This…
The aim of this paper is to present a short introduction to supergeometry on pure odd supermanifolds. (Pseudo)differential forms, Cartan calculus (DeRham differential, Lie derivative, "inner" product), metric, inner product, Killing's…
This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures. 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations.…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…
A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell…
In this paper a new method is derived for constructing electromagnetic surface sources for stationary axisymmetric electrovac spacetimes endowed with non-smooth or even discontinuous Ernst potentials. This can be viewed as a generalization…
Electrometry near a dielectric surface is performed using Rydberg electromagnetically induced transparency (EIT). The large polarizability of high n-state Rydberg atoms gives this method extreme sensitivity. We show that adsorbates on the…
We propose a basic theory of nonrelativistic spinful electrons on curves and surfaces. In particular, we discuss the presence and effects of spin connections, which describe how spinors and vectors couple to the geometry of curves and…
The Feynman demonstration that electromagnetic field momentum is real-even for static fields-can be made more pedagogically useful by simplifying its geometry. Instead of Feynman's disk with charged balls on its surface, this article uses…
In this paper we introduce a space with some additional topologies using filter bases and renew the definition of Riemann surfaces of algebraic functions. We then present a Galois correspondence between these Riemann surfaces and their deck…
We first write down a very general description of nonlinear classical electrodynamics, making use of generalized constitutive equations and constitutive tensors. Our approach includes non-Lagrangian as well as Lagrangian theories, allows…