Wavelet Electrodynamics I

TL;DR

This paper introduces a novel wavelet-based representation for Maxwell's equations solutions, offering a localized and adaptable alternative to traditional plane wave expansions, with connections to relativistic coherent states.

Contribution

It develops a new wavelet representation for Maxwell solutions that is localized in space and dynamically adapted, improving upon traditional Fourier-based methods.

Findings

Wavelet representation is well-localized in space.

It provides a dynamic adaptation to the Maxwell field.

The approach relates to relativistic coherent states.

Abstract

A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and well-localized in space at the initial time. The wavelet representation of a solution is analogous to its Fourier representation, but has the advantage of being local. It is closely related to the relativistic coherent-state representations for the Klein-Gordon and Dirac fields developed in earlier work.