相关论文: The method of Fourier transforms applied to electr…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well-known to also be solutions in all spacetimes with conformally-related metrics. This provides a sense in which electromagnetism alone cannot be used to…
We revisit a newfound construction of rational electromagnetic knots based on the conformal correspondence between Minkowski space and a finite $S^3$-cylinder. We present here a more direct approach for this conformal correspondence based…
This article examines the consequences of the existence of an upper particle momentum limit in quantum electrodynamics, where this momentum limit is the Planck momentum. The method used is Fourier analysis as developed already by Fermi in…
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
The quaternion spaces can be used to describe the property of electromagnetic field and gravitational field. In the quaternion space, some coordinate transformations can be deduced from the feature of quaternions, including Lorentz…
The present paper has a number of distinct purposes. First is to give a description of a class of electromagnetic knots from the perspective of foliation theory. Knotted solutions are then interpreted in terms of two codimension-2…
In this note we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters…
In this paper we consider the classical relativistic motion of charged particles in a knotted electromagnetic field. After reviewing how to construct electromagnetic knots from maps between the three-sphere and the two-sphere, we introduce…
The formula for the electric field of a point charge moving with constant velocity is derived using the symmetry properties of Maxwell's equations - its Lorentz invariance. In contrast to conventional treatments, the derivation presented…
A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules is introduced.
Point-form relativistic quantum mechanics is used to derive an expression for the electromagnetic form factor of a pseudoscalar meson for space-like momentum transfers. The elastic scattering of an electron by a confined quark-antiquark…
A general method of solving the drift kinetic equation is developed for an axisymmetric magnetic field. Expanding a distribution function in general moments a set of ordinary differential equations are obtained. Successively expanding the…
A new mathematical model for the description of three electron quantum dots in 2D space is created, and ground states of this system in external magnetic field is investigated. The Schrodinger equation for three two-dimensional electrons is…
Kinematics and dynamics of a particle moving on a torus knot poses an interesting problem as a constrained system. In the first part of the paper we have derived the modified symplectic structure or Dirac brackets of the above model in…
One of the goals of the present paper is to propose an elementary method to find a general formula for the Fourier transform containing a pair of complex gamma functions with a monomial sm in terms of Gauss's hypergeometric functions 2F1.…
The Fourier transform (FT) represents a key tool in modern spectroscopy which drastically reduces measurement times and helps to improve the signal-to-noise ratio in spectra. Fourier transforming exponentially decaying time domain signals…
Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including…
We study graviton-photon conversions in an environment of the uniform and constant magnetic field considering Euler-K\"ockel-Heisenberg-type nonlinear corrections in electrodynamics. We take the transverse-tracefree gauge for gravitons and…
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of…