Related papers: Wavelet Electrodynamics I
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
We present a numerical method for solving the free-space Maxwell's equations in three dimensions using compact convolution kernels on a rectangular grid. We first rewrite Maxwell's Equations as a system of wave equations with auxiliary…
All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld…
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…
A formally exact discrete multi-resolution representation of quantum field theory on a light front is presented. The formulation uses an orthonormal basis of compactly supported wavelets to expand the fields restricted to a light front. The…
Matched wavelets interpolating equidistant data are designed. These wavelets form Riesz bases. Meyer wavelets that interpolate data on a particular uniform lattice are found.
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
In this paper, using the Newman-Penrose formalism, we find the Maxwell equations in NUT space and after separation into angular and radial components solve them analytically. All the angular equations are solved in terms of Jaccobi…
We present an application of variational-wavelet analysis to quasiclassical calculations of solutions of Wigner equations related to nonlinear (polynomial) dynamical problems. (Naive) deformation quantization, multiresolution…
It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered.
We study transverse magnetic (vector valued) wave-packets in the time dependent Kerr nonlinear Maxwell's equations at the interface of two inhomogeneous dielectrics with an instantaneous material response. The resulting model is…
We present a Parseval tight wavelet frame for the representation and analysis of velocity vector fields of incompressible fluids. Our wavelets have closed form expressions in the frequency and spatial domains, are divergence free in the…
Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the…
Closed-form, normalizable solutions of Dirac's equation propagating within a semi-infinite cylindrical waveguide are obtained in terms of ordinary and modified Bessel functions. These relativistic wave packets induce quantum backflow on a…
We present the applications of variational-wavelet approach for computing multiresolution/multiscale representation for solution of some approximations of Vlasov-Maxwell-Poisson equations.
We give the Lagrangian formulation of a generic non-minimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first order…
General solutions of relativistic wave equations are studied in terms of the functions on the Lorentz group. A close relationship between hyperspherical functions and matrix elements of irreducible representations of the Lorentz group is…
A simple method is presented which enables us to construct scalar field solutions from any given Einstein-Maxwell solution in colliding plane waves. As an application we give scalar field extensions of the solution found by Hogan, Barrabes…
The system of Maxwell equations with an initial condition in a vacuum is solved in a cylindrical coordinate system. It derives the cylindrical transverse electromagnetic wave mode in which the electric field and magnetic field are not in…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider application of FWT to metaplectic…